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THE NATURE OF MUSIC

ORIGINAL HARMONY IN ONE VOICE

BY

JULIUS KLAUSER

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PREFACE

This work was originally planned in two parts, but
only six chapters and one section of Chapter VII which
was to conclude Part I, were written at the time of the
author's death, Monday, April 22, 1907.

The one section of Chapter VII has been omitted
from the book because it was not left in the form in
which it would have been published. The title of the
chapter is "Potential Harmony of Melody. Expan-
sion of Tonality. Chromatic Harmony. Modulation."

Asterisks in the manuscript have been preserved in
the text ; they indicate where footnotes were to have
been supplied.

Dates in the manuscript show that Chapter III was
finished during September, 1904, and Chapter IV
April 9, 1905.

These six chapters unrevised are published as they
were left, with one exception. To make space for the
examples on page 238 a sentence has been omitted. It
reads, "Thus the full thorough-bass index of the above
terce-form would be ^ of which 6 is the abbreviation."

The Bird-songs published as an appendix were
probably not intended to form a part of the book, but
I wish to preserve them and they may be of interest.
Twenty-five, Nos. 62-86, are entitled "Birds of Idle-
wild 1903," however with the exception of a few from
Silver Lake near Oconomowoc most of these songs
were heard and recorded during several summers
at Idlewild near Sturgeon Bay, Wisconsin. In the

vi PREFACE

manuscript Nos. 1-9 and 43-86 were written on the
staff, but Nos. 10-39 were indicated only by sylla-
bles and 40-42 by letters, in consequence of which
the pitch of these songs is not quite certain.

To Miss Luise Haessler I wish to acknowledge my
thanks for the help she has given me in copying most
of the examples, all of the bird-songs and in supplying
a paragraph of explanation page 254 and three ex-
amples pages 230-252.

L. E. K.

WiLLiAMSTOWN, MASSACHUSETTS, June, 1909.

CONTENTS

CHAPTER I

Introducing First Principles

SEC. PAGE

1. Qiiestions 1

2. Homophony or Mime in One Voice 4

3. Origin of Music 6

4. Music-Feeling, the Source and Fountain of Music. ... 8

5. Cause of Union. Shaping Principle 10

6. World-Energy 11

7. World-Rhythm. Universal Form 12

8. World-Harmony. Universal Principle of Form and

Relation 12

9. Cardinal Principle 15

10. One Music 15

11. Rationale of Mu^ic 17

12. Common Reports of Common Feeling 17

13. Elemental Form 22

14. Elemental Relation 22

15. Melody, a Composite, not an Element 23

16. The Efficient Accent and Regnant Harmony 24

17. Principle of Potential Harmony 26

18. Basis of Verification 27

CHAPTER II

Rhythm and Tone

19. Definitions 30

20. Analysis of Rhythm 31

21. Analysis of Tone 33

viii CONTENTS

BEC. PAGE

22. A Toners Harmonic Thread 35

23. Harmony in One Voice. Common Reports 36

24. Harmonic Evolution. The Major Tonic 40

25. Rhythm-Cadence and Rhythm-Repose 42

26. Tone-Cadence and Tone-Repose , 45

27. Melody, Harmony and Rhythm 48

CHAPTER III

Original Dissonance and Consonance in One Voice

28. Genesis of the Major Consonance, Musics First Reg-

nant Harmony 53

29. Genesis of Cadence-Harmxmy or Original Disso-

nance in One Voice 61

30. Distinction between Original Harmony in One Voice

and Chord-Harmony 68

31. The Seven Original Tones. Analysis 75

32. On Symbols 86

33. The Five Components of Harmony 89

34. The Five Original Cadences. Mode Defined 91

35. Progression and Resolution 96

36. A First Music-Lesson 98

37. Work for Students 101

CHAPTER IV

The Efficient Accent and Regnant Harmony of Melody

38. Regnant Harmony in One Voice and Its Principle of

Genesis Explained 102

39. Chords Derived from the Original Consonance and

Dissonance in One Voice 133

40. The Tone-Region. Its Diatonic Scales 141

41. Musical Moments. Power and Originality of Music 149

42. Subrhythm and Rhythm-Expansion. Music's Classic

Form 160

CONTENTS ix

CHAPTER V

Obigin and Nature of Minor

BBC. PAGE

43. Origin of the Minor Consonance 176

44. Original and Duplicate Forms of Harmony 184

45. Origin in One Voice of the Minor Form of Disso-

nance. Original Cadences of the Minor Mode . . . 185

46. Three Regnant Minor Harmonies and Their Bytones

and Cadences 198

47. Harmonic Percepts of Minor Origin 222

48. A Toners Harmonic Pedigree 224

49. Chords Derived from the Minor Forms of Consonance

and Dissonance in One Voice 231

CHAPTER VI

Chords in the Light of Their Origin

50. Description and Summary of Chords Thus Far De-

rived 237

51. Simple and Compound Chords Defined 243

52. Melody the Original Reporter of Harmony, Therefore

the Natural Preceptor and Guide in the First Studies

in Chords 277

Bird Songs 291

Explanation of Symbol Numbers 305

Index 307

CHAPTER I

INTRODUCING FIRST PRINaPLES

1. Questions

Science has not yet fathomed the mystery of the
prigin and early evolutional stages of music. Our
knowledge of the evolution of music is confined to the
records of a few thousand years of history. Its his-
tory plainly shows that music has passed through pro-
gressive stages of evolution from simplicity to com-
plexity. But how it began far back in the ages, the
causes of its genesis, its shaping energies and forces,
its essential nature, these and like questions still wait
for a scientific solution. Sound emerges from and
evanesces in silence. We assume that incalculable
ages ago there was a time when music as yet unborn,
unheard, lay dormant in silence, a mere potentiality.
The evolutional study of music therefore begins with
silence. All that is music is potential in and an evolu-
tion of an embryo, namely, the composite of elements
upon the genesis of which depended the genesis of
music. What is this composite.? ^Vhat are its ele-
ments ? What is the principle or cause of their union ?
Where and how did and does this union take place.?
These are leading questions which confront us in this
study. We investigate melody, rhythm, harmony, to-
nality, the tone-realm or tone-system. What are all
these things ? What is the origin and nature of each ?

.^, I }. 'I < ' : THE NATURE OF MUSIC

Which are elements and which are composites?
Which is the original and all-inclusive composite?
the raison d'etre of all the others, in short, the essence
of music? Theoretical predilections or subjective
bias cause some of us to give the supremacy to melody,
others to harmony. We still speak and write about
"the intimate connection between melody and har-
mony, " about " harmonized melody" and " melodized
harmony." All this plainly implies a common belief
that melody and harmony are separable. Are they,
have they ever been separable or separated ? If not,
one of the two is an element of the other. In fact, one
of the two includes, is the raison d'etre of the other.
Which is it ? Science has produced no final answers
to these questions. Let any one, musician or layman,
consult the testimony of his unprejudiced inner feel-
ing and experience of music and he will say with
Mozart, ** Melody is the essence of music." I quote
Mozart because he was completely free from theoreti-
cal bias. He felt and knew this to be true, he felt and
knew it instinctively just as we all do. In other
words, the truth of this common testimony of com-
mon feeling has not been scientifically proved. Nor
has it been disproved. Why not ? Primarily because
the nature of its source, that is, the nature of common
music-feeling, has not been fathomed. Yet the exist-
ence of this common feeling is everywhere recognized
in the books, this feeling is the source of every truth
that has entered the books, its testimony is every-
where appealed to and is our only resource in every
last analysis wherever and whenever rules fail to apply
or cannot be ascertained. The situation has a pe-

INTRODUCING FIRST PRINCIPLES S

culiar interest. We all share in this common feelings
yet do not succeed in translating it into common
thought, do not succeed in expressing it in so many
words. Unless this can be done it will be impossible
to answer any of the above questions. If it really be
true that melody is the essence of music, the original
and all-inclusive composite of music's elements and
principles, then it is also true that melody is the
raison d'etre of harmony, in other words, that har-
mony is and from the beginning always has been an
element of melody. I shall endeavor to demonstrate
in the following pages that this is true. But how
can it be true ? It is flatly contradicted by the entire
history, theory and practice of music. All the books
teach us that melody antedates harmony by unknown
ages and that harmony was discovered and introduced
only a few centuries ago. Is not this evidence con-
clusive, final, insuperable.^ Here let us ask a plain
question. What do the books or authorities mean by
harmony ? Without exception they mean chords, that
is, combinations or concords of several tones. No
other form or conception of musical harmony has
thus far appeared. To speak of harmony is to speak
of chords. To study harmony is to study chords.
Every treatise on harmony is a treatise on chords. It
is the common belief and teaching over the whole musi-
cal world that the chord is the one and only, therefore
by implication, the original form of musical harmony.
The evolutionist has the hardihood to question the
truth of this common belief and teaching, he does
not regard the complex chord as a spontaneous gen-
eration, he reasons that so complex a form as the

4 THE NATURE OF MUSIC

chord is rooted in and evolved from antecedent sim-
pler forms of harmony, that the development of har-
mony is a progressive evolution from simple to com-
plex which began with the genesis of music in one
voice. This explains the subtitle of this book, " Ori-
ginal Harmony in One Voice." Everything hinges
on the question of the origin and nature of music's
specific forms of harmony, that is, of consonance and
dissonance. All harmonists know that this ques-
tion still remains unanswered. A single obstacle has
stood in the way of its scientific solution, namely, the
prevailing chord-idea and chord-view of harmony
based on physical acoustics. The age of the chord
reaches back a few centuries. The age of harmony
reaches back through all the ages to the genesis of
music in one voice. The development of original
harmony in one voice occupies the entire period of
homophony, the first and longest evolutional chapter
in music and the most important chapter for scientific
research-

2. Homophony or Music in One Voice

The term homophony is used in these pages strictly
in the sense of music in one voice or part as distin-
guished from polyphony and chorded music in several
voices or parts. The material for the evolutional
study of homophony is complete. We find it in the
simple songs of birds and primitive man, in ancient and
mediaeval melodies, in folksongs and dances, in modern
music down to our own time, for the works of all the
great composers contain countless motives, phrases
and passages in one voice. Thus homophony, the

INTRODUCING FIRST PRINCIPLES 5

form in which music first arose, survives to this hour.
In essence and trend there is no difference between the
homophony of to-day and that of all the past, between
that of a song-sparrow and that of Bach, Mozart,
Beethoven and Wagner. We here confront facts of
prime importance. Homophony is the one and only
form common to all music past and present. Homo-
phony is therefore the one and only tie connecting all
music of all time. Nowhere but in homophony can
we study and discover origins, first principles and
causes, the energies and forces from which music
proceeds, the incipient stages of progressive evolution
from tone to tone, relation to relation, harmony to
harmony, in self-fulfilment of inherent laws, in short,
nowhere else can we find the explanation of the essen-
tial nature of music and of common music-feeling.
Hence the importance of homophony as a field for
scientific research. Homophony presents and verifies
its facts in a most unique and convincing manner since
its reports completely exclude personal prejudice and
eliminate the personal equation. The personal ele-
ment of choice and bias did and does not enter into
music until a second voice or part was and is added to
a first voice or part, that is, until we add other voices to
a given melody. Homophony discovers this remark-
able psychological fact. Its reports are self -reports,
that is to say, they are not what you and I or ten thou-
sand others may think, elect and debate, they are
what homophony itself elects, asserts and reports.
These self -reports are common to all of us, they are the
common reports of common feeling and apperception,
moreover, they are immutable and discover the funda-

0 THE NATURE OF MUSIC

mental dat^ of music and music-feeling. In the field
of homophony all investigators therefore stand on
firm and common ground ; here we set out with a com-
mon point of view and may join in a common purpose,
namely, the translation of self-reports into the simple
words of common thought. By nature we are all
homophonists ; the music-consciousness has its awak-
ening in homophony; we sing and whistle homo-
phony; each of us has the power within himself to
produce and reproduce in feeling and thought any
homophonic melody ; each of us may observe, study and
analyze homophony at his leisure in himself and in
others and may learn to translate its self-reports into
words; each of us may verify these reports in himself
and others; in short, the study of the psychology of
homophony lies within the reach of every musical lay-
man. The conditions for the evolutional study of
homophony are favorable for another reason. The
awakening of music-consciousness and the evolutional
sequence of tones, relations and harmonies in the de-
velopment of each individual musical mind corre-
spond with the genesis and early developmental stages
of music itself. Supposing then that the material re-
presenting the early stages of homophony did not exist,
we could reproduce that material by tracing the psy-
chological development of the musical mind from tone
to tone, relation to relation, harmony to harmony.

3. Origin of Music

The origin of music is due to the union of two ele-
ments. The two elements are rhythm and tone.
Rhythm was intoned, and forever after there was

INTRODUCING FIRST PRINCIPLES 7

music. Let any one intone a simple rhythm and he
will then and there unite the two elements and engen-
der music in its original form of homophony. What
is intoned rhythm ? Simply, tone-rhythm, the original
and indissoluble composite of music's elements and
principles, the embryo in which all that is music is
potential. What is rhythm ? Universal form of mo-
tion. What is tone.^ The specific form of sound
peculiar to music. What is this specific form ? Har-
mony of sound, in one word, harmony. In music, a
tone is and always has been a harmony. We shall see
that the harmonies of music are the harmonies of rela-
tions, that they assume one of two forms peculiar to
music, namely, the form of consonance or that of dis-
sonance. The original forms of consonance and dis-
sonance had their genesis in one voice, that is, they arose
in homophony. Thus when we intone rhythm, each
tone that we express is one or the other, a consonance
or a dissonance. This is true of every tone in the
homophony of birds and man. Subsequent analysis
will show that the genesis of music depended on the
genesis of its first harmony. The first harmony is
the perfect or major consonance which we call the
tonic. Let any one rhythmically reiterate one and
the same tone thus : M T M f * I ^ etc. He will
then and there engender and express the first har-
mony which far back in the ages emerged from silence
and announced the genesis of music. At bottom,
music per se is tone-rhythm. At bottom, our common
feeling of music is the feeling of music per se, that is,
the feeling of tone-rhythm. As we proceed let us
bear the following points in mind. In music, tone is

8 THE NATURE OF MUSIC

not separable from rhythm. All relations of tones
are tone-rhythmic relations. All forms of tones are
tone-rhythmic forms. Music's specific original forms
of consonance and dissonance could not arise apart
from rhythm. These original forms lie at once at the
foundation of music and of common music-feeling.
In our common feeling of music itself, as just defined,
let us seek to discover the true nature and funda-
mental principles of music.

4. Music-Feeling, the Source and Fountain of Music

Where did and does this Union of Elements take
place .? Within the organism, within us, in feeling.
Hence, music-feeling, the source and fountain of
music. The harmonic forms of tone specific to music
had their genesis in feeling and are the direct products
of causes operating in feeling. The voice of music
is an inner voice, a spiritual voice. Thus music
dwells within, proceeds from within, is understood
within. The germ or raw material of musical sound
entered into feeling from without. But until that germ
had been planted and had taken firm root in feeling
it could not develop and blossom into the perfect
tone or consonance upon the genesis of which de-
pended the genesis of music. Feeling alone could,
did and does transmute the raw material of external
physical sound into the perfect harmonic form of
tone with which music began. Why ? Because the
causes of this transmutation are psychical or spiritual
causes which exist nowhere outside of feeling, that is,
outside of the mind. These causes explain why it is
that every first crude effort to intone rhythm is an

INTRODUCING FIRST PRINCIPLES 9

effort to shape and express the perfect tone or con-
sonance with which music began; they explain why
it is that the perfect tone or consonance exists nowhere
outside of feehng, outside of the mind. This is con-
clusively proved by the ascertained fact that under
acoustical analysis every tone is a dissonance. But
even the form of this acoustical dissonance is not the
same as that of the original dissonance of music. That
and why this is so is explained by the proximate or
immediate cause of the psychogenesis of the specific
harmonic forms of music. This cause is relation,
A tone's specific relation is the immediate cause of its
specific harmonic form. From first to last the origi-
nal harmonies of music, headed by the perfect tone
or consonance, arose one by one in an evolutional
sequence of relations in obedience to an inherent shap-
ing principle. As we proceed to trace the psycho-
genesis of this evolutional sequence of correlated har-
monies we shall obtain a view of music in the light of
its origin and development and so discover the nature
of our common feeling of music. Let us be explicit
as to exactly what is here meant hy feeling of music.
By music-feeling I mean simply and only the feeling
of music per se, that is, the feeling of tone-rhythm,
that is, the feeling of united rhythm and harmony,
that is, the feeling of melody, the essence of music.
Here at the outset let us understand that this study is
not concerned with an analysis of feeling in its con-
nection with any specific emotions, sentiments and
associated ideas which are evoked by music. All
these are most important precisely because they are
purely personal, but their proper place is in poetry.

10 THE NATURE OF MUSIC

autobiography and aesthetics. In a study like this such
an analysis of personal experience would be out of
place and would lead us into the cloudland of vague-
ness, mysticism and speculation. Here let us seek the
common truth in our common experience of music.
We shall, however, consider certain fundamental emo-
tions, first because they are common to all of us and
next because they are inseparable concomitants of
tone-rhythmic feeling. The spirit and the matter of
music are inseparably united as idea and form, as
message and messenger of truth and beauty. The
tone-rhythmic messenger is the bearer of the spiritual
message. Our common knowledge of that message
is confined to what can be learned from the messenger.

5. Cause of Union, Shaping Principle

Both rhythm and tone Sive forms of balanced motion.
A shaping principle common to both is the cause of
their affinity and union. This shaping principle is
equilibrium. Equilibrium is harmony. Harmony is
equilibrium. Tone - rhythmic equilibrium is tone-
rhythmic harmony. Tone-rhythmic harmony is tone-
rhythmic equilibrium. The feeling of tone-rhythmic
equilibrium or harmony is our common feeling of
music. The feeling of tone-rhythm and its shaping
principle, while it explains why every initial effort to
intone rhythm is an effort to shape and express the
perfect harmonic form of tone essential to the genesis
of music, it does not explain why that effort is made,
that is, it does not explain the cause which gave
and gives the impulse to that effort. What is this
impelling cause.? It is a spiritual cause, a common

INTRODUCING FIRST PRINCIPLES 11

emotion, an inseparable concomitant of tone-rhythmic
feeling, namely, the innate desire to shape and ex-
press with no other end and aim than the pleasure of
gratifying that desire. This impelling desire of the
inner life or human spirit to give form to its moods
and tenses for pure joy and love of expression is the
creative impulse to which all the arts owe their rise
and development. Goethe's dictum "art is but
form" is comprehensive, since form in art is the
direct product of the human spirit and is not separa-
ble from the idea which it embodies. Equilibrium or
harmony is the shaping principle of all form of mo-
tion, of all physical /orm of expression, of all spiritual
form of expression. We are here confronted by a
world-principle, a principle inherent in the physical
and psychical forces, a principle governing all animate
and inanimate form of cosmic expression. This uni-
versal principle of harmony and the principle of har-
mony in music are one and the same. This princi-
ple is the ejSicient cause of the genesis in feeling of the
original forms of harmony, the evolutional anteced-
ents of chords.

6. World-Energy

World-energy is manifested in motion. Its mani-
festations may be summarily divided as follows:
First, motion in process. Second, record of previous
motion or process. The first includes all sensible
motion within and about us. The second includes
all the forms or works of nature and all the works of
man. All motion is accentual, wherefore all process
and record of motion are accentual.

n THE NATURE OF MUSIC

7. World-Rhythm. Universal Form

World-motion is accentuated motion, in one word,
is rhythm. Rhythm is form not law of motion. Let
us not confound form, which is rhythm, with the
principle or cause of form, which is inherent in
and proceeds from energy itself. World-energy is
manifested in world-rhythm. Hence this principle.
Rhythm is the universal form of expression. At bot-
tom, the terms expression, manifestation, language,
are synonymous. Not man alone speaks. All things
speak, each in its own peculiar language, but all in
common rhythmic accents in time and space. Vibra-
tion, pulsation, undulation, are so many names for
accentuated motion, that is, for regularly recurring
periods of rhythm.

8. World-Harmony. Universal Principle of Form
and Relation

World-rhythm everywhere makes for world-har-
mony, world-equilibrium. World-energy persists in
its, perpetual rhythmic struggle for the maintenance
of world-harmony, world-equilibrium. Hence this
all-pervading, all-shaping, all-governing principle.
Harmony (equilibrium) is the universal principle of
form and relation in time and space. The universe
is one rhythm proceeding from one energy and
maintaining one equilibrium to which the rhythm
and equilibrium of all its parts from greatest to
smallest are relative. Hence the harmony and
unity of the universal whole, the interdependence and
interrelation of all things, the reign of law and order

INTRODUCING FIRST PRINCIPLES 13

in time and space. In this connection, harmony,
equihbrium, balance, unity, are interchangeable
terms. The ceaseless rhythmic struggle and ''stream
of tendency" within us and all about us ceaselessly
makes for harmony. This rhythmic struggle and
its governing principle are manifested throughout
inorganic and organic nature in every movement and
every form or record of movement. Harmony
(equilibrium) is a fundamental principle of evolu-
tion. In fulfilment of this inner principle of " being
and becoming," all things pass through rhythmic
stages of progression and resolution, that is, rhythmic
stages of evolution. Life from moment to moment '
is a rhythmic struggle for equilibrium. The works
of man are records of his physical, mental, moral
and spiritual struggle for equilibrium. In his music-
works man has recorded and will continue to record
the essence of his universal and spiritual experience
in his only universal and purely spiritual language,
music. The realm of music, the tone-realm, is an
evolutional product of the inner life or spirit; it
is the spiritual counterpart and image of the uni-
versal whole, of its perfect law and order in time and
space. Music is the concrete language of universal
harmony, law and order. Music-feeling is univer-
sal feeling, that is, the concrete feeling of universal
harmony, law and order. I emphasize concrete
because all that is music and music-feeling is con-
crete reality, a concrete and vivid inner experience, a
common experience in all of us. In music, rhythm
is form, relation, law and order in time; tone
(harmony of sound) is form, relation, law and order

14 THE NATURE OF MUSIC

in space; the tone-rhythmic embryo or composite
of the two unites pure time-form and pure space-
form, pure time-relation and pure space-relation;
this composite, as we shall demonstrate, is melody,
the essence of music, the free spirit of the free tone-
realm. Melody makes for pure and perfect har-
mony in time and space and thus fulfils the inner
law and purpose of its being. In our common feel-
ing of melody we shall discover the identity of
harmony and equilibrium. As we proceed to trace
the evolution of tone-rhythm we shall observe the
operation of this universal principle in the domain
of the mind. Harmony (equilibrium) is the govern-
ing principle, the will of the material and spiritual
universe. In the human spirit this principle mani-
fests itself in a common emotion, in a common desire
for and love of harmony, to gratify which is to be
led by, to follow, to obey, the universal will. This
spiritual desire and love discovered its voice in
melody, rhythm was intoned; the heart thus found
a perfect vehicle for all its moods and tenses. Hence
music, its genesis, its raison d'etre^ its function, its
messenger, its message. Thus music and its forma-
tive principle are deeply rooted in what Goethe
calls "eternal things" and "the great whole;"
its composite rhythmo-harmonic relations are what
that poet-evolutionist calls "abiding relations." In
the light of the principle of world-harmony I under-
stand Schopenhauer's definition of music, " das innere
Bildder Welt."

INTRODUCING FIRST PRINCIPLES 15

9. Cardinal Principle

Harmony (equilibrium) as just defined is the
cardinal principle responsible for the genesis and
evolution of music and music-feeling, for all that is
law, order, form, relation, proportion and structure
in music. Thus all the principles and laws of
music, of its elementary forms and their original
relations and of the gradual expansion of its forms
and relations, are so many different manifestations
of the operation of this one all-shaping and all-
explaining principle. Under the impulse of princi-
ples and laws operating in feeling music sprang into
being and, passing through a series of natural and
interdependent stages, evolved from simple to more
and more complex forms, from a state of nature to
an art. Nature-music and art-music differ only in
degree, not in kind; the same fundamental prin-
ciples and laws underlie both.

10. One Music

Nature-music includes the songs of birds and all
those human melodies of the homophonic period in
the production of which man was guided wholly by
intuition and the impulses of the heart and simply
obeyed his innate feeling of the principles and laws
of tone-rhythm. This intuitional evolution of nature-
music reached its culmination in that lovely and per-
fect flower, the folksong. Nature had spent incal-
culable ages in the production of this perfect form
of melody, had thus fulfilled her mission and laid
the foundation for the art of pure music. From the

16 THE NATURE OF MUSIC

simplest homophonic motive and phrase to the
perfect symmetry of the folksong this nature-music
is the pure music of intuition and the heart, the pure
expression of concrete music-feeling. Nature had
not only produced the germs which were destined
to develop into the great art of pure music but
had chosen, followed, prepared and pointed out the
true path for the development of this art. This
path of intuition and concrete music-feeling was
chosen and followed by the only art of pure music
which the world has produced. This pure art is
modern music which is distinctively the product of
Western civilization and the only music-art directly
connected with and based on nature-music. Hence
one music, one continuous evolution from the earliest
beginnings of nature-music to the art of the present
time. This one music is the only music which
concerns us in these pages. Whatever else may be
said of the manifold theories to which the modern
art of music has given rise, one thing is true of all,
namely, all seek to explain and conform with the
nature and testimony of intuitive music-feeling in
their common endeavor to discover and present the
true principles and laws of the art of music. Man
has produced other species of music-art whose
forms and theories are not based on intuition and
concrete feeling. An extinct art of this species is
that of ancient Greece. An extant art of this species
is that of China. Yet when we consider the beauti-
ful tributes paid to music by Homer and Confucius
we are led to infer that these two unmusical arts
had been preceded by an evolutional period of

INTRODUCING FIRST PRINCIPLES 17

nature-music when both Greek and Chinaman were
guided by intuition and the heart, when Hke the
birds they freely sang just as they happened to feel.
Why in those two eases the natural attitude toward
music was forsaken in favor of arbitrary theories is
a question closely connected with the life and spirit
of the two nations, a discussion of which does not
enter into the plan of this book. Our subject has
been defined, it is one music, in the nature-stages of
which human selection was unconsciously governed
by natural selection, in the art-stages of which human
selection was consciously governed by natural selec-
tion.

11. Rationale of Micsic

The elemental what of music is form and relation
of united rhythm and tone. The explanation of
this form and relation, their inherent principles and
laws, will discover not alone the true nature of
this elemental what, but also answers to its how?
and why? Elemental tone-rhythm and its indwell-
ing principles and laws of self-development there-
fore constitute the what, how and why, in a word,
the rationale of music. What.? is the question of
ultimate importance. Until this essential question
is answered the inquiries how.? and why.? are futile
since they lack a subject, since, in other words, we
do not know what we are inquiring about.

12. Common Reports of Commxm Feeling

Whether their theories are based on acoustics,
physiology or psychology, all investigators set out
with a common view of the ultimate question What

18 THE NATURE OF MUSIC

is music? a question so often set aside as an insol-
uble mystery. This common view of theorists is
shown in three significant essentials the importance
of which is greater than at first appears.

First: Admittedly or tacitly all premise that music
is what we hear it to be and thus transmute the
form of the ultimate question What is music .^ into
What do we hear music to be ? or briefly, What do
we hear.? That music is what we hear is not a
remarkable observation for what else could it he?
However, the question What do we hear.? really
means What do we all hear in common.? and this
question no one has as yet succeeded in answering.

Second: At the outset all agree that what we hear
is consonance and dissonance. This again trans-
mutes the form of the ultimate question into What
is consonance and what is dissonance .? A scientifi-
cally verified answer to this question has not yet
appeared in the books, and there are those who
believe that this answer cannot be discovered in the
three sciences mentioned above, wherefore it should
be sought elsewhere.*

Third: All acknowledge the existence of such a
thing as common music-feeling to which the appeal
is general whenever and wherever laws and rules
either fail to apply or cannot be found. This gen-
eral appeal to music-feeling is equivalent to a general
belief in its essential validity, a general belief that
in it the ultimate and whole truth of music lies
dormant, a general belief that the feeling is common
to all. If there is such a thing as common music-
feeling, then there are such things as common music-

INTRODUCING FIRST PRINCIPLES 19

perception, as common reports of common feeling
verifiable by common observation. What are these
common reports and their immutable principle?
This question has not yet been answered. The
answer to this question would discover the true
basis of music and its science, it would be the initial
step toward a common conception of the ultimate
what of music, it would eventually result in a com-
mon recognition and adoption of the one true basis.

In these pages it is my purpose to show that such
things as common reports verifiable by common
perception do exist and may be clearly presented
and explained. The ultimate question What is
music .^ now assumes the following form: What are
the common reports of common feeling and per-
ception of consonance and dissonance, their inher-
ent principles and laws.^ It is clear that this is a
psychological question, a question addressed to the
inner ear of the mind, a question of psychological
acoustics, not of physical acoustics. Though this
question places the present writing upon an inde-
pendent basis and defines the writer's position,
the psychology of this position still requires some
explanation.

We are told by M. Hauptmann * that it is custom-
ary to begin a treatise on harmony with a learned
chapter on acoustics the half-truths in which, how-
ever, have little if any influence upon and are often
not again referred to in the subsequent chapters of
the book. Acoustics treats the question What do we
hear? on its physical side and therefore objectively,
as every one knows. Music as we hear it does not

20 THE NATURE OF MUSIC

exist objectively, as we shall see. The acoustic
series, consisting of fundamental and overtones,
teaches us that every tone is a dissonance and proves
this to be a fact, and thus at the outset music and
acoustics are irreconcilable antagonists. But this
physical tone is not a dissonance in the specific
musical sense of the term ; it is in truth a discord, and
discords have nothing to do with music. Although
it is the custom in music-treatises to present only the
first six tones of the acoustic series, yet this arbitrary
omission of the remaining objectionable because dis-
cordant overtones does not eliminate them, they are
there just the same, and are met as they should be
by physical science. Whatever be their pitch all
tones have the same internal physical formation,
therefore all tones are discords. If one tone is a
discord what a blood-curdling horror such an amor-
phous physical composite as the chord ought to be!
But common music-feeling and perception reject
all this as false. If we really heard tones in their
actual physical forms all hands would be raised to
stop the ears. Notwithstanding all this most of our
music-theories are based on physical acoustics; a
scientific basis for music being required, and no
other being at hand we seize upon physics for an
initial chapter. Music's pure and perfect conso-
nance, music's specific form and relation of tone,
these things do not exist objectively, they are sub-
jective products of psychological development, direct
products of music-feeling, which is the feeling of
composite rhythm and harmony. Roughly stated,
elemental tone-rhythmic feeling impelled by an

INTRODUCING FIRST PRINCIPLES 21

inherent immutable principle, equilibrium, has re-
solved objective physical sound or discord into sub-
jective harmony.

The rejection by music-feeling and perception of
physical acoustics as a basis directly points to psy-
chology for the solution of music's ultimate problems
and the discovery of music's cardinal principle.
Though the conviction that there is such a princi-
ple has often been expressed the psychologist has
thus far been unable to explain what it is; he has
left the true nature of common music-feeling shrouded
in mystery and, like the physicist and physiologist,
has left the problem of consonance and dissonance
unsolved. The psychologist has followed one of
two courses: either he has made a comparative
study of music and music-feeling in the light of the
data of physics and physiology, like C. Stumpf, or
he has delved more or less deeply into metaphysical
speculations and aesthetics. The physiologist deals
with the physical organ of hearing and its function,
and in his hands the question What do we hear?
assumes the form How do we hear.? which is a
subordinate question that predicates a knowledge
of music's ultimate what When psychology has
once answered the ultimate question, then only will
physics and physiology gain a legitimate subject
for musical research the importance and value of
which to music can alone be estimated in the
future.

The writer's position thus roughly sketched may be
summed up as follows: The true nature of music
per se, of its specific forms and relations, of its

■22 THE NATURE OF MUSIC

inherent principles and laws, are problems of psy-
chology the solution of which can alone be found in
what I have called the common reports of common
feeling verifiable by common perception.

13. Elemental Form

Form is vehicle or messenger, not message, but
bearer of message. We are here primarily concerned
with the messenger, not with the message of music,
since all that can be learned of the latter depends upon
what can be learned of the former. The two should
not be confounded. Elemental form or messenger
of music is united rhythm and tone. In this elemen-
tal form lies music's elemental truth and beauty,
the study of which involves neither vagueness nor
speculation and alone concerns us in these pages.
Vague, mysterious, inscrutable, yet none the less
real and important is the spiritual message of music,
a message of universal harmony and unity. How-
ever, the spiritual message of truth and beauty, the
emotions, poetic and religious sentiments and the
aesthetic and metaphysical speculations and theories
to which it gives rise, belong not to music alone, but
to all the arts and to all things. By the word feeling
in connection with music I mean simply and only
feeling of united rhythm and tone, which is music-
feeling per se and common to all of us.

14. Elemental Relation

A tone's relation in time is its rhythmic relation.
JA tone's relation in space is its harmonic relation.
Thus tone-relation is a composite of time-relation

INTRODUCING FIRST PRINCIPLES 23

and space-relation, in one word, is a rhythmo-har-
monic relation. Every tone in music is heard, felt,
thought, expressed and recorded in such a com-
posite relation, every tone-moment is a rhythmo-
harmonic moment. It is true that in analysis we
seem to separate this composite, now observing the
rhythmic form and relation and now the harmonic
form and relation, yet we do not and cannot fully
comprehend the one apart from its relation to the
other. The word harmony in its specific musical
sense means harmony of sound, which is tone. In
this sense one tone, every tone is a harmony, as will
be explained in the next paragraph.

15. Melody y a Composite, not an Element

Nothing could be more untrue than the time-
honored teaching and belief that melody, harmony
and rhythm are the three elements of music. Music
has two, not three elements. Rhythm is an element.
Harmony (tone) is an element. Melody is not an
element. Melody is a composite of music's two
elements, rhythm and harmony (tone). It is impos-
sible to conceive of melody either without rhythm
or without harmony (tone). Hence the obvious truth
that melody is a composite and not an element.
Everything from a motive in two tones onward,
whether it issues from the throat of a bird or was
penned by a classic composer, is a melody, a com-
posite of rhythm and harmony (tone). Melody is
the essence of a music-idea or thought. Melody is
the original and essential vehicle of music. Melody
is the original, universal and sovereign voice and

24 THE NATURE OF MUSIC

genius of music. Conversely, music ever has been,
is, and ever will be melody. Melody is the raison
d'etre of music's harmony. Why this rhythm ? Why
that harmony ? The answers to these questions lie in
melody. Love of music and love of melody are one.
No melody, no music-idea or thought. No melody,
no harmony. No melody, no music. The great
and greatest in music are its melodies; types in
music are types of melody and from first to last
music's great masters are melodists.

The above conclusions are verified by common
report of common feeling and perception of original
harmony in one voice. In a book^ published in
1890, the writer introduced the subject of harmony
in one voice naming it meloharmony^ the inherent
harmony of melody.

16. The Efficient Accent and Regnant Harmony

In a preceding paragraph it was stated that the
principles and laws of music are rooted in the cardinal
shaping principle, equilibrium. The rhythmo-har-
monic forms and relations of music in one voice or
homophonic melody discover the nature and oper-
ation of two evolutionary principles which next
require provisional introduction and explanation.
First and most important of the two is the efficient
accent which is the efiicient cause of the genesis of
tones and tone-relations, that is, of music's specific
and basic harmonies.

The eflScient accent is the heavy 'periodic accent oj
rhythm^ it is the harmony-generating and harmony-

* Th£ Septonate and the Centralization of the Tonal System.

INTRODUCING FIRST PRINCIPLES 25

maintaining accent of music. Under the name
rhythmo-harmonic accent or point, I presented this
subject fourteen years ago in the book above alluded to.

In one-voice music, not only is each tone in a
melody a harmonic, that is, a root or third or fifth or
seventh or ninth, but every moment in a melody
is ruled by a particular harmony which I call the
regnant harmony.^

In one voice the regnant harmony arises on the
line of least resistance, it elects and asserts itself,
it is generated in feeling by the efficient accent, it
determines and reports the exact harmonic form
and relation of each tone; these forms and rela-
tions are immutable, since in every given case we
all of us hear and perceive the same form and same
relation.

We shall see that the original harmonies entered
into being one by one as integral and correlated
threads of an ever increasing web of forms and
relations in an orderly sequence of regnant har-
monies, a sequence which nolens volens repeats itself
in the development of every musical mind, thus
establishing a traceable psychological connection be-
tween music's present and past. We cannot study
and trace this evolutionary sequence and psycho-
logical development in multi-voice music for the
simple and obvious reason that in such music the
regnant harmonies are due to personal election, fancy
and taste. In one voice the regnant harmony elects
itself, while in more than one voice the choice of har-
monies is personal. In one voice we perforce agree,
while in several voices we are at liberty to disagree.

26 THE NATURE OF MUSIC

17. Principle of Potential Harmony

The next evolutionary principle to be introduced
is that of potential harmony, which I define as fol-
lows: Every harmonic relation in experience is poten-
tial in every tone in experience. Thus all harmonic
relations are potential in all tones. In other words,
any harmonic relation may be duplicated on any
tone. Let us explain.

There are original tones, original harmonic forms,
original harmonic relations. The seven tones of the
major scale constitute the first group of original
tones. Certain of these tones first arose in the
harmonic form of consonance, certain others in that
of dissonance. This specific consonance and this
specific dissonance are therefore the original har-
monic forms. Again, each of these seven originals
first arose in a certain definite harmonic relation as
a root or third or fifth or seventh or ninth. The
original relation of a tone is therefore the relation in
which a tone first arose. Everything is and has
been derived from relation; harmonic form and
harmonic relation are connate; the former is due to
the latter, the former changes when the latter changes.
Since each original tone entered into being in a cer-
tain original relation, the fundamental importance
of relation is manifest.

In the psychological process of development each
tone and relation entered into experience first as a
mere feeling, it remained latent in feeling until it was
seized upon by consciousness when it became a per-
cept, and last of all it became a concept. The

INTRODUCING FIRST PRINCIPLES 27

harmonic idea of music is therefore a complex of har-
monic percepts, each of which is either an original
harmonic relation, or has been derived from an origi-
nal relation. How derived? Through, the evolu-
tionary principle of potential harmony in cooperation
with the efficient accent, the principle of harmonic
genesis, roughly as follows: Each toners original rela-
tion is duplicated on other tones. For example: the
tone known as the Tonic (also called keynote) first
arose as a root and eventually appeared as third,
fifth, seventh and ninth, thus duplicating the origi-
nal relations of other tones. Like duplications were
in time effected on other original tones which had
their genesis in other relations. We shall see that
these duplications are responsible for the genesis of
new tones and new harmonic relations thus opening
the way to new duplications, and we shall see that the
expansion of harmonic relations and of the tone-sys-
tem is the direct product of this psychological process,
in short, that harmonic relation and our tone-system
are inseparably linked in their development as cause
and consequence. But how did the seven original
tones arise ? How did the first consonance and first
dissonance arise .^ Unless these origins can be ex-
plained the principle of potential harmony has no
material to develop, no valid basis to rest on, is
but an empty phrase. The above questions will be
answered in the two subsequent chapters.

18. Basis of Verification

A brief summary of the position outlined in the
preceding paragraphs will lead the way to a simple

28 THE NATURE OF MUSIC

explanation of how the test of truth is to be applied
in the subsequent study and analysis of music. The
essential points are as follows : —

The "being and becoming" of music are due to the
union in feeling of rhythm and tone.

Form and relation are form and relation of united
rhythm and tone.

All tones are harmonic. Original harmony is har-
mony in one voice; it asserts itself and is latent in
common music-feeling, therefore in all of us. Har-
mony in one voice reports the same relations in all
of us.

Melody is the composite of the two elements,
rhythm and harmony (tone); it is the original and
universal voice of music.

Common music-feeling is united rhythm-feeling and
tone-feeling.

One music, one basis of music, one common music-
feeling, one all-shaping principle in which all princi-
ples and laws are rooted. This cardinal principle
is equilibrium, is common to and inherent in both
rhythm and tone, and is the cause of their union, and
it dwells and operates in common feeling in all of us.

All who take any degree of pleasure in music are
musical and share in the common feeling. All such
may by guidance and study transmute latent feeling
of united rhythm and tone into definite observation,
intelligent appreciation, understanding.

Community of feeling leads to community of per-
ception and thence to community of conception. All
may learn the common reports of common feeling and
verify such reports by personal observation.

INTRODUCING FIRST PRINCIPLES 29

The test of truth here indicated is the simplest.
What all perceive or observe in common is the truth.
Truth is the correspondence of an expressed idea with
common experience. The truth of music Hes in
music itself, in music stripped of all associated ideas
and sentiments; it lies in tone-rhythm, and in tone-
rhythm we will seek it. Two simple examples will
illustrate our test of truth.

1. Whether we know it or not we all feel and ex-
press a dual rhythm in dual periods, a triple rhythm
in triple periods. Hundreds and thousands sing, beat
time and march to the music of a national air in com-
plete ignorance of the rhythm which they feel and
express in common. However, the moment we learn
to observe a dual rhythm by its dual periods and a
triple rhythm by its triple periods, we all acquire the
same knowledge in the same way, namely, by trans-
muting a common feeling into a common perception
or observation.

2. Whether we know it or not we all feel and ex-
press tones as roots, thirds, fifths, sevenths and ninths,
some in cadence, some in repose. The same hun-
dreds and thousands feel and express these harmonic
relations of tones with the same complete ignorance
of what they are. When these harmonic relations are
learned they are learned in the same way, namely, by
transmuting common feeling into common observa-
tion.

CHAPTER II

RHYTHM AND TONE

19. Definitions

Rhythm is balanced motion. Tone is balanced
sound.

Rhythm is order, form and relation in time. Tone
is order, form and relation in space (pitch).

Rhythm is harmony (equilibrium) in time. Tone
is harmony (equilibrium) in space (pitch).

United rhythm and tone is united order, form, rela-
tion and harmony in time and space.

The elemental forms and relations of rhythm
which underlie all music-rhythms are not specific to
music, they exist everywhere.

The elemental harmonic forms and relations of
tone which underlie all harmonic forms and rela-
tions of music are specific to music, they exist in
music alone.

Numbers are symbols of order and relation. The
numbers 2 and 3, their multiples and combinations
are the symbols of rhythmic order and relation of
tones, of order and relation in time. The numbers
1, 3, 5, 7, 9 which indicate a root or fundamental,
its third, fifth, seventh and ninth are the symbols of
harmonic order and relation of tones, of order and
relation in space (pitch).

RHYTHM AND TONE 31

20. Analysis of Rhythm
Rhythmic balance is generated and maintained by
regularly recurring accents. Common rhythmic feel-
ing impels us to follow up an initial group of two
pulses by another, two such groups by two more, and
so on. Likewise we are impelled to follow up an
initial group of three pulses by another, two such
groups by two more, and so on. Examples are given :

1. TWO-PULSE RHYTHMS

2. THREE-PULSE RHYTHMS

etc

*)C 1_L/TIL/^LJL^ rr^

')L.C_r ^CQ CLI CD

etc.

Our spontaneous desire to arrange pulses in regular
accentual groups, and to repeat and develop an initial
group, is no more nor less than the natural desire to
keep balance, to keep time, to obey the inherent and
innate shaping principle, equilibrium. To keep
time is to keep balance, to keep balance is to keep
time.

32 THE NATURE OF MUSIC

In the above examples each pulse, each group of
pulses, each combination of groups, is a period of
rhythm. Henceforth in these pages the term period
will be employed exclusively in this connection with
rhythm. Rhythm-periods are balanced h'm^-periods.
Rhythmic accents are balance-generating and balance-
maintaining time-accents. A period of time is a
rhythmic moment, a time-accent is an accentual
moment in feeling and consciousness. Under the sway
of innate rhythm the inner consciousness moves
forward in time from pulse to pulse, from accent to
accent, in other words, from moment to moment, from
now to now. We shall analyze this forward move-
ment in time, and shall study the psychology of this
moment, this accent, this now; it holds the secret of
music and of common music-feeling.

Rhythmic feeling, in obedience to the indwelling
shaping principle, impels us to vary the accents of
successive pulses or moments so that heavier accents
so alternate with lighter accents that they recur at
regular intervals of time, thus forming regular groups
and maintaining the rhythmic balance. In the above
examples the sign > indicates the heavy accents, and
the examples show that the difference between one ele-
mentary rhythmic form and another is a difference in
the order of heavy and light accents. Thus the two
forms of dual rhythm are light-heavy and heavy-light,
while the three forms of triple rhythm are light-light-
heavy, light-Z^^av^z-light, heavy -light-light. All music-
rhythms are based upon these five elementary forms.
These accents of varying intensities, their regular
alternations and the recurrent heavy accents are of

RHYTHM AND TONE S3

the utmost importance ; their psychology will discover
the hitherto overlooked key to the origin and true
nature of music's specific and basic harmony.

Metre and rhythm are not alone often confounded,
but are sometimes treated as identical, which is wide
of the truth. Rhythm is not metre, metre is not
rhythm, neither in music nor in versification. Metre
is measure of rhythm-periods, that is, of time-periods
of tones. Our metrical symbols are symbols of meas-
urement; they symbolize rhythm, time. Metrical ac-
cents so-called do not exist. Feeling of rhythm came
first, perception of rhythm came next, metrical and
numerical symbols of rhythm came last.

21. Analysis of Tone

Sound that wavers in pitch is unbalanced, is unmu-
sical, is not harmonious, is not tone. Sound main-
tained at an unwavering pitch is balanced, musical,
harmonious, in a word, is tone, the unique voice of
music. The shaping principle, equilibrium, which is
inherent in common feeling, impels us to make for
balanced sound or tone just as it impels us to make
for balanced motion or rhythm. So long as we main-
tain sound at an unwavering pitch, so long do we gen-
erate in feeling the perfect balance or harmony of
tone. This pure harmonic form of tone to the genesis
of which in feeling music owes its origin and exist-
ence is the major consonance, music's first or original
consonance which to-day we call the Tonic-harmony
of the Major mode, the harmony of complete repose.
This perfect tone or harmony opens the first chapter
of tone-genesis, a new subject in our science ; it is an

S4 THE NATURE OF MUSIC

inner product of feeling, has no existence outside of
feeling and now requires psychological analysis. In
thought or voice maintain a sound at an unwavering
pitch and you will generate this perfect tone or har-
mony in feeling. Whatever the pitch may be the
result will be the same. For convenience and clear-
ness of illustration therefore we will suppose the pitch
to be that of C. While mentally sustaining this tone
we are at first conscious only of a single tone as at a)
in the example below. Analysis will, however, soon
discover that instead of sustaining only a single tone
we are in truth sustaining a harmonic complex of
tones comprising a root or fundamental, its major
third, pure fifth and octave, as shown below at b),

a) 6)1 3 5 8

li

\~~.^^^

KJ .^

^

To be more explicit, while at first ,we are conscious
only of the single tone C, which is a root or funda-
mental, analysis soon discovers the presence of a
third (E), a fifth (G) and an octave (C), which are
concomitant elementary tones or harmonics and which
together with the root make up the harmonic form of
this isolated tone. Hence this truth : Every isolated
tone is a harmonic complex of root and elementary
harmonics, that is, a composite of root, major third,
pure fifth and octave; in short, an isolated tone is
always a major consonance. Each reader may verify
in and for himself that this is so; why it is so will be
explained presently. The fact here requiring empha-
sis is this: An isolated tone always reports itself

RHYTHM AND TONE S5

as the root of a major consonance. The word root
defines the harmonic relation ; the term major conso-
nance defines the harmonic /orm. We shall soon find
tones reporting themselves as a third or fifth of this
consonance and in many other forms and relations.
In each of these relations we shall discover that the
tone arises in the mind together with elementary har-
monics, that the form varies with the relation, that the
form and relation of every tone are therefore harmonic;
in fine, that every tone is a harmony. Meanwhile the
original major consonance requires further analysis.

22. A Tone's Harmonic Thread

The harmonic complex which a tone generates and
reports in common feeling may be called the harmonic
thread of a tone. The harmonies of music form a
closely wrought web of innumerable harmonic threads.
Consciously and unconsciously we feel a tone's har-
monic thread, but unless we accurately observe its
harmonic thread we cannot appreciate the exact form
and relation of a tone. The thread of the major con-
sonance in the above example presents a root, third,
fifth and octave. Each higher and lower octave is
another root of a like series of harmonics wherefore
we may change the octave-number 8 into a root-
number 1 as follows: —

1351351 1531531

i

BSEE^ . . -H

w-

-^- * etc. * -^ -I^

This shows that the harmonic thread of a major
consonance extends through the whole range of tone-

36

THE NATURE OF MUSIC

pitch. Once generated in feeling we move at pleasure
up and down from tone to tone on this thread taking
the tones in the above order or making leaps, since in
doing this we but follow the line of least resistance
in obedience to the inherent shaping principle, equi-
librium. This first of music's harmonic threads
introduced a variety of intervals into experience,
namely, the pure octave, fifth and fourth, major and
minor thirds, sixths and tenths, as shown below : —

i

8ve

5th

4th

maj. 3d

min. 3d

^

-«?-

-&^

maj. 6th min. 6th maj. 10th min. 10th

^2-

^^m

There is however something vastly more important
than these intervals or steps from tone to tone. It is
the tones themselves which give rise to all these inter-
vals and which resolve themselves into three harmonic
'perceptSy namely, a root, a major third, a pure fifth.
Briefly, each tone in the above intervals is one of these
three harmonic percepts. The harmonic percept is
therefore the thing of primary importance, the essen-
tial thing to understand and to know. As we proceed
it will be well to bear this distinction between an inter-
val and a harmonic percept in mind.

23. Harmony in One Voice, Common Reports

As we have seen, the major consonance is a complex
of three tones or harmonics. Like the root, each of
the other two tones generates in feeling the entire

RHYTHM AND TONE

87

consonance-thread, therefore each includes the other
two as concomitant elementary harmonics, or briefly,
as concomitants. Thus the root includes third and
fifth as concomitants ; the third includes root and fifth
as concomitants; the fifth includes root and third as
concomitants. All three appear in the following
melody, in each tone of which we all hear and feel
the same harmonic complex or form and the same
harmonic relation as specified by the harmonic num-
bers 1, 3, 5 over the notes.

13151351

^

I

_,fi-

r^

This provisionally illustrates what I mean by origi-
nal harmony in one voice, which asserts and reports
itself without chords. The numbers 1, 3, 5 explain
what I mean by the common reports of common feel-
ing and perception, since they faithfully register the
inherent relations which we all hear and feel in com-
mon. The number 1 indicates a root. The numbers
3 and 5 imply a root and indicate the relation of a
tone to its root. I have said that an isolated tone
generates and opens up its thread of harmony both
above and below and that we follow the thread up or
down at will. In the above melody we move from
root up to third, then back to root, then down to fifth
and so on. That every tone arises in a thread of har-
mony is not the only point to be emphasized. In this
melody we are now on a root, now on a third, now on
a fifth of a thread. The word now is used with pur-

38 THE NATURE OF MUSIC

pose. It means that each tone fills a moment in con-
sciousness, a rhythmic moment or period of time; it
means that in music a tone is indissolubly united with
rhythm from the moment it enters until it makes its
exit. In its rhythm we find the time-relation of a
tone. In its harmonic thread we find the pitch- or
space-relation of a tone. Rhythm or balanced motion,
and tone or balanced sound, are thus inseparably
united. This union of two balances or harmonies
of time and space, which holds the secret of music's
original harmony, requires careful analysis. This
moment of union, the product of which is pure har-
monic tone, is an accentual moment. The principle
of harmonic genesis I have already named the eflScient
accent.

The subject of original harmony in one voice and
its common reports here introduced may now be more
fully illustrated by a few examples which contain
other tones, harmonic relations and harmonic per-
cepts which will be explained in the proper place. At
present it is enough to demonstrate that such things
as harmony in one voice and common reports really
exist. The first example adds four other tones, a
number of other harmonic relations and two other har-
monic percepts, the minor seventh and major ninth: —

C) 1315335 931^33137353 1

^■^^-^ Jf rr^^f^^r^^^

crtj''^" '' 'LdJ'Ciircrij''f

* The harmonic numbers indicate either root or relation to root. These
numbers are large for major and small for minor intervab. From Chap. III.
L. E. K.

RHYTHM AND TONE

The next example adds two chromatics : —
135 31^313^35513 5 1

m

I

The harmonies and harmonic relations reported in
these melodies assert themselves spontaneously; they
are immutable because common to all of us ; you can-
not change them unless you add other voices or chords;
but even though you add only one more voice, in so
doing you add something of your own choice and are
no longer dealing with harmony in one voice, which
chooses itself. In order to understand the sequel it
is imperative that this distinction between that which
elects itself and that which you and I elect should be
clearly apprehended. The common reports of self-
asserting harmonies and harmonic relations are spe-
cific to music in one voice, 1 have made observa-
tions for more than twenty years and have met no one
even of moderate musical endowment, whether child
or adult, whether student, musician or layman, who
did not readily appreciate a tone's inherent harmony
and therefore harmony in one voice. For the first
time in our science we find in these common reports
of harmony in one voice the explanation of the genesis
and development of tonality and of our tone-system.
In passing it may be stated that our tonality and our
tone-system are inseparably linked in evolution as
cause and consequence.

40 THE NATURE OF MUSIC

24. Harmonic Evolution, The Major Tonic

The evolution of music's harmonies beginning with
the genesis of the major consonance is a psychological
process as beautiful as it is simple. Harmonies have
succeeded each other one by one in an orderly and
clearly traceable sequence of antecedents and conse-
quents, perhaps the only complete sequence of any
kind thus far presenting itself to psychology and there-
fore of importance to that science. Apart from origi-
nal harmony in one voice and its inherent principles
this evolutionary sequence of harmonies could not be
traced. Why ? Because harmony in one voice asserts
itself and its reports are common reports and it ex-
cludes the personal equation. When we consider that
there is such an evolutionary sequence and that the
first series of harmonies in this sequence is repeated
nolens volens in every developing musical mind, we
readily realize the signal importance of this sequence
alike to the science and history of music and to music-
education. The harmonies of the individual tones in
the above melodies are latent in all of us, each tone
being a harmonic complex containing elementary
harmonics or concomitants. We have seen that an
isolated tone at first appears to be a single tone, that
later we discover it to be a complex of root, third and
fifth. This third and fifth were always present in the
tone as elementary harmonics or concomitants. A
tone without concomitants does not exist. This third
and fifth were therefore latent in feeling and eventu-
ally they were perceived and differentiated, whereupon
they were expressed in melody and together with

RHYTHM AND TONE 41

their common root became the harmonic basis of
tonality. We shall see that newly differentiated tones
in their turn generate new harmonic complexes con-
taining new elementary harmonics which in their turn
are differentiated and generate new harmonies with
new elementary harmonics, and so on. This psycho-
logical change from latent feeling to perception and
expression roughly describes this evolutionary process.
The tonality of the major consonance of an isolated
tone has already been identified as the Tonic of the
Major mode. Alike we all feel its purity, stability,
repose, perfect balance and unity; to all it is a centre
of gravity, restful and satisfying. We have explained
all this as due to its perfect harmonic form, this unique
form as due to the union of elements, this union as due
to the inherent shaping principle, equilibrium. How-
ever, the mere fact that an isolated tone is always a
major consonance and always the Major Tonic, though
so obvious, does not suflfice. It requires explanation.
Why does an isolated tone always report this conso-
nance ? To say that the shaping principle is the vera
causa is but a statement and does not answer this
question. It therefore remains to explain how this prin-
ciple operates, how it shapes these harmonies in feel-
ing. The above melodies present roots, thirds, fifths,
sevenths and ninths. Each tone arises in a thread
of harmony. On certain tones the harmony changes :
one tone now reports itself a root and now a fifth;
another tone reports itself now a third and now a
ninth; another tone reports itself now a seventh and
now a root. Analysis will show that all these harmonic
complexes, percepts and relations are due to the in-

42 THE NATURE OF MUSIC

fluence of rhythm as implied by the word now, A
tone being an accentual moment, a series of tones is
a series of accentual moments. We will study and
analyze these accentual moments. I have already
said that they hold the key to the harmonic form and
relation of tone, which is the secret of music. This
key is latent in all of us; all may discover it.

25. Rhythmic adence and Rhythm-Repose
The analysis of rhythmic periods of time is the sub-
ject before us. Each period is marked by an accent.
Some accents are heavier, some are lighter. Heavier
and lighter accents alternate in such a way that the
heavier accents recur regularly in time. These alter-
nating accents are alternating accentual moments.
Periods marked by heavier accents are called heavy
periods, those marked by lighter accents are called
light periods. Heavy periods marked by heavier
accents are moments of stability, repose, balance,
centres of gravity, moments of equilibrium. Light
periods marked by lighter accents are moments of
instability, unrest, unbalance; they are in relative
equilibrium, in cadence ; they impel us to move for-
ward to a heavy period for repose, balance. Rhythmi-
cally we are therefore in cadence on lighter accents, in
repose on heavier accents. This rhythmic movement
of regularly alternating cadence-moments and repose-
moments is illustrated below : —

P

"^^#

r

1—

--/

etc.

1.

Now

now.

now

now.

now

now,

etc.

2.
S.
4.

Light

Cadence

Unstable

heavy,
repose,
stable,

light
cadence
unstable

heavy,
repose,
stable,

light
cadence
unstable,

heavy,
repose,
stable,

etc.
etc.
etc.

RHYTHM AND TONE 43

The four texts in this example describe and analyze
our common feeling and perception of elemental dual
rhythm. The alternating accentual moments marked
now-now are explained by the terms light-heavy,
cadence-repose, unstable-stable equilibrium. Rhythm,
as I have previously stated, is the universal form of
expression, all form of expression being either process
or record of the rhythmic accentuation of energy
making for equilibrium. Hence we speak of the uni-
verse as one energy, one rhythm, one equilibrium.
It is common to speak of accented and unaccented
tones in music and syllables in poetry, but in truth
there are no unaccented tones or syllables. Every
movement of energy in the whole universe, be it ever
so slight and delicate, is an accent. Moreover, all
movements are in correlation, wherefore all accents are
relative and the term light-heavy expresses this rela-
tivity. We cannot therefore truly speak of one move-
ment or accent since movements and accents succeed
each other periodically and are inseparably related as
light-heavy. Regular alternations of light and heavy
accents appear in walk as well as in march, in run as
well as in dance, in speech as well as in song, in prose
as well as in poetry, in all work as well as in all play,
in all movements of body, mind and spirit. Observe,
for example, the nondescript sounds which we spon-
taneously utter in place of the affirmative yes and nega-
tive no. The order of relative accents in the former is
light-heavy; in the latter it is the reverse, heavy-light.
These relative accents are the same in our expression
of yes and no by a movement of the head. In
nodding yes the head moves slightly backward on a

44 THE NATURE OF MUSIC

light accent and is then brought forward on a heavy
accent. In no the head is jerked to one side on a
heavy accent and then moves back on a Hght accent.
Similar dual movements and successions of relative
accents appear in our spontaneous positive and nega-
tive gestures. Positive certainty, conviction and as-
sertion are expressed by raising the hand on a light
accent and bringing it down on a heavy accent. Un-
certainty, surprise and interrogation cause us to raise
the hands on a heavy accent, then to relax and drop
them on a light accent. Down-accents are heavy
accents of positive gravity.

This analysis shows that every rhythmic moment in
consciousness is either a repose-moment or a cadence-
moment. Rhythm-repose is perfect balance; rhythm-
cadence is relative balance tending to perfect balance.
This relation of cadence and repose is inseparable in
our feeling, percept and concept of rhythm. In other
words, there must be a play of light accent upon heavy
accent, else there is no feeling or perception of rhythm.
The play of one light accent upon a heavy accent is the
embryonic form of rhythm, and a motive consisting of
two such accents is the shortest conceivable motive in
music. This inseparable relation of cadence and re-
pose is an important fact as we shall presently see.
Of the two elements, rhythm and tone, rhythm is first,
universal and fundamental, while tone owes its speci-
fic musical form to rhythm. Cadence and repose first
appeared in rhythm, and their inseparable relation is
the basis of all rhythmic form and relation in music.
The study of this relation in tone is our next step in
analysis.

RHYTHM AND TONE 45

26. Tone-Cadence and Tone-Repose

Every tone in music is in cadence or in repose.
Tone-cadence originated in rhythm-cadence. Tone-
repose originated in rhythm-repose. Not only are
tone-cadence and tone-repose directly derived from
rhythm-cadence and rhythm-repose, but this relation
of cadence and repose is inseparable in tone as it is in
rhythm, it is the basis and explanation of the har-
monic form and relation of tone as it is that of rhyth-
mic form and relation. These truths assert themselves
overwhelmingly in our common feeling and percep-
tion of every measure of music; they report them-
selves moreover in every measure of music in one
voice, in which they first arose. The connection of the
two truths, first, that all tones are harmonic, second,
that all tones are either in cadence or in repose,
straightway leads us to the logical conclusions that
there is an original cadence-harmony as well as an
original repose-harmony, and that in their genesis these
two harmonies are inseparably related, that both
cadence-harmony and repose-harmony arose one in
relation to the other, in short, that they arose together.
This inseparable relation of cadence and repose is the
key to the mystery of harmonic form and relation of
tone called consonance and dissonance, the subjects
of the next chapter, in which the truth of these conclu-
sions will be subjected to the explanation and test of
common reports of common feeling and perception.

The major consonance of an isolated tone already
identified as the Tonic-harmony in Major is the origi-
nal repose-harmony, and its three components I name

46 THE NATURE OF MUSIC

repose-tones. Over and under these repose-tones and
in relation to them have arisen four other tones which
tend, some up, some down, into the three. These
four are components of the original cadence-harmony,
and I name them cadence-tones. Repose-tones had
their genesis on heavy rhythmic accents, cadence-
tones on light rhythmic accents. If it is true that
cadence-harmony and repose-harmony could not have
arisen except in inseparable relation one to the other,
how are we to explain the undeniable fact that the
repose-harmony not only came first and was first
voiced in melody, but came alone and unattended by
any other harmony! Granting the inseparability of
the relation of cadence and repose and the interde-
pendence of their respective harmonies, how is it pos-
sible to explain the origin of the repose-harmony
except it be the direct result of the resolution of a pre-
viously existing cadence-harmony. This is a subtle
point, and it strikes at the root of the problem to be
solved. Subsequent analysis will show that the gen-
esis of this unique major consonance or repose-har-
mony was due to the resolution of a latent feeling of
dissonance or cadence-harmony. The three original
repose-tones and four original cadence-tones, which
together represent the seven diatonics of the Major
mode, are the subjects of our next example: —

a) h) c)

13 5 3 5,9

i

9

-Z7-

-zr

G>-

Repose Group Cadence Group Resolution

RHYTHM AND TONE

47

The Major Tonic is the root of the original repose-
harmony. The Major Dominant is the root of the
original cadence-harmony. This Tonic-thread com-
prises root, third and fifth. The Dominant-thread
comprises root, third, fifth, seventh and ninth.
Though the root of the Dominant-thread is omitted
at b) and c) the four cadence-tones report this to
be their common root and harmony as the numbers
imply. The two subjoined melodies include both
groups of tones, and the accompanying numbers indi-
cate the common reports of original harmony in one
voice : —

a)

18 5 3,5 31

i

1

E

r r r r 'r r r T r r r V 7

h)

r

^359531 53513 1

i

I

^M=^

r

EZjT

These melodies, like those already presented, are but
provisional illustrations of harmony in one voice and
its common reports. We shall presently enter into
the minutest analysis of these self-reporting relations
in order to study and explain their inherent principles
and laws. Meanwhile we will note these salient
points: the formative influence of rhythm upon tone
and the indissolubleness of the two; the insepara-
bility of the relation of cadence and repose, the
universality of this relation, its appearance first in

48 THE NATURE OF MUSIC

rhythm, then through rhythm in tone; hence com-
posite tone-rhythm, melody, music. Neither cadence
nor repose can be felt, perceived or conceived except
in relation one to the other, not in rhythm, not in
tone. Except for this basic relation there would be,
could be, no harmonic form and relation of tone, no
melody, no music. Cadence seeks repose, that is,
seeks resolution in repose, equilibrium. This is illus-
trated in the second last example at c). But resolu-
tion is not a principle or cause, as some theorists
declare, nor is progression; ^ the shaping principle and
causa causarum is equilibrium. It may be stated in
passing that music's great multiplicity of harmonies,
modes and keys are derived from the two original har-
monic genera of tones, cadence-harmony and repose-
harmony.

27. Melody, Harmony and Rhythm

Terms if not carefully defined lead to inevitable con-
fusion. The progress of knowledge under the impulse
of new discoveries modifies old and attaches new mean-
ings to familiar terms. In the opening chapter I
pointed out the fallacy of the common teaching that
melody, harmony and rhythm are the three elements
of music and have since demonstrated that melody is
not an element in any sense but is the composite of
music's two elements, rhythm and harmony. The
meaning of the term melody thus undergoes a complete
and unavoidable change. In music itself melody and
harmony have never been separable or separated. In
view of this truth the time-honored separation of the

1 See The Septonaie, Chap. II. L. E. K.

RHYTHM AND TONE 49

two which still prevails as the direct result of false
theories can no longer be continued. Separate books
on melody and separate books on harmony will be
valueless and will not be written in the future. Such
phrases as ** the intimate connection between melody
and harmony" no longer have any sense. Never hav-
ing been separable or separated, melody and harmony
do not require connecting. Another conception of
melody, namely, a conventional form constructed
by rule and composed of certain specified groups of
phrases in a variety of ** geometrical patterns," also
requires modification, a modification clearly and elo-
quently trumpeted in the works of Liszt, Berlioz and
Wagner, of Schumann, Brahms and MacDowell.
Formalism in our classics has played not only an
important but an essential part in music's evolution
and masterpieces. But here we are concerned with
melody. Than its form, nothing could be at once more
free and more law-abiding yet less subject to any given
or conceivable code of rules. Melody is as free as
thought and imagination, and its forms are as limit-
less as are the forms of nature; it is the essence of
music. Anything from a succession of two tones
onward is a melody, a music-idea, and out of such
ideas do genius and craft evolve masterpieces of music-
art. It is jejune folly to say that melody is exhausted,
that new forms cannot be created.

The term harmony is universally used in the sense
of chord, and everywhere the study of harmony means
the study of chords. But the accepted meaning of
this term is completely changed by the discovery that
original harmony asserts itself in one voice without

50 THE NATURE OF MUSIC

chords that original harmony in one voice and chord-
harmony in several voices require the most careful
distinction, that the former is the evolutionary fore-
runner of the latter and that the latter is rooted in and
explained by the former. Harmony and chord there-
fore can no longer be regarded as synonymous terms.
The identification of music's harmony and shaping
principle with universal harmony and the universal
shaping principle adds new, truer and deeper mean-
ing to this term.

The new meaning and importance attached to the
term rhythm in preceding definitions and analyses can-
not be overemphasized. After all it is not so long ago
that G. Weber told us that "rhythm is of no conse-
quence." Now we discover that rhythm is at the
bottom of everything in music, that the relation of
cadence and repose had it not first existed in rhythm
could not have appeared in tone, that cadence and
repose are two interdependent and inseparable ele-
ments at the foundation of rhythmic and harmonic
relation, that rhythm-cadence and rhythm-repose at
once explain the origins and solve the problems of
form and relation, of dissonance and consonance.
Therefore everything in music is relation and has been
derived through relation. From light to heavy accent,
from cadence to repose, from unstable to stable equi-
librium, such are rhythmic form and relation, such
through rhythm have arisen harmonic form and rela-
tion.

Elsewhere I have defined music as follows : Melody,
the flower; harmony, the plant that bears the flower;
rhythm, the root of the plant that bears the flower.

RHYTHM AND TONE 51

Although this legendary definition omits the seed,
tone or balanced sound; the nursery, common feeling;
the potential life, energy; the inherent shaping prin-
ciple, equilibrium; and although this definition is not
in complete accord with the facts presented in the fore-
going pages, yet it has a psychological value inasmuch
as it indicates the true sequence of observation which
is always the inverse of the evolutionary sequence.
To explain: Observation always proceeds from what
is most apparent to what is less and less apparent.
This inverse sequence has been followed by music-
observers. Melody, the flower, was observed first,
was the first subject of music-theory. Next, but
yesterday, came the observation and theory of har-
mony, the plant, in the form, however, of chords.
Then last of all came rhythm, the root. In fact, the
scientific inquiry by musicians into rhythm is so recent
that we can truly say it has just begun.* Thus far
this subject has been in the hands of those who
may be called separatists who separate the insepa-
rable, namely, music's rhythm, harmony and melody.
Melody without harmony, a tone without harmony,
are unfeelable, unperceivable, do not exist. The
moment of tone-genesis being a rhythmic moment it
follows that rhythm, harmony and melody have never
been separable in feeling. Because this inseparability
was not perceived, rhythm, harmony and melody
were separated in theory, but not in practice. To-
day they are united in common feeling, and it is safe
to postulate that they always have been united. We
judge of what has been by what is. The music of
to-day is connected with the music of all the past in

52 THE NATURE OF MUSIC

a sequence of effects and causes, each cause being the
effect of a previous cause. I have proved, and will
adduce further proof, that melody is the composite of
rhythm and harmony. This is nothing new to music-
feeling where melody always has been a composite,
but it is new to theory and, owing to its discovery of
harmony in one voice, completely changes the point of
view of theory.

Knowledge is evolution of perception. Truth per-
sistently knocks at the door of consciousness, sure of
being admitted sooner or later to enrich the store of
knowledge and experience.

CHAPTER III

ORIGINAL DISSONANCE AND CONSONANCE IN ONE VOICE

28. Genesis of the Major Consonance^ Music's
First Regnant Harmony

The fundamental forms of tone are dissonance and
consonance. Both are products of feeling, both first
arose in one voice, both are offsprings of the elemen-
tal relation of rhythm-cadence and rhythm-repose.
Briefly, /orm is derived from relation^ the forms of dis-
sonance and consonance from the rhythmic relation
of cadence and repose. This truth lifts the veil of
mystery which has hitherto hidden from view the true
nature and origin of dissonance and consonance.
What man did not feel he could not, it is safe to say,
did not express, and music from first to last is a crea-
tion and expression, of music-feeling. Man's first ex-
pression of tone was admittedly in song. We will
study these first utterances.

The first attempts to pitch a tone comprise two
moments of time: first, a sliding; second, an arriving.-
These two moments, previously described as now-
noWy light-heavy, cadence-repose, unstable-stable, are
two correlated and interdependent rhythmic accents
which are inseparable in feeling, perception and con-
ception. Of the two, the first is tend^ the second is
end; the first resolves into the second, the second is
attainable only through the first, since apart from the
feeling of tend there is no feeling of end. Below I

54 THE NATURE OF MUSIC

indicate cadence or tend by a wave-line which resolves
into repose or end as shown by a straight line : —

-Bepose
Cadence

The first or sliding moment in pitching a tone is
cadence, unstable equilibrium, relative harmony, tend ;
in it the entire cadence-thread of harmony is potentially
present. The second or arriving moment is repose,
stable equilibrium, perfect harmony, end; in it the
entire repose-thread of harmony is potentially present.

Feeling thus resolves wavering into unwavering
pitch, unstable into stable equilibrium, relative har-
mony into perfect harmony, apparent chaos into per-
fect order and unity, a light accent into a heavy accent,
cadence into repose, aspiration into attainment, tend
into end, latent feeling of dissonance into consonance.

This heavy accent of rhythm I have already named
the efficient accent of tone-genesis, that is, of the genesis
of harmony. This end of tend was the genesis of
music's first tone, the birth of music itself, of melody.
This first tone was not only the first harmony, but was
the first regnant harmony generated by the efficient
accent. This first harmony is the genus consonance,
our Major Tonic-harmony.

The power to place a tone in the voice and to express
exact pitch was acquired through the evolutionary
process of resolution above described. In the first
crude attempts at pitch the entire process of sliding
and arriving is intoned. But when the power to ex-

DISSONANCE AND CONSONANCE 55

press exact pitch has been acquired the first or sliding
part of the process is carried out silently. Though
when trained we place tones automatically, neverthe-
less the voice has to be adjusted to each tone, infinitesi-
mally short though this moment of adjustment may be.
The process of resolution just analyzed explains
why when we pitch an isolated tone we invariably
make for the eflScient accent and generate in feeling
the repose-thread of the original major consonance,
our Major Tonic-harmony, music's first regnant har-
mony, as follows: —

o) b) e)

1351 1351 1351

i

i^i' . >> - [*^i^^

w

The origin of this genus consonance is now ex-
plained. How and why this gr^ni^^-harmony came
first is now explained. Its genesis is due to the reso-
lution of the latent Reeling of dissonance (relative har-
mony) into the major consonance (perfect harmony).
The operative cause is the efficient accent which on
the line of least resistance makes for complete equi-
librium. Briefly, the efficient accent is the cause of
resolution. Man first felt and expressed the relation of
cadence and repose rhythmically, but when he joined
sound to this rhythmic relation he eventually evolved
the feeling and expression of tone-cadence and tone-
repose. Tone-cadence is dissonance, it first arose in
one voice. Tone-repose is consonance, it first arose
in one voice. How music's original dissonance arose
in relation to music's original consonance will be
considered presently. Meanwhile, it may be observed

56 THE NATURE OF MUSIC

that music springs from one source, not from two
sources. At the basis of music there is unity, not a
duahty as many think and teach. Music started with
one harmony, the Major Tonic-harmony, and all sub-
sequent harmonies are traceable through a chain of
relations back to the first. Major and Minor are two
modes, but Major preceded Minor and Minor was
derived from Major. Major and Minor are therefore
not two tonalities, they are two modes of one tonality,
hence the unity of tonality. Tonality is the sum of
tone-relations, and music began the development of
tonality with the regnant Tonic-harmony of the Major
mode. Again: rhythm and harmony are two ele-
ments, but in tone, in melody, in music, the two are
indivisible, one, hence unity. If there be any duality
it should be cadence and repose. But is this duality ?
No. Cadence and repose are the two inseparable
and interdependent elements of the unity relation.

The simplest songs of birds, the simplest specimens
of primitive human music, the improvised songs and
intoned calls of children, the intoned cries of street-
venders, all these songs, calls and cries are based upon
the genus consonance, our Major Tonic-harmony.
Since in evolution birds antedate man, we may assume
that the birds were the first singers, concert-givers and
music-teachers. Japan, for example, has few or no
singing birds, therefore no feathered music-teachers.
Perhaps this explains why Japan is a nation without
song. From a collection of bird-songs observed by
me and accurately written both as to rhythm and
harmony, a few are here selected and arranged in
three groups which exemplify three stages of develop-

DISSONANCE AND CONSONANCE

57

ment from simple to more and more complex. The
first group marks an early stage in which only the
tones of the Major Tonic-harmony appear.
1. 2. 3.

53535161 5

8.

1 5 3 3 5 1

3 5

^

■>{ f f I ^r^j

^s

m

ipzz^c

-• — • — 0-

9.

11111

^^^^^^

The next group adds two cadence-tones, marked x,
to the regnant Tonic-harmony.
1. 2.

151535 1 51513535

^tf-!\' i\sr^:iv:\' rj'iH

i

35 353 535

^

I

The appearance of the above cadence-tones marks
a more advanced stage of development. A much

58

THE NATURE OF MUSIC

higher stage is exemplified in the next group of songs
which introduce two additional regnant harmonies,
namely, the Dominant-harmony (marked V) and the
Subdominant-harmony (marked IV), both of which
arise in relation to the Tonic-harmony (marked I).

2.
5 5 5

3.

551 35555

i

i

I^P^S

ga

V V

r r if r r ^^

6.

i

1 5

^

£:

3

^

6.

3 13 13 5

i^

i

^

IV I

In these few bird-songs the harmonic basis of music
is plainly revealed, and the subject of tone-relations is
fully opened up. The harmonic numbers symbolize
the common reports of inherent relations. The har-
monic analysis of the cadence-tones and cadence-
harmonies and the connection of the successive stages

DISSONANCE AND CONSONANCE

59

of development here suggested will engage our atten-
tion later on. Also for future reference I here add
three more bird-songs, the first two of which report
the Minor consonance and mode, while the last intro-
duces a chromatic marked by a star.
1. 2.

i^^

m

s

^ — i^ — ^

±

ms-^if t I'f n

I * V

In their first efforts to discriminate the concomitant
harmonics of an isolated tone, students most frequently
feel and express the octave first, next the fifth, last of
all the third, as follows : —

1115 13orll5 31

I

I

k±

The psychological law here operative is this. The
closer the proximity of tones the more difficult is it to
perceive, differentiate and express them. By impli-
cation the larger intervals were expressed first, the
smallest last. Thus octaves, fifths and fourths, thirds
and sixths came before the whole step, and last of all
came the half step. All the first-named intervals are
present in the Major Tonic-thread of harmony and
appear in the first group of the above bird-songs. The
cadence-tones in the second and third groups of these

60 THE NATURE OF MUSIC

songs exemplify the introduction of the whole step and
half step. The evolutionary sequence of regnant har-
monies begins with the Major Tonic. The evolu-
tionary sequence of intervals begins with the intervals
formed by the tones of this first regnant harmony.
The Major Tonic-harmony is the only harmony which
has entered into consciousness hy way of its root.
We shall see that the Dominant-harmony was intro-
duced by its fifthy the Subdominant-harmony by its
third.

While we may affirm with certitude that the Major
Tonic-harmony was the first of all harmonies, we can-
not tell what was its exact pitch or key, simply because
we do not know. However, the terms Major and
Tonic imply mode, relation, tonality and also relative
pitch but not fixed pitch, since this Major Tonic arises
on any isolated tone of any pitch. Like the birds we
sing melodies and correctly express their inherent har-
monic relations or tonality, completely unconscious the
while of fixed pitch or key, although we are expressing
key-relations. Fixed pitch is indicated when we say
C Major, D Major, E Major, and so on, by which we
mean that the Major Tonic is pitched or keyed on
C, D, E, wherefore the notes C, D, E are called key-
notes and wherefore the terms keynote and Tonic are
used interchangeably. Because the feeling of the
harmonic relations we call tonality are common to all
of us, because they underlie all music of bird and man,
because they would exist even though systems of fixed
pitch and notation had never been invented and
adopted, because they are the essential thing to appre-
ciate and know, because our complex system of nota-

DISSONANCE AND CONSONANCE 61

tion so completely conceals the unity and simplicity
of harmonic tonality, for these and other reasons un-
necessary to mention, nothing could bring us closer to
these innate relations, or prove a greater desideratum
and simplification than a set of symbols which dis-
regards any fixed pitch and which is uniformly the
same in every key. The syllables do, re, mi, etc., sup-
ported by the harmonic numbers adduced from ori-
ginal harmony in one voice fully meet the case.
Music's first harmony and germs consonance, our
Major Tonic-harmony, is now presented thus : —

13 5

do mi sol

We may say with certitude that do was the first
Tonic and root, that mi was the first major third and
that sol was the first pure fifth. These are the only
three tones and harmonic percepts in our first group
of bird-songs. In the second group of songs note the
first cadence-tones, re and la, the former as fifth intro-
ducing the Dominant-harmony, the latter as third
introducing the Subdominant-harmony. But we are
advancing too fast and will next consider the origin of
the genus dissonance.

29. Genesis of Cadence-Harmony or Original
Dissonance in One Voice

We say that a leading-tone tends up, a seventh tends
down. Tend is cadence; its objector end is repose.
No chord is required to generate and illustrate this re-

62 THE NATURE OF MUSIC

lation, since it reports itself in one voice as exemplified
below : —

3 1 5^ f^S .T^ 9^

ti— -do re— —do re -—"mi fa"**- mi la«i«^sol

^ — — =^=^^ .^^-4J

F

r

-r t-~r ^"^ f^

Cadence connotes cadence-harmony, dissonance,
incompleteness, hence the tend to repose in the above
cadence-tones i% re, /a, la. Repose connotes repose-
harmony, consonance, completeness, hence no tend
but an end as reported by the above repose-tones do,
mi, sol. Our example presents no chords, but it does
present harmonies, since each tone arises in the mind
together with concomitant harmonics and is therefore
a harmony. Thus a cadence-tone reports one har-
mony, a repose-tone reports another harmony, and
the resolution of one tone into another is the resolution
of one harmony into another. Were it not for the
inherent harmony of tone there would be neither the
feeling of cadence nor the feeling of repose, no form
and relation of tone in the musical sense. Because of
this harmonic form and relation inseparable in tone we
all share in the common feeling of the above cadences,
of harmony and harmonic relation, of dissonance and
consonance in one voice.

Our example introduces four cadence-tones ti, re,
fa, la in addition to the three repose-tones do, mi, sol.
These four cadence-tones are components of the genus
dissonance; they lie directly over and under the three
repose-tones of the genus consonance in relation to

DISSONANCE AND CONSONANCE 63

which they first arose. In correlation the repose-tones
of the genus consonance report do as common root or
root of this genus. In correlation the cadence-tones
report sol to be their common root and the root of the
genus dissonance. Examples follow: —

1

do

5

sol

3

mi

1 9

do la
1

7

fa

5

re

3

ti

1
sol

1.

Genus Consonance.

19-

Root

2.

Genus Dissonance.

Root

The genus-rooi do is the Major Tonic. The genus-
root sol is the Major Dominant. Tones are ninths or
sevenths or fifths or thirds or roots of harmonic threads,
and the number over each indicates a root or relation
to root. Sol first arose as fifth in the genus conso-
nance, thereafter asserted itself as root of the genus
dissonance. Sol is therefore the first nexus, common
tone or bond-tone of two harmonies, since it connects
the two genera, dissonance and consonance, as shown
below: —

9^53 fl 6] 3 1

la fa re ti sol sol mi do

^^m

ij

Bond-tone
Dissonance Consonance

The origin in rhythm of the inseparable relation of
cadence and repose, the consequent genesis of the

64 THE NATURE OF MUSIC

latent feeling of dissonance and consonance, and the
genesis of consonance through the resolution of this
latently felt dissonance, these important points were
explained in the foregoing section. One by one these
latent cadence-tones of dissonance were perceived,
differentiated and expressed. First of these to appear
in melody were the whole steps re in relation to do and
rriiy la in relation to soL Much later came the half
steps ti in relation to do, Ja in relation to mi. In our
example of cadences re tends down to do and up to mz,
la tends down to sol, fa tends down to mi, ti tends up to
do. For practical and theoretical reasons too obvious
to require mention I name ti the upleader,fa the down-
leader.

The evolutionary sequence of cadence-tones in this
order, namely, re, la, fa, ti, is supported by history in its
records of primitive scales and melodies. As evidence
witness the so-called great scale, small scale and the
pentatonic scale in which the great and small scales
are united. In these scales there are no half steps,
since fa and ti do not appear. All are given and
analyzed below: —

1. Great. 2. Small. 3, Pentatonic.

153 5315 3 5 3^-)<>

do re mi sol la do re mi sol la

i

i

r r c I — I r f r I —

The harmonic numbers indicate the common re-
ports of original harmony verified by common percep-
tion. The Major Tonic-harmony is regnant, the

DISSONANCE AND CONSONANCE 65

tones re and la cadence up and down into do-mi-sol,
the regnant harmony. Ascend or descend on this
pentatonic scale in every conceivable rhythm, yet the
harmonic relations remain unchanged. However, the ^
analysis of a scale has little purpose, for a scale is but a
record of tones in use during a certain period of his-
tory; briefly, scales are so many tone-systems of his-
tory. What is of essential importance is the analysis
of the melodies which are responsible for these tone-
systems the progressive development of which has
resulted in our present complex system. Thus far we
have accounted for and exemplified but one regnant
harmony, the Major Tonic. How a second and a
third regnant harmony were generated are subjects
presently to be considered. Here an important fact^
to which we shall revert later on may be mentioned. I
It is this : During the regnancy of the Major Tonic- I
harmony la always reports itself as third of /a, while I
the remaining tones of the germs dissonance during |
this regnancy of the Tonic always report themselves
in their ^^Tii^^-relations, ti as third, re as fifth, fa as
seventh of sol, the Dominant. La reports itself as
ninth only during the regnancy of the Dominant-
harmony, which is the genus dissonance. The tone la,
as we shall see, plays a leading and significant part in
the development of harmony and tonality.

The above explanations of the genesis of the four
cadence-tones and the order of sequence in which
they arose are further supported by deduction and by
induction ; by deduction from the principles of causa-
tion and harmonic genesis set forth in these pages,
by induction through data derived from exact analysis

66 THE NATURE OF MUSIC

of bird-music, primitive music, music-feeling and
progressive mental development in music. I say
exact analysis advisedly, since in the past no basis for
exact analysis of primitive music and common music-
feeling has been discovered. For the first time in the
history of music-science such a basis presents itself
in original harmony in one voice. The principles,
causes and conclusions thus far presented and exem-
plified are directly due to the discovery of original har-
mony in one voice, and its incontrovertible evidence in
the common reports of common feeling and percep-
tion. Thus original harmony and its common reports
place all observers and analysts on common ground,
a common basis from which to make observations and
draw conclusions from such observations, a point of
view at once new and common. Dissonance and
consonance, the most fundamental and perplexing,
therefore the foremost problem of music-science, have
remained a mystery, an unsolved problem, and now
find a simple solution through original harmony and
its common reports. Some musicians may object as
follows: Everybody knows that dissonance and con-
sonance did arise and are at the foundation of music,
that the cadence-tones not only did appear over and
under the three tones of the Tonic chord, but arose
in relation to this Tonic-triad and came to stay. The
facts are self-evident. Why not stop here and be satis-
fied ? It is otherwise with the scientific observer who
seeks causes; he cannot stop and has no rest until he
finds the causes that explain how forms and relations
came to be what they are. Our story of genesis is
simply this. In obedience to inherent principles

DISSONANCE AND CONSONANCE 67

rhythm and tone met, merged and became one, then
rhythm-cadence and rhythm-repose became tone-
cadence (dissonance) and tone-repose (consonance),
and forever after there was music.

The foregoing analyses and examples conclusively
prove, first, that original harmony is harmony in ane
voice, that tones are heard, felt and expressed in ca-
dence or repose as roots or thirds or fifths or sevenths
or ninths, that tone and tone-relation connote har-
mony and harmonic relation, that harmonic form and
harmonic relation in one voice are self-asserted, fixed
and immutable, and by implication that the reports
of original harmony are common reports ; second, that
dissonance like consonance had its genesis in one
voice, that the genus dissonance and the genus con-
sonance are respectively the harmonies of the Major
Dominant and Major Tonic, and by implication that
tonality is fundamentally and wholly a question of
harmony, and that original harmony in one voice is
its basis; third, that the Major Tonic was the first
regnant harmony, and this implies the priority of
Major tonality ; fourth, that melody instead of being
an element, as generally supposed, turns out to be a
composite of rhythm and harmony, and by implica-
tion that melody is the original vehicle of dissonance,
consonance and tonality, in short, of music per se ;
in fine, that dissonance is neither more nor less a har-
mony than consonance, the former being unstable and
relative equilibrium, the latter, stable and perfect
equilibrium. ^

68 THE NATURE OF MUSIC

30. Distinction between Original Harmony in
One Voice and Chord-Harmony

Music-history everywhere identifies the beginning
of harmony with the first use of chords. Every
treatise on harmony is a treatise on chords. The
concurrence of at least two tones, therefore a chord, is
everywhere considered indispensable to the percep-
tion, conception and presentation of a consonance and
a dissonance. Everywhere the study of harmony and
harmonic analysis means the study of chords and
chord-analysis, and no other basis having been dis-
covered, the chord is everywhere regarded as the basis
of harmony. These facts plainly show that the con-
ception of harmony as chord is universal. The rea-
sons for my dissent from this common view are rooted
in the following facts and conclusions. The chord is
Si form of harmony, but is not the original form, there-
fore the chord is not the basis of harmony. The
original form is the basis, it is dissonance (cadence)
and consonance (repose) in one voice. The concur-
rence of two or more tones, that is, a chord, is not
requisite to hearing, feeling, perceiving, conceiving
and presenting a dissonance and a consonance. A
single tone suflices for all this since, as has been
demonstrated, each of a series of single tones is a dis-
sonance or a consonance. Harmony is a discovery,
not a "modern invention" as Spencer declares.
Original harmony in one voice, old as music itself
and belonging to all time, is the spontaneous product
of feeling; it antedates chord-harmony and belongs
to the historic and prehistoric periods of homophony.

DISSONANCE AND CONSONANCE 69

Chord-harmony, on the other hand, is a compara-
tively recent product, a product of reflection and
theory, and its roots reach deep down into original
harmony from which it is a psychological evolution.
Though their connection has so long remained con-
cealed, it is safe to infer that the two, original harmony
and chord-harmony, have never been separated in
feeling, and that the feeling of the former has ever
directed and guided the course of development of the
latter. The feeling of original harmony in one voice,
being the universal and basic harmonic sense, may be
designated as the common harmonic sense. The truth
of this is demonstrated and proved by the common
reports of common feeling and perception.

The common view of the chord as the only form and
as the basis of harmony has not alone created much
confusion in the theories of music, but its general ac-
ceptation as an ultimatum has acted as a check upon
scientific research. The questions What is music ? and
What is common music-feeling ? so often set aside as
insoluble mysteries, are not separable since the answer
to the first lies hidden in and awaits the answer to the
second. But these primary questions could not be
answered until the solution of the basic problem of
consonance and dissonance had been discovered and
a theory of music based on this solution had been ex-
pounded. The curious, among whom I count myself
as most curious, may well ask why so simple a solu-
tion of the problem as that of cadence and repose in one
voice has so long remained concealed. This oversight
may be assigned to two principal causes and fallacies
already suggested: first, to the chord-basis of har-

70 THE NATURE OF MUSIC

mony; second, to the persistent and futile attempts to
base the theory of music on physical acoustics. There
are three evolutionary chapters of harmony which may
be provisionally indicated here.

1. Homophonic Harmony. This is original har-
mony in one voice, which is the inherent harmony of
single melodies. By single melodies I mean all music
in one voice. This chapter represents the primary
age of music.

2. Polyphonic Harmony. This is the inherent
harmony of combined melodies, that is, of two, three
or more coincident melodies. This chapter may also
be called contrapuntal harmony and constitutes
music's middle age.

3. Chord-harmony. This, the only form thus far
recognized, is the supporting and accompanying har-
mony of single and combined melodies. This chapter
represents music's modern age.

These three chapters and corresponding ages over-
lap; they mark a psychological advance from simple
to complex and from the indefinite to the definite ; they
correspond to the three psychological stages of music's
childhood, adolescence and maturity. The golden
thread by which all these forms of harmony are con-
nected in evolution has preserved only what was favor-
able and useful, so that in modern music all three are
employed in composition. The distinction here under
consideration may now be carried a step farther.

Original harmony (one voice always understood) is
natural harmony by natural selection. Chord-har-
mony is personal harmony by personal selection. The
forms of original harmony select, assert and present

DISSONANCE AND CONSONANCE 71

themselves ; in any single melody they are identical in
all of us, they are completely free from personal selec-
tion and therefore from the personal equation. Con-
cisely stated, personal selection cannot enter into
original harmony, in which the forms are uniformly
the same. In chord-harmony, on the other hand, we
are compelled to make a personal selection not only of
this or that series of specific constituent chords, but also
of the number of voices to be employed. Briefly, a
melody may be chorded in many ways while the origi-
nal harmony of a melody is uniformly the same. Thus
it is clear that the forms of original harmony are im-
mutable since they cannot be changed except by add-
ing other voices or chords. But the moment we do
this, two things happen simultaneously : first, the har-
mony is no longer in one voice; second, personal
selection usurps the place of natural selection in that
we add our own thought, and thus transform some-
thing that was universal into something that is per-
sonal. Hence the distinctions between natural and
personal harmony, between natural and personal
selection. The examples shown on page 72 illustrate
these distinctions and will suggest others.

The common and immutable forms at a) are due to
natural selection, while the forms in all the subsequent
examples are due to personal selection. Concisely
stated, everything in more than one voice is personal.
The harmonic numbers in examples 6), c), d) and
e) agree with those in example a), w^hereby it is shown
that the chord-forms of personal selection may repro-
duce and elaborate the original forms of natural selec-
tion in a variety of ways. Original harmony is there-

72

THE NATURE OF MUSIC

fore not only the basis of chord-harmony, but the
inseparable bond between the two is that of feeling and
thought, of the simple and more complex, of lower and
higher forms corresponding to lower and higher evo-

a)

h)

^^^m^^^

e)

d)

$

^— ^-i

^==4

s

rr^m=^

T

0)

3 5 13 1 3

9)

13 13

^m

4^

i^

f

^

rf=f

f=f

^>~i-t-t-f-

T=P=

F¥^

^

^

r

r

lutionary states of mind. Not alone may original
forms be reproduced in chord-forms, but as seen in
examples /), g) and Z^),^ a single melody may imply a
great variety of other chord-forms, and these examples
exhibit a more advanced state of personal selection
than those which precede.

^ Ex. h) could not be deciphered. L. E. K.

DISSONANCE AND CONSONANCE 73

The eye and ear are concerned in the following dis-
tinction. In a written series of single notes, as in
example a), you can see the notes, but you cannot see
the harmonies, because single notes present no visual
images of harmonic forms. Therefore in one voice
you are compelled to hear. With chords it is different.
In a series of written chords you not only see the notes,
but you can also see the chords, because each chord
presents a distinct visual image easily remembered.
This explains why in the study of chords or harmony,
as it is called, students so readily fall into the perni-
cious habit of guidance by sight in place of guidance
by hearing. It explains why most students recognize a
chord when they see it, while so few recognize a chord
when they hear it; why most students do their work
at the piano and cannot hear what they have written
unless they play it, while so few hear before they write
and hear what they write as they write. In original
harmony the forms are invisible; in chord-harmony
they are visible. In the former the exercise of har-
monic feeling, perception and conception is unavoid-
able and a necessity from the start; in the latter this
exercise is interfered with, and in most cases is ex-
cluded by the insidious visual habit just described, and
the necessity for this exercise is constantly urged upon
students. In the former you cannot move one step
without hearing; in the latter, owing to the visual
habit, it is possible to work through an entire treatise
without hearing. First the idea, then the sign; first
hear, then write ; this subordination of symbol to idea,
of sight to hearing, should be a matter of course.

Original harmony and chord-harmony are con-

74 THE NATURE OF MUSIC

trasted in the next examples for a special purpose.
In a) we hear Weber, in b) we hear Wagner.

In common parlance we would say that these two
examples present one and the same melody, and that
b) is a harmonization of a). This is not true. It
would be true were melody an element; it is not true,
because melody is a composite of two elements,
rhythm and harmony. The two melodies look alike
but how unlike they sound. Are we to believe the
eye or the ear ? The harmonic numbers indicate the
ear's testimony. Compare these numbers in the two
examples. Melodies are thoughts. As melodies and
thoughts, a) and b) are distinct; both are equally
individual and natural. It is true that a given single
melody as at a) suggests a variety of different har-
monizations, but let us remember that it is also true
that every such harmonization results in the trans-
formation of one distinct and individual melody and
thought into another distinct and individual melody
and thought, no two of which can possibly be the same.
In a separate chapter I will present the potential har-
monies of a tone, which subject includes that of the
potential harmonies of a melody. Here it is enough
to have pointed out the germinal, essential and indi-
vidual force and character of melody as thought both
spontaneous and constructive. When a composer

DISSONANCE AND CONSONANCE 75

presents one or more phrases or sentences in the form
of one voice, he employs this form of thought for purely
artistic and aesthetic reasons, the selection of the
specific form of thought whether in one or more
voices always being personal. Not so with the har-
mony. While the composer's selection of one voice
is always personal, the inherent harmony of this one
voice is never personal; it is always original, univer-
sal, immutable harmony. This distinction between
one-voice and multi-voice harmony will appear in
other connections in subsequent sections.

31. The Seven Original Tones, Analysis

The seven original tones are the components of the
two harmonic genera^ consonance and dissonance.
Three of the seven are derived from the former, four
from the latter. These seven tones are the seven dia-
tonics of the Major mode. Their minute analysis
being our immediate concern, they are again pre-
sented.

13 5.^-^135, 9

sol — ti — re — fa — la

do — mi — sol

Tonic or Do Dominant or Sol

A harmony is named by its root, hence the harmony
of the Tonic or Do, the harmony of the Dominant or
Sol. The harmonic numbers indicate either root or
relation to root. These numbers are large for major
and small for minor intervals. This rule for marking
major and minor intervals will henceforth be strictly
adhered to. Our example contains but one minor
interval, namely, /a, which is the minor seventh of

76 THE NATURE OF MUSIC

its root. The above tones may be read as follows:
Tonic-root, third, fifth; Dominant-root, third, fifth,
seventh and ninth.

Every tone is a distinct harmonic percept and con-
cept. A harmonic percept is our perception of the
common report of a tone as root or third or fifth or
seventh or ninth. A harmonic concept is our thought
or conception of a tone in any one of these relations.
Concepts are rooted in and spring from percepts just
as percepts are rooted in and spring from feeling.
Harmonic feeling is never wrong, but harmonic per-
cepts may be wrong and cause wrong concepts. True
knowledge is true perception of relations. False per-
ception and consequent false conception is the danger
to be averted. This danger is averted in the present
study by the common reports of common feeling and
perception. Since concepts are based on percepts,
since the former are true if the latter are true, we will
for the present fix our attention upon the latter.

The seven original tones present eight distinct har-
monic relations, each of which is a harmonic percept,
as follows : do is root, mi is major third, sol is pure fifth,
of the Tonic (harmony understood); sol is root, ti is
major third, re is pure fifth, fa is minor seventh, la is
major ninth, of the Dominant. Of these tones sol,
the bond tone of the two harmonies, appears twice:
first as fifth, then as root.

Some of these harmonic percepts are original,
others are duplicates. A harmonic percept is original
when it is the first of its kind: such are do, the first
root; mi, the first major third; sol, the first pure fifth;
fa, the first minor seventh; la, the first major ninth.

DISSONANCE AND CONSONANCE

77

A harmonic percept is a duplicate when an original
percept is repeated on another tone: such are sol as
root, ti as major third, re as pure fifth. This shows
that the seven tones and eight harmonic relations of
the two harmonic genera, consonance and dissonance,
have introduced ^7;^ original harmonic percepts into
music. These five are now presented each with the
tone that first produced it.

13 5 7 9

do — mi — sol — fa — la \

Three of these spring from the original consonance
(Major Tonic), two from the original dissonance
(Major Dominant). The expansion of harmony and
tonaHty is due to the repetition of these harmonies and
percepts on other tones, a subject to be treated in the
chapter on potential harmony. The exact analysis
of the above harmonic percepts now confronts us.
These five percepts and the seven original tones are
all included in the following simple folksong which we
will analyze: —

5 3

3 5 5 3

5 9

i:

S

m

i==F^

S

mi re re mi fa
Dominant

mi fa sol mi
Tonic

re la

5 3^5333 553

3 3

I

k±=£i

^ — wl-^

sol mi fa sol mi mi mi re re mi fa
Tonic Dominant

-^ -^ -i&-
ti ti do

Tonic

78 THE NATURE OF MUSIC

The reader with a trained ear will not stumble or
hesitate over the numbers which mark the harmonic
relation of each of the above tones; without pause or
effort he at once recognizes E as mi and major third
of Tonic, F as /a and minor seventh of Dominant, G
as sol and pure fifth of Tonic, and so on. Through
practice he has developed and transmuted common
harmonic feeling into common harmonic perception,
that is, true feeling of harmonic relations into true
perception of harmonic relations, something that he
once only felt into something that he now positively
knows. The result is that he recognizes these rela-
tions automatically ; he not only perceives them in the
concrete as in the above melody, but he can think of
them in the abstract since in his mind they have taken
shape as ideas and concepts.

On the other hand, the reader whose ear is not
trained has all this to learn. He may well ask : How
am I to know that the first tone in this melody is a
major third, that the second is a minor seventh, and
so on ? This analysis will at once answer this ques-
tion and explain harmonic relations in one voice. In
the succeeding questions and answers we will start
at the bottom.

What proof is there that I share in common music-
feeling, in a word, that I am musical ? It lies in the
fact that you take pleasure in music, which in the
absence of music-feeling would not be the case.

What proof is there that my feeling of tone-relation
is true ? It lies in the fact that you are able to follow
and express (sing or hum) a melody since each tone
in a melody simultaneously reports a definite relation

DISSONANCE AND CONSONANCE 79

in time (rhythm) and a definite relation in space (har-
mony) and this double report is the same in all of us.
That you feel this double report, although you may not
know what it is, is proved by your ability to follow and
express a melody. Feeling of melody is feeling of
united rhythm and harmony, melody being the com-
posite of elements and the original vehicle of music.

What proof is there that each single tone in a melody
is a harmony ? It lies in the fact that each tone arises
in the mind together with elementary tones called con-
comitants. This complex of a tone and its concomi-
tants I have already named the harmonic thread of a
tone. The harmonic thread of a tone is the specific
harmonic form of a tone.

What causes the genesis in feeling of the specific
harmonic thread or form of a tone ? The proximate
cause is the relation of that tone. This form-gener-
ating relation inheres in and is reported by melody in
each of its tones and, as we have seen, this relation is
at once relation in time (rhythm) and relation in space
(harmony). Since this relation is asserted in melody
it follows that if you feel the melody then do you feel
the relation and, by implication, the harmonic thread
or form of each tone in the melody. Your feeling of
the harmonic thread of each tone in the above folk-
song is true.

What course am I to follow in order to learn to
recognize and analyze these harmonic threads and so
transmute what I feel into true perception and know-
ledge.^ Sing the first phrase of the above folksong
over and over again for the purpose of making sure
that you retain the feeling of the relation of the first

80 THE NATURE OF MUSIC

tone to the other tones of the phrase. To retain the
feeling of the relation is equivalent to retaining the
feeling of the harmonic thread of their first tone, mi.
Having made sure of this feeling, sing mi and on the
line of least resistance, drop on the thread of har-
mony from one component to another until you reach
a tone which reports a stopping-point, a point of com-
plete repose, a harmonic centre of gravity; for this
tone is the unmistakable root or fundamental tone of
the thread. You will find the harmonic thread to be
as follows : —

3 15 3 1

^^

mi do sol mi ffo = Root and Tonic

Having found the root, move back on the thread to
the tone you started on and go down and up on the
thread repeatedly as shown below : —

Once you recognize the root then the rest of the
analysis is simple, namely, the number and names of
components, the interval-relations of the components
to the common root, the proving of the common root
not alone by discovering that it is the most stable of all
the components, but by further discovering that it is
the only tone in the thread to which the other tones

DISSONANCE AND CONSONANCE 81

relate in the harmonic order of third and fifth in the case
of this first tone and as third, fifth, seventh and ninth
in the cases of other tones in this folksong. You will
discover that in dropping on the thread you passed
one root and followed the thread to the lower octave
of that root, that when you pass a root you repeat
the same series of tones in a lower octave. In fine,
you have analyzed the harmonic thread of the first
tone (mi) and recognize this tone to be a large or major
third because it lies two whole steps over its root.

As a prelude to proceeding with this analysis the
last question and answer may be given in a briefer
form. How in one voice am I to know that a tone
is a root or third or fifth or seventh or ninth ? By
feeling its momentary relation and analyzing its har-
monic thread.

Second tone fa, minor seventh. The harmonic
thread of this tone hsisfour components; its root is the
Dominant. This thread is given at a) followed by an
exercise at 6).

a) b)

, 5 3 1 ,531

h-f/^ h' ujiJ^

fa re ti sol— root or Dominant fa sol

Third tone sol, pure fifth. Its analysis follows.
0 h)

5 3 1 5 3 1

i

m

sol mi do =root or Tonic sol do

82 THE NATURE OF MUSIC

The next three tones are repetitions of the first,
namely, mi, major third.

Seventh tone re, pure fifth of the Dominant. This
time the Dominant-thread reports but three compo-
nents.

a) 6)

5 3 1 .531

^- ""=^-|-j i~TT^

r J ^ r » j »

re ti sol = root or Dominant re sol

The next five tones are repetitions of percepts already
analyzed.

Thirteenth tone la, major ninth of Dominant.
This time the Dominant-thread reports five compo-
nents.

a)

9^531

i

-^

rrfW

la fa re ti «>/= Dominant la tci

Excepting the last two all the remaining tones are
repetitions of those already analyzed.

Last tone hut one, ti, major third of Dominant.
On ti as on re the Dominant-thread reports three
components.

a) h)

3153 1 31531 31

J

W^t.: L^rr.rrfl^M

^&^i^

ti sol re ti «oZ= Dominant ii sol

DISSONANCE AND CONSONANCE 83

Last tone do, the Tonic, root of Tonic-harmony,
the genus consonance and music's first regnant har-
mony.

a) b)

1531153 1351

f^^^i^r^i^ij

3^

do sol mi do do do do do do

Here ends the analysis of the common report of the
harmonic relation and form of each individual tone
in this melody. However, the harmonic analysis is
not yet complete. As we sing and think over this
melody we observe in addition to the fact that each
tone reports a harmony another fact, namely, that
certain rhythmic groups of these tones relate to and
report the predominance of a specific harmony, which
I have already named the regnant harmony. Thus
in each small phrase we observe a change from one
regnant harmony to another, now the Tonic, now
the Dominant, as marked in the example. Thus the
first small phrase changes from Tonic to Dominant,
the second from Dominant to Tonic, and so on. Reg-
nant harmony being the special subject of the next
chapter w^e need pause here only for a few observa-
tions. We note that these changes of harmony are
instantaneous and recurrent; hence the implication
of rhythm in causing these changes. So far I have
accounted for the genesis of but one regnant har-
mony, the Tonic, since every conceivable succession
of Tonic-components generates the Tonic-harmony

84

THE NATURE OF MUSIC

and cannot possibly generate any other harmony.
The answer in the next chapter to the question How
did a second regnant harmony arise? becomes in-
creasingly important. Sol, originally fifth of Tonic,
could not appear as a root until the regnant Domi-
nant-harmony had been generated. In passing let us
observe that the Tonic-harmony, whether represented
by do or mi or sol, is always a three-tone thread. A
review of the foregoing analysis will show on the other
hand that the Dominant-harmony is a three-tone
thread on ti and re, sl four-tone thread on fa, a five-
tone thread on la. From these threads of three, four
and five tones are derived the chords composed of
corresponding numbers of tones and known as the
Tonic -triad, the Dominant - triad, the Dominant-
seventh chord and the chord of the major ninth, in all
their forms and positions.

While the regnant Dominant appears in the above
folksong the tone sol does not appear in it as a root.
The following melody is selected because it presents
sol as root. In fact, it presents the five original per-
cepts, and the seven original tones in their eight rela-
tions to the Tonic and Dominant.

3 ^351391

1^3511 6

i

y r^ r f »

^

a

I

^3

^

mi fa mi re do ti la sol fa sd fa mire do do sd
Tonic Dominant. Tonic.

This analysis suffices to establish the following
theses as scientific truths.

DISSONANCE AND CONSONANCE 85

1. Original harmony is harmony in one voice and
the harmonic basis of music.

2. The original dissonance and consonance had
their genesis in one voice, and their component tones
are the seven original tones here identified as the seven
diatonics of the Major mode.

3. Harmony in one voice asserts itself; each indi-
vidual tone reports itself as root or third or fifth or
seventh or ninth, and these reports are common and
unalterable.

4. Rhythmic groups of tones generate and assert
their relation to a particular subharmony ; now it is one
regnant harmony, now it changes to another regnant
harmony. In one-voice music the regnant harmonies
arise by natural selection, in multi-voice music they
are due to personal selection. Regnant harmony de-
termines the exact relation of each tone in a melody.

5. From the original dissonance and consonance
are derived three fundamental forms of harmony,
namely, the three-tone, four-tone and five-tone forms ;
five original harmonic percepts, namely, 1, 3, 5, ?, 9.

6. The mode-idea had its origin in the basic rela-
tion of cadence and repose,m which relation the original
dissonance and consonance had their origin. From
the first the mode has been harmonic and is based on
the two harmonic genera of tones. The tones of the
two genera being the seven Major diatonics it follows
that the Major mode is the original mode.

7. Melody is the composite vehicle which has intro-
duced one by one all these tones, percepts, forms and
regnant harmonies of the Major mode.

The harmonic reports given in the above analyses

S6 THE NATURE OF MUSIC

cannot be changed, not by tempo, slow or fast; not
by dynamics, loud or soft; not by interpretation,
legato or staccato ; they are what they are, not by man's
will, but by the universal will and immutable laws
inherent in tone-rhythmic relation. The prevalent
chord-conception of harmony is responsible for the
distinction between harmonic tones and melodic tones ;
the component tones of a "presiding chord" being
called harmonic while the tones that lie over and under
and play upon the chord-tones are called melodic.
This distinction has lost its usefulness since it has been
demonstrated that each individual tone, whether it
belongs to the "presiding chord" or not, is harmonic.
Were this not true there would be and could be neither
tone-cadence nor tone-repose, neither dissonance nor
consonance, no relation in the musical sense, in short,
no music. The truth that every tone is harmonic is
here based on the testimony of the inner ear which is
the testimony of common feeling and perception. This
truth is reported in all music, primitive and artistic,
before Bach, of Bach, after Bach.

32. On Symbols

The symbols thus far employed are notes, syllables
and harmonic numbers. To these we will add scale-
numbers, for which purpose the seven original tones
are now presented in the familiar form of the Major
scale.

15 3^ 59or33 1

—y ■■

"~7

--

Cy

II

fc\

^

^

f^

11

Vs}

^

II

%J

-&-

25>~

do

re

mi

fa

sol

la

ti

do

1

2

3

4

5

6

7

8

DISSONANCE AND CONSONANCE 87

Here the syllables indicate the mode-tones; the
notes, the pitch or key of the mode-tones; the upper
row of numbers, the inherent harmonic relations ; the
lower row of numbers, the scale-order from the first
to the eighth tone. Scale-numbers are outside, not
inside numbers. Street-door numbers tell us nothing
of what is going on inside of a house ; no more do scale-
numbers tell us what is going on inside of a tone ; that
is, they give us no intelligence whatever of the inherent
harmonic relations of tones. To be sure the scale-
numbers 1, 3, 5 happen to correspond with the har-
monic numbers over do^ mi and sol, but the fact that
we know that re, /a, la and ti are respectively the
second, fourth, sixth and seventh tones of the scale
by no means implies the slightest knowledge of the one
thing we should know, namely, the inherent harmonic
relations of the tones. We have seen that during the
regnancy of the Tonic, re is 5, fa is 7, la is 3, <i is 3 ;
that during the regnancy of the Dominant, the rela-
tions of these tones are the same except in the case of
/a, which is a ninth. There are no harmonic percepts
answering to the scale-numbers 2, 4 and 6. The habit
of orientation by means of scale-numbers is so fixed
that when students begin the study of one-voice har-
mony they are very apt to confuse the scale-numbers
with the harmonic numbers and vice versa. Scale-
numbers serve a useful purpose, but that purpose
should be defined. We will define all the above sym-
bols and so avoid the confusion which would otherwise
be inevitable.

1. A note with and without modifying sharp, flat or
natural, is the sign and index of the relative pitch of a

88 THE NATURE OF MUSIC

tone. This defines the note according to its position
on the staff.

The metrical shape of a note is the sign and index
of the relative length of the rhythmic period of a tone.

2. A syllable is the sign and index of the mode-
relation of a tone. By means of the syllables we are
able to think and express the mode-relations without
any connection with fixed pitch or key. But the terms
mode-relation and key-relation become synonymous
the moment the mode-relations are pitched or keyed
in staff-notation. C Major means (fo-Major pitched
or keyed on C, but Major always is c?o-Major whatever
be the pitch or key of mode.

3. A harmonic number is the sign and index of the
inherent harmonic relation of a tone.

4. A scale-number is the sign and index of the rela-
tive position of a tone in a scale. In the Roman form
these numbers are employed as indices of the sub-
harmonies, that is, of regnant harmonies. Thus, for
example, the Tonic is marked I, the Dominant is
marked V, the two roots being the first and fifth tones
of the scale.

Of all these signs the harmonic numbers are the
most important. Through the discovery of original
harmony in one voice these harmonic numbers have
gained a theoretic and practical value which hitherto
they have not possessed. Their report in one voice is
exact, synthetic and complete: exact, because their
harmonic report is the common report of common
feeling and perception ; synthetic, because their exact
report of inherent harmonic relation includes the feel-
ing and idea of mode, key and interval; complete.

DISSONANCE AND CONSONANCE 89

because their exact and synthetic reports are indis-
solubly associated with rhythm, and therefore embody
the complete intelligence of a tone's relation. This
harmonic report of a tone's relation is therefore the
essential and fundamental thing to observe, name and
know.

33. The Five Components of Harmony

There are hut Jive components of harmony, namely,
root, third, fifth, seventh, ninth. The truth of this
generalization is in no way impaired by the fact that
there are numerous modified forms of these five.
Some harmonies have three, some four, some five com-
ponents, but none exceed the number oi Jive. The
ninth is the genetic limit oj harmony. Common har-
monic feeling and perception report and admit no
harmonic components beyond the ninth. Root, third,
fifth, seventh and ninth, being the only harmonic per-
cepts, they are the only harmonic components. Chord-
theories have admitted elevenths and thirteenths as
components of chords and therefore as components of
harmony. Such elevenths and thirteenths are purely
theoretical concepts, which are as false as they are
arbitrary since they have no foundation in and are
confuted by common feeling and perception. On
page 90 will be found two examples which present
these elevenths and thirteenths in their true light as
arbitrary computations of intervals from a given root
which at a) is the Tonic and at h) is the Dominant.

The lower row of numbers in both examples indi-
cates the arbitrary chord-intervals from 1 to 13. The
upper row of numbers in both examples is the true

90 THE NATURE OF MUSIC

index of the common harmonic report of each tone in
correlation with all the other tones. Compare the
two sets of numbers. In a) the chord-intervals 7, 9,
11 and 13 are respectively 3, 5, ? and 9, which are
components of the Dominant. In h) the chord-inter-
vals 11 and 13 are respectively 1 and 3 of the Tonic.
The large notes in both examples show that both of
these chords combine components of' two harmonies ;
each contains two roots.

a) 13 5-135^9

k±

i)

1 3 5 7 9 11 13
1 3 5,91 3

i

i

1 3 5 7 9 11 13

Chords formed by combining the component tones
of one harmony I name simple chords ; such, for exam-
ple, are all the forms of the major triad. Chords, like
those in the above examples, which are formed by com-
bining the component tones of two or more harmonies,
I name compound chords.

Tones which relate to but one root I name simple
harmonics; such are 1, 3, 5 of the Tonic and 1, 3, 5,
7, 9 of the Dominant. Tones, like sol in example a),
which simultaneously relate to two roots I name com^
pound harmonics.

Simple and compound chords and harmonics are

DISSONANCE AND CONSONANCE 91

subjects to be treated later on. Meanwhile the
above examples clearly point out the necessity for
making careful distinctions between harmonic com-
ponents which never exceed the number of five and
chord-components which are not limited; between har-
monic intervals and chord-intervals; between har-
monic concepts, supported and verified by common
feeling and perception, and chord-concepts, which the
common reports prove to be false, and which therefore
are arbitrary, misleading and untenable.

34. The Five Original Cadences. Mode Defined

The relation of cadence and repose is the basis
of mode. The relation of tone-cadence and tone-
repose originated in the relation of one harmony (dis-
sonance) to another harmony (consonance). This
inter-harmonic relation is mode-relation. The pre-
ceding account of the origin and nature of original
dissonance and consonance in one voice is equivalent
to an account of the origin and nature of the Major
mode. The original mode is Major because the ori-
ginal consonance is major. The aggregate relations
of the two harmonic genera may be called briefly the
major consonance and its cadences.

Melody has brought forth two modes : first, the Major
mode based on the major consonance and its cadences ;
second, the Minor mode based on the minor conso-
nance and its cadences. The origin of the former has
been explained; the origin of the latter is the subject
of a later chapter. In mode-parlance what has just
been called the major consonance and its cadences
is the Major Tonic (-harmony) and its cadences.

9« THE NATURE OF MUSIC

Three marks succinctly symbolize the mode-idea as
follows : —

In the above order these marks signify rising ca-
dence, falling cadence, repose. Join these marks and
we form a simple sign for the Major mode, thus : —

The Major Tonic and its cadences are the five origi-
nal cadences of music. They are given below where
each tone is numbered according to its genus-relsition.

I 3
o)3 1515 3, 395 6) 3 1

ti do re do re mi fa mi la sol

:|^

In a) the cadences are single, in b) they are com-
bined in chords. Ti resolves in an upward half step,
fa in a downward half step : I therefore name ti the
upleader, fa the downleader. Of the original four
cadence-tones re is the only one that reports both a
rising and a falling cadence ; in both of its cadences re
resolves in a whole step. La reports its falling cadence
by resolving in a downward whole step. Of these
five original cadences two are rising, three are falling,
two resolve in half steps, three in whole steps.

Although we may be able to hear these whole and

DISSONANCE AND CONSONANCE 93

half steps and able to name the two tones in each,
although we may be able to perceive and name all
intervals from primes to elevenths and able to define
tjiem as pure, major, minor, augmented and dimin-
ished, double-augmented and double-diminished, yet
at the same time we may have no perception and may
be completely ignorant of the one thing essential to
our intelligent and true appreciation of a step and an
interval, namely, the inherent harmony of each of the
two tones that form a step and interval. For exam-
ple. Besides hearing that the two tones in the first
of the above cadences are ti and do and that the step
is a half step and an upward resolution, you should
hear that you are stepping from the third of one har-
mony (Dominant) to the root of another harmony
(Tonic). The perception of these harmonic and
inter-harmonic relations is imperative. Far from in-
veighing against the customary study and practice of
intervals, I consider the working out of intervals from
each tone in the octave both a necessary discipline
and an essential part of every student's mental equip-
ment and technique. But students are warned to dis-
criminate with care between interval-numbers which
indicate the distance from one tone to another and
harmonic numbers which indicate the harmonic rela-
tion of each individual tone to its root.

There being no melody apart from mode each
tone in a melody is a mode-tone. There are three
groups of mode-tones : 1. Diatonics. 2. Chromatics.
3. Enharmonics. We have seen that tone connotes
harmonic form and harmonic relation, and that a
specific form is due to a specific relation. There-

94 THE NATURE OF MUSIC

fore these three groups of mode-tones are three
groups of mode-relations. Both mode and tonality
mean tone-relation, and at one time the two terms
were synonymous. The evolutionary expansion qf
tonality consequent on the development of modern
music has changed all this. While tonality compre-
hends all that is mode, mode does not comprehend all
that is tonality. Definitions will explain. The mode
is the sum of relations in one key. Tonality is the
sum of relations in all keys. The mode is concerned
with the interharmonic relations of one key, tonality
with the interharmonic relations of all keys. Thus
tonality is a general term and comprehends all that is
mode. The evolution of the mode is therefore the
first chapter in the evolution of tonality: the three
groups of tones and relations are three evolutionary
stages of tonality. The first stage culminated in the
completion of the foundation-group of seven diatonics,
which is the subject still before us. We have symbol-
ized and named each of these tones by a syllable, a
note in the key of C, and a scale-number. Each is
also known by a technical name which is added to the
other names in this example.

Tonic Super- Mediant Sub- Dominant Sub- Subtonic Tonic
tonic dominant mediant

L/ ■■ - -- - n

/f ^ a M

fc\

a

O'

■ n

\s)

a>

11

do

I

re

n

mi

III

fa

IV

ad
V

la

VI

a
VII

<fo
I

The unity of the mode-idea is exemplified by all
these symbols except the notes which fix the pitch or
key of mode on C.

DISSONANCE AND CONSONANCE 95

Original harmonic forms and relations are the pro-
totypes of all like forms and relations. Such proto-
types are the major consonance, the four-tone and
five-tone dissonance, the Major mode, the five original
percepts 1, 3, 5, ?, 9, the upleader ti, the downleader
fa. We shall see that the evolutionary expansion of
tonality and of the tone-system are due on the one
hand to the multiplication of these prototypes, on the
other hand to the production of new types which in
their turn are multiplied. The multiplication of exist-
ing types will be explained by the psychological prin-
ciple that all forms and relations in experience are
potential in and pitchable ^ on all tones in experience.
The production of new types will be explained by the
psychological principle of tone-genesis, the eflficient
accent. Meanwhile the relation of tonality and tone-
system requires definition. The tone-system is the
index and scale of tones in use. The tones had their
origin in relation, therefore, in tonality. Tonality and
tone-system therefore stand in the relation of cause
and consequence. The development of the latter was
dependent on and concurrent with that of the former.
The diatonic stage of tonality caused the diatonic divi-
sion of the octave which resulted in the diatonic scale-
system. The chromatic stage of tonality caused the
chromatic division of the octave which resulted in the
chromatic scale-system. The enharmonic stage of
tonality caused the enharmonic division of the octave
which resulted in our modern enharmonic scale-sys-
tem. This division of the octave is due to tonality,
not to equal temperament as physicists believe. Tem-

^ Reading uncertain. L. E. K.

96

THE NATURE OF MUSIC

perament there is in musical instruments like the
piano, but in music itself there is no temperament. A
piano is tempered for the purpose of meeting psycho-
logical not physical requirements; to temper a piano
is to shape physical means to psychological ends.
Tonality is a question of psychology, not of physics.
No two half steps, no two whole steps, no two intervals
of any denomination, have exactly the same length.
The cause lies in tonality, which is a web of harmonic
threads. In evolution thread upon thread has been
added to this web, so that at the present time the
meshes of its thousand threads are so fine and delicate
that they almost co^iceal the diatonic ^^ni^^-threads with
the result that some theorists have denied the existence
of such a thing as mode or key. Two simple exer-
cises will fix the two gr^/ii/^-threads which comprise the
seven diatonics, in the mind of the student.

a)

3 5

b)

ti re fa la sol mi do

V I

la fa re ti

V

do mi sol
I

35. Progression and Resolution

Steps from tone to tone are either progressions or
resolutions. The step from a cadence-tone to a re-
pose-tone is a resolution on the line of least resistance.
Every step not a resolution is a progression. Every
step being either the one or the other of the two the
distinction between the two is very important. Since

DISSONANCE AND CONSONANCE

97

tones are either in cadence or repose we proceed from
tone to tone in four ways as follows : —

1. From cadence to repose = resolution.

2. From repose to cadence = progression.

3. From cadence to cadence = progression.

4. From repose to repose = progression.

These four species of steps appear in the next exam-
ple: cad. and rep. indicate respectively cadence-tone
and repose-tone : the slurs indicate resolutions, and all
the other steps are progressions.

1

do

3 1

H do

re

5

sol

1

do

m

i

*

rep. cad. rep. cad. rep. rep. cad. cad. rep.

In the following ascending and descending scales
each progression and resolution is marked pro. and
res. respectively. There are two rising cadences or
resolutions in ascending and three falling cadences or
resolutions in descending. The step from fa up to
sol at N.B., although it proceeds from a cadence-tone

a)

15 3 7N.B. 5 3 3 1

i^ ! ij

pro. res. pro. pro. pro. pro. res.

mi

h)

1335 1351

i^

1 — I — [

■^T^

m

pro. pro. res. pro. res. pro. res.

98 THE NATURE OF MUSIC

to a repose-tone, is a progression, because the cadence
of /a falls to mi and does not rise to soL All such
evasions of the inherent cadence of a tone are classed
as progressions.

The moment a series of tones is thought rhythmi-
cally it at once becomes melody and asserts its inherent
regnant harmony, which in both of the above examples
is the Tonic.

In a former writing [" The Septonate "] I misnamed
progression by calling it a principle. Progression is
neither a cause nor a principle. The same is equally
true of resolution. Both progression and resolution
are effects of causes inherent in the rhythmo-harmonic
relation of the two tones forming a specific step.

From rhythm we have derived the basic relation of
cadence and repose. In their application to tone the
terms cadence and repose have thus far been used in
exclusive connection with the four original cadence-
tones {ti, re, fa, la) and the three repose- tones (do, mi,
sol), in short, with the Major Tonic-harmony and its
cadences. From this their original and restricted
sense we are presently to use these terms in a wide and
general sense as applying to tone-relation in general.
Since every tone may appear in cadence or repose it
follows that this basic relation derived from rhythm
and then connected with specific tones will henceforth
apply to tones and tone-relations in general.

36. A First Music-Lesson

The material to be presented is as follows : —
1. Rhythm : simple dual and triple. 2. Harmony:
the Major Tonic and its five diatonic cadences.

DISSONANCE AND CONSONANCE 99

Method to proceed from generals to particulars, from
perception to conception.

The purpose of a first lesson is to transmute a
child's latent feeling of the inherent rhythm and
harmony of melody into accurate observation. Pre-
sent a simple diatonic melody and point out its rhythm
and harmony in a general way, leaving particulars for
the last part of lesson. Next present and explain ma-
terial as follows: —

1. Rhythm: dual and triple forms: light and
heavy accents: relation of these alternating accents
to form, to keeping time and balance : no rhythm, no
form : rhythm the foundation of form. Let the child
express rhythm: beat it, walk it, talk it, as follows: —

Simple Dual Forms.

a) light heavy) b) heavy light) ^

now now ) '^ now now) ^

Simple Triple Forms,

a) light light heavy ) ^^ h) light heavy light ) j. ^

now now now ) now now now) *^

c) heavy light light)
now now now)

Select words whose relative accents correspond with
all these forms.

2. Harmony: Let the student learn first the three
repose-tones of the Tonic, their syllables and harmonic
numbers ; next, the four cadence-tones, their syllables
and harmonic numbers; next the five diatonic ca-
dences. Observe that the repose-tones and cadence-
tones each combine in a harmony and chord and
resolve the cadence-chord into the repose-chord.

100 THE NATURE OF MUSIC

This is the harmonic foundation, it is all in you.
Observe and verify it in yourself and others. Hear it,
feel it; name it, think it; sing it, play it; read it, write
it, and, as a child of six once prompted me, **then
know it."

3. Now return to the simple melody with which
you started. Define its rhythm, name each of its
tones by a syllable, point out each cadence-tone and
repose-tone and give each its harmonic number indi-
cating its harmonic relation.

For many years I have given this first lesson to
students of all ages. If desirable the above material
may be divided so as to occupy two or three lessons.
To learn the lesson and learn it thoroughly is impor-
tant ; how long it takes to accomplish this is unim-
portant. Study music and be a musician. Music
is the what ; technique is the how. The latter equals
zero if not based on the former. The musician has
something to say; he has the right to speak and be
heard; his technique is a means to an end; his art is
music. On the other hand, the mere technician has
nothing to say; he has no such right; his astounding
technique amounts to an astounding facility in saying
nothing; what should be a means becomes an end in
itself; his art is mechanism; his expression is jejune
jingle. It is never too late to learn a first music-
lesson.

DISSONANCE AND COIs^SOMNCE' lOV

37. Work for Students

Work and write out the following material in all
keys, namely, in C, G, D, A, E, B, FJ^, Cjj: ; in F, BK EK
Al7, DK GP, Ct;.

Consonance Dissonance Resolution

13 5 3 5,9

i

_^5-/« 1

f

do

I

mi

•U

a
V

fa la

V I

i

Two Rising Cadences

Three Falling Cadences

-g ^

^^j

n,^ ' '^

-&- ■'>— /

-(S?-

Additional work for students will be indicated from
time to time as we proceed.

CHAPTER IV

THE EFFICIENT ACCENT AND REGNANT HARMONY
OF MELODY

38. Regnant Harmony in One Voice and Its
Principle of Genesis Explained

In preceding chapters we have traced the genesis
of harmony back to music in one voice or homophony.
In the chapters before us we are to trace the evolution
of homophonic harmony in a sequence of cause and
effect. Through the sudden transference of the har-
monic basis of music from the chord to homophony,
through the consequent lengthening of the age of
harmony from a period of evolution extending over
but a few centuries of chords to a period reaching
back from the present to the first beginnings of music
unknown ages ago, in short, through the discovery of
original harmony in one voice and its common reports,
the subject of homophony suddenly stands forth in
a new light and gains a new theoretic and historic
significance and prominence. In the common reports
of homophonic harmony, the enumeration of which
we have begun and will continue, we have found
the long-sought key to common music-feeling and
a common basis for testing truth. These reports
have guided us in explaining and verifying the
genesis of consonance and dissonance in one voice,
and will as securely guide us in tracing the genesis of

ACCENT AND REGNANT HARMONY 103

new homophonic harmonies. We have accounted for
the genesis of the foundation-group of seven com-
ponent tones and five harmonic percepts of the origi-
nal consonance and dissonance, and I have named
this original group the Major Tonic and its cadences.
From this original group new forms of harmony intro-
ducing new tones and new harmonic percepts have
been derived. How.? Through rhythmic relation
like their antecedents. The cause of the genesis of
consonance and dissonance we discovered to be the
rhythm-derived relation of cadence and repose.
Rhythmic relation has produced all subsequent
new forms of harmony. The psychology of this
evolutionary process is next defined in terms apply-
ing to every stage in the development of homo-
phony. Existing tones in existing relations generate
and report only existing forms of harmony, while in
new or changed relations they generate and report
new forms of harmony. Next we will apply these
principles to the foundation-group of tones. The
seven original tones in their original relations in
cadence and repose generate and report only the origi-
nal forms of harmony in which they arose, while in
new or changed relations they generate and report
new forms of harmony introducing new tones and
new harmonic percepts. The evolution of harmony
is therefore the direct cause of the expansion of
tonality and consequent expansion of the tone-sys-
tem. Each developmental step in music was there-
fore dependent on and due to the evolution of har-
mony, and the three successive and interdependent
stages of music, namely, homophony, polyphony and

104 THE NATURE OF MUSIC

chords, are so many stages of harmonic evolution.
Hence this logical conclusion. Root, trunk and over-
spreading boughs, all music from first to last is one
growth of one psychological tree of tone-relations and
forms of harmony. All tone-relations and forms of
harmony in one voice, where did their genesis take
place.? In feeling, under the impulse of indwelling
causes. In what form were they first embodied and
expressed ? In melody, the original voice and vehicle
of tone-language, the indissoluble composite of rela-
tion and form in time (rhythm) and relation and
form in space (harmony), the essence, heart and soul
of music. All that is essential and potential in
homophony is embodied in melody. Thus our study
of homophony resolves itself into that of the common
reports of our common feeling and perception of
melody. Are we not all of us melodists ? What is
all primitive music but primitive melody, formal
music but conventional melody, modern music but
free melody.? All along the line, are not all the
great composers melodists ? Are not their works
immortal because their melodies are immortal.?

This introduction to the several chapters before us
may be concluded with a few observations which
will focus our attention upon the special subject
directly before us. One regnant harmony after an-
other had its genesis in feeling and was embodied
in and reported by melody. In a book published
fourteen years ago [" The Septonate "] what I now call
harmony in one voice I there named meloharmony,
the inherent harmony of melody; what I now call
regnant harmony I there named ruling or governing

ACCENT AND REGNANT HARMONY 105

harmony; what I now call the efficient accent was
there named the rhythmo-harmonic accent or point.

1. The evolutionary sequence of ho mo phonic har-
monies is a sequence of regnant harmonies which
melody brought forth one by one beginning with the
regnant Major Tonic, the nucleus in relation to which
the others arose. A regnant harmony asserts itself
during every moment in melody. The regnant har-
mony of the moment selects and asserts itself, it
determines the exact harmonic relation of each tone
in melody and we all hear it in common. Therefore
all melodies are based on regnant harmonies, the
simplest on one such harmony (Major Tonic), the
more complex on two or more such harmonies.

2. The efficient accent is the heavy recurring
rhythmic accent of melody; it is the principle of
harmonic genesis and development in homophony,
and has generated one regnant harmony after an-
other. The shortest melody consisting of two tones
has but one efficient accent: the cuckoo-song is an
example. Longer melodies are connected by a series
of such accents. As a melody proceeds from one
such accent to another one of two things happens:
either the initial regnant harmony is maintained and
repeated, or a new regnant harmony is generated. We
are to study the causes in both cases. Two condi-
tions were indispensable to the development of music
beyond the stage of one regnant harmony, the Major
Tonic. These were first, the lengthening of melody
from one efficient accent to a series of such accents;
second, the genesis of a second regnant harmony.

3. The component tones of the regnant harmony

106 THE NATURE OF MUSIC

are named regnant tones. The tones lying over and
under and cadencing up and down into the regnant
tones are named bytones. Bytones are components
of other harmonies named byharmonies. Regnant
harmony, regnant tone; byharmony, by tone; let us
bear these terms and their meanings in mind. The
first regnant tones to appear in melody were do, mi,
sol, of the regnant Major Tonic : the first bytones to
appear were the original cadence-tones re, la, fa and ti,
which as we have seen arose in relation to the Major
Tonic-harmony. Of these embryonic melodies there
are two types: first, those lowest in the order of
development composed of regnant tones only and
representing harmonic perception and harmonic rela-
tion in their incipiency and within their narrowest
confines ; second, those next in order of development,
which introduce bytones along with the regnant tones,
thus marking an advance in harmonic perception
and relation. Melody based on one regnant harmony
could advance no further; the second type of melody
brings its first chapter of development to a conclusion,
and this first chapter of melody corresponds with
the first developmental chapter of harmony. From
first to last the development of melody is dependent
on that of harmony; melody could not advance
another step until a second regnant harmony arose
in relation to the first. When this step was taken
a significant change was suddenly effected, for at one
bound harmonic relation expanded from that of
bytone to one regnant harmony to that of one reg-
nant harmony to another regnant harmony; at one
bound melody entered into a new region of inexhaust-

ACCENT AND REGNANT HARMONY

107

ible fertility and initiated a new chapter in music-
evolution, the end of which has not yet been reached.
Let us be explicit on this point. Melody started with
one regnant harmony as a nucleus, in relation to
which it produced other regnant harmonies, in relation
to which it produced still others, and so on ad infini-
tum, thus evolving an ever increasing psychological
web of correlated threads of harmony. How then did
melody recombine the seven original tones in new
relations which generated one regnant harmony after
another ?

4. In every conceivable combination of the tones
do, mi, sol, melody reports the regnancy of the Major
Tonic (I). In other words, a second regnant har-
mony is not latent or potential in this type of melody.

5 1 3 5 3 1 5

5. Melody first introduced bytones on its light
rhythmic accents. In this their original relation the
cadence-tones re, la, fa and ti do not disturb the
regnancy of the Major Tonic and could not have
generated a second regnant harmony. The exam-
ple below presents re and la, which are the first two
bytones to appear in melody, re in cadence to do and
mediating between do and mi, la in cadence to sol,
1153351 35535

i

-•/-^

jW=rm.

I

108 THE NATURE OF MUSIC

6. But at the moment when melody introduced
re and la on its heavy rhythmic accents (eflBcient
accents) the great transformation takes place. Sud-
denly re and la are transformed into regnant tones
reporting regnant harmonies. The efficient accent
on re generates the regnant Dominant-harmony (V):
the efficient accent on la generates the regnant Sub-
dominant-harmony (IV). These common harmonic
reports of melody are next exemplified.

51 5 353 535 1

±=4

i

Pipy, i 0 J lF^J#^^=^^

IV

Each of the above efficient accents reports a change
of regnant harmony; the mode relation of one regnant
harmony to another is at once established in this
pentatonic or five-tone stage of melody, and melody
is enriched by the addition of two new regnant har-
monies. The regnant Major Tonic, as we have seen,
arose independently on an isolated tone. Not so with
the regnant V and IV, which arose in relation to and
were dependent on the previously existing regnant I.
This dependence on and genesis in relation to ante-
cedent harmonies distinguishes all other harmonies
from the original regnant I, which has no antece-
dents. We observe further that while the regnant I
entered into being by way of do its root, the regnant
V was first represented and reported by re its ffth,
the regnant IV by la its third. Such are the common
reports of common feeling and perception, at once
the simplest and surest test of truth. The efficient

ACCENT AND REGNANT HARMONY 109

accent of melody has generated these first three
regnant harmonies in the order I, V, IV, and the reg-
nant harmony of melody arises of itself, asserts itself
and is unalterable in one voice. We note that
evolving melody in spinning the psychological web
of correlated threads of harmony began with one
thread, do, mi, sol of I ; melody next added the by tones
re and la on light rhythmic accents, re reporting V as
byharmony, la reporting IV as byharmony; melody
next introduced re and la on eflScient accents and so
produced the regnant V and IV. Thus far we have
traced the genesis of harmony, and the addition of
the regnant V and IV to I opens new channels of
development and so many changes and possibilities
in harmonic relation that it may be well to present
the more noticeable points one by one.

7. The melodies in our last two examples are
pentatonic, that is, composed of the five tones do,
re, mi, sol, la, which we have abeady identified as
the pentatonic scale. Enough has been explained
to show the archaeologist that in his endeavor to
establish the true chronological order of primitive
melodies his conclusions are to be deduced not alone
from the number of individual tones or the scale of
a given melody, but from the inherent harmonic con-
tent and relations of that melody. The scale is not
the thing of essential importance, but the inherent
harmony is the important thing, the true guide and
test. Melodies composed of the components of reg-
nant I exclusively are earliest; melodies containing
the bytone re are later, those containing the bytone la
are still later; those containing the regnant V and IV

110 THE NATURE OF MUSIC

are still later. The pentatonic stage of melody is evi-
denced in all primitive music in one of three ways :
either these melodies precede or are approaching the
pentatonic stage, or they have reached it or they have
passed it. Not only was the pentatonic stage the
natural product of the progressive development of
music j>er se, but the entire development of the lan-
guage and art of music up to the present time was
dependent on the attainment and passage remote
ages ago of the pentatonic stage of melody.

8. Certain tones like do, mi, sol and others first
appeared in melody in the relation of regnant tones
(components of regnant harmonies). Certain tones
like re, la and others first appeared in the relation
of by tones (components of byharmonies). We have
seen how V and IV were transmuted from byhar-
monies to regnant harmonies. We are about to see
how regnant I is transmuted into a byharmony.
The point to be noted here is this. Every such
change of a tone's original relation to a new relation
marks not alone the progress of melody consequent
on the progressive development of its inherent poten-
tial harmony and harmonic relations, but it at once
marks the progressive development of the harmonic
sense, which is the proximate cause of the progress
of melody and expansion of harmony, and which
steadily though slowly led to the eventual discovery
or perception of harmony itself. The evolution of
harmonic perception affords a striking example of
the extreme slowness of the evolutionary processes of
perception in general. Although from the first and
through countless ages melody has asserted its inherent

ACCENT AND REGNANT HARMONY 111

harmony, yet man's discovery or perception of harmony
and its introduction in the form of chord date back
but a few centuries. However, this great slowness is
offset by what followed, for this discovery of harmony
was magical in its effects, initiating as it did an era
of development in music which for rapidity of pro-
gress and wealth of productivity has no parallel in
psychology and history.

9. When we were dealing with but one regnant har- ^^
mony and its bytones (Major Tonic and its cadences)
the term repose applied exclusively to the original re-
pose-harmony or major consonance and to the stable
period of rhythm-repose in which this stable harmony
arose. Then, too, the term cadence applied exclusively
to the original cadence-harmony or dissonance and to
the unstable and relative period of rhythm-cadence in
which this unstable and relative harmony arose. But
now that we have introduced three regnant harmonies
all this is changed. Now and henceforth the terms
cadence and repose become general and apply to rhyth-
mic and harmonic forms and relations in general while
the terms hytone and byharmony, regnant tone and
regnant harmony become the specific and unmodifi-
able terms of analysis. Thus, for example, what we
hitherto called the Major Tonic and its cadences we
now specify as reg. I and its bytones. Presently we are
to analyze reg. V and its bytones, reg. IV and its by-
tones. Here let us note the fact that every regnant
harmony has its relative byharmonies.

In taking up the analysis of the broad relation of
regnant harmony to regnant harmony let us bear in
mind the following general truths: 1. Every tone

112 THE NATURE OF MUSIC

reports a harmonic form and relation. 2. Every
tone reports a consonance or a dissonance, is in
cadence or repose, is a by tone or a regnant tone.
3. Every step from tone to tone, from harmony to
harmony, is a progression or a resolution. 4. All
these reports are common reports.

10. The regnant harmony of the moment is the
repose and equilibrium of that moment. Whether the
regnant harmony of the moment be I or V or IV or
any other it is the repose and equilibrium of that
moment. This is illustrated in our last example
where the regnant harmonies appear in this order,
I — V — I — IV — I — V — ^I. Here we note the wider
application of the term repose in the sense of the
equilibrium of the moment.

1 1 . The regnant harmony of one moment relates to
the regnant harmony of the next moment. But the
relation of a byharmony is confined to the single
moment of one regnant harmony. See last example
but one. The basic rhythmic links of a melody are
its series of efficient accents, and the basic harmonic
links of a melody are its series of regnant harmonies.
Since the tones that fall on efficient accents generate
and report the regnant harmonies, and since the
moment from one such accent to another is that of
one regnant harmony to another, it is clear that these
rhythmic and harmonic links of melody are insepara-
bly united and interdependent. The minute analysis
of this relation of and movement from one regnant
harmony to another now confronts us.

12. The steps from I to V and I to IV are
progressions; see below at a) and c). The steps

ACCENT AND REGNANT HARMONY

113

from V to I and IV to I are resolutions ; see below at
b) and d). In these resolutions V and IV are in
cadence to I. Here note the wider application of the
term cadence in this connection with regnant harmony.
Though the regnant harmony of the moment is the
repose and equilibrium of the moment, we observe
at b) and d) that it may be in cadence, that is, in
unstable equilibrium.
a) 1 6 6)5 1 c) 5 3 d)S 5

i

^

3

I

IV IV

In the progression I — ^V at a) re reports V as
consonance with sol as concomitant 1 and ti as con-
comitant 3. But in the resolution and cadence V — I
at b) re reports V as dissonance, and in this cadence-
relation all the original cadence- tones, namely, ti, rCy
fa and la, assert themselves as components of the
genus dissonance in that they each and all claim sol
as their common root. Not until melody had pro-
duced regnant V in this cadence-relation was it pos-
sible for la to assert itself as 9. This genesis of
regnant V in cadence belongs to melody's pentatonic
stage and was generated by the efficient accent on re.
During this stage sol which already existed as 5 of
I could next be related as 1 of V, and la, which already
existed as a bytone and as 3 of the byharmony IV,
could next be related as 9 of V. In short, during
this stage melody became enriched by many new
intervals resulting from the combinations of re, sol
and la during the regnancy of V in cadence. Illus-
trations of some of these intervals follow.

114 THE NATURE OF MUSIC

155115135

i

^m

w^

1

V

1

V

3

V

5

i

^^

^

I V I V9 I

9553951 55 95

i

11

g

V9

V9

V9

Next when the concomitants ti as 3 of V and fa as
7 of V were differentiated as individual tones the
melody emerged from its pentatonic stage and was
again enriched by many new intervals resulting from
combinations of sol^ re and la with ti and /a during
the regnancy of V. Some examples are given.

i

w^

wm

i

V

1

W^-

?

^

i

I

1 3

' 7

1 1

I

5 7

3 1

3 15

w

f

r^i

V,

ACCENT AND REGNANT HARMONY

115

75395 193 1 317531

I

V9

I etc.

Here note the fact that regnant V is sometimes a
consonance, sometimes a dissonance with four com-
ponents as V?, sometimes a dissonance with five
components as V9. Hence this general truth: The
regnant harmony of the moTnent may be either a con-
sonance or a dissonance.

Attention is again called to the first example of this
paragraph. Both in the progression I — ^IV at c) and
the resolution IV — I at d) regnant IV is reported
a consonance by la. In both relations la reports do
as concomitant 5 and /a as concomitant 1. Regnant
IV again enriches melody with new intervals result-
ing from combinations of its components/a, la and do.
A few examples appear below.

i

IV

IV

IV

35 13 5 3 351 351 531

i

^

lf=t

m

?==;

¥

W

I

3 5

IV I IV I

135135 5135

IV
13 5 1

s

^

'■i''i

IV

116 THE NATURE OF MUSIC

Here we observe that regnant IV, though it is
a consonance, is in cadence to I. Hence this truth :
Consonances as well as dissonances may be in cadence.
Further analysis will extricate us from what here
threatens to become a tangle of terms. This may be
avoided by at once stating the following general truth
which opens up and covers the whole subject of
regnant harmony and its byharmony. Both byhar-
monies and regnant harmonies may be either conso^
nances or dissonances : the former are always in cadence
or unstable equilibrium, the latter may be either in
repose (stable equilibrium) or in cadence (unstable
equilibrium). Byharmony and dissonance, regnant
harmony and consonance, these are not interchange-
able terms. Confusion of these terms will result in
complete confusion. Distinction between these terms
will preserve complete clarity.

13. In the harmonic analysis of melody the series
of questions to be answered are these: 1. What is
the regnant harmony of the moment ? Is its form a
consonance or a dissonance ? What are the regnant
tones and their relations ? 2. What are the bytones,
their relations, the forms of harmony they represent ?
These leading analytical questions apply to all music
since music the world over, past and present, primitive
and modern, one-voice and multi-voice, is one in kind.
These questions therefore apply to bird-melodies as
well as human melodies, to oriental as well as occi-
dental music, to Greek and Ecclesiastical melodies
as well as to folksongs and dances, sonatas and
symphonies.

14. Owing to the changes from one regnant

ACCENT AND REGNANT HARMONY

117

harmony to another reported by the efficient accent
of melody each of the seven diatonics appears now
as a regnant tone, now as a bytone. Thus what is
a regnant harmony at one moment is transmuted
into a byharmony the next moment and the reverse.
Our next example presents I with bytones, V with
bytones and IV with bytones, and all these regnant
harmonies and byharmonies are diatonic. A har-
mony is classed as diatonic when all its concomitants
or components are diatonic.

131 313 151 515 353

ii

TJTTI 4 ' n-t^^lr^t^-^

I

5 3 5

V
3

I

13 1

V
5

I
15 1

i

nJ^.ii\n

t=t

i=£:

li — • — tt

IV

IV

53 5353 393333 313 1

#=&^

:^

IV V I

W

IV

V9

N.B.

Except at N.B. all the above regnant harmonies
are consonances. Except at N.B. the second tone in
each measure is a bytone, but this second tone in
every measure including N.B. is in cadence. With
one exception all the byharmonies are consonances
in cadence. The exception is reported by /a during
the regnancy of I when the byharmony is a four-
tone dissonance as shown by the report of /a as 7. At

118 THE NATURE OF MUSIC

N.B. the regnant harmony is V9 owing to the presence
of la which is at once a regnant tone and in cadence
and, strange to say, resolves into its own harmony.
The ninth is the first harmonic component distin-
guished by these pecuHarities, especially that of
resolving into its own harmony, and la being the
original ninth it was the first tone that appeared in
this paradoxical relation. This characteristic insta-
bility of la as ninth during the regnancy of V, caused
by its position beyond the octave of its root, will be
further illustrated as we proceed seriatim to analyze
the diatonic bytones of each of the three regnant
harmonies under consideration. Let us remember
that at present we are dealing exclusively with dia-
tonic harmonies as defined a moment ago.

A, The diatonic bytones of reg. I are ti 3, re 5,
fa 7, la 3. During this regnancy these bytones persist
each in the harmonic report just given. Even when
playing upon the same regnant tone fa and la persist
in their respective reports as r and 3 as will be heard
in the following fugue-subject of Bach here tran-
scribed from Cj^ to C Major: —

5357531 5737531531

i

:it=3^=^=j=^

^

I V I V I

Previous examples present a sufficient number of
illustrations of these bytones, and what still remains to
be said of them will be found in the chapter on cadences.

B, During the regnancy of V there are but two
diatonic bytones, namely, do 1 and mi 3 as follows : —

i

ACCENT AND REGNANT HARMONY 119

193391 191393 315513

s

--^=t

m

^5E£

Q

313515637 73537373

^>-^jj-^'^f^^UMji

7I99I7 7I7I7I97539I7593 1

f^^^4fi^-gfeif;i|f£^i-. H

The bytone do plays on regnant ti and re, the
by tone mi plays on regnant re and /a. The cadences
of regnant la to regnant sol and <i appear in the
first two measures and are emphasized through
jermaias in the last two measures. These steps of
do, mi and la are the only cadences in our example,
all the other steps being progressions from one reg-
nant tone to another.

C. Regnant IV has four diatonic bytones. They
are mi 3, sol 5, ti 3, re 5. Unless we generate the
feeling of regnant IV we cannot perceive the true
harmonic relations and reports of its bytones. In the
subjoined example of the common reports of these
bytones the feeling of IV is generated in the opening
measures.

13 5 3

351 131151 153

120 THE NATURE OF MUSIC

353 33 3 3353555 3 5

^

^^E^^^^^^-^-j-itti:^

I ! ! I L

Noteworthy among these reports are the series of
major thirds 3 — 3 — 3 (third last measure) and the
series of pure fifths 5 — 5 — 5 (second last measure).
These reports have a bearing on certain important
harmonic questions to be considered later on. We
have now presented the diatonic bytones of each of
the harmonies I, V and IV.

15. Certain changes in the rhythmic distribution
of regnant tones and bytones mark concomitant
changes from an earlier to a later stage of melohar-
monic development, therefore of psychological devel-
opment. Most of the examples thus far given illus-
trate the earlier of the two stages when regnant
tones and bytones occupied the rhythmic periods in
which they first arose, the former appearing on the
heavy (efficient) periods of rhythm-repose, the latter
on the light and unstable periods of rhythm-cadence.
Rhythmic movements being characterized by regular
alternations of light and heavy periods and accents,
that is, by regular alternations of rhythm-cadence
and rhythm-repose in obedience to the universal
shaping principle of equilibrium, we may define this
basic and universal relation of rhythmic cadence and
repose as that of a rhythmic Dominant to a rhythmic
Tonic, since the intoning of this relation caused the
genesis of dissonance (V9) in rhythm-cadence and
consonance (I) in rhythm-repose, therefore of the real

ACCENT AND REGNANT HARMONY

121

Dominant and the real Tonic. The distribution of
regnant tones and bytones illustrative of melodies be-
longing to the earlier of the two stages is as follows : —

Coincident rhythm-repose (heavy period and accent)
and tone-repose (regnant tone).

Coincident rhythm-cadence (light period and ac-
cent) and tone-cadence (by tone).

The later of the two stages is illustrated by melodies
in which regnant tones and bytones exchange their
original rhythmic positions, the former occupying
the cadence-periods, the latter occupying the repose-
periods of rhythm, as follows: —

Coincident rhythm-repose (heavy period and accent)
and tone-cadence (by tone).

Coincident rhythm-cadence (light period and ac-
cent) and tone-repose (regnant tone).

This shifting of bytones from light to heavy rhythmic
periods indicates a great advance in the development
of melody consequent on that of the harmonic sense.
Illustrations appear below.

5135353135315153

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5131 735131533753 [1]

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t=t

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122

THE NATURE OF MUSIC

Further illustrations of diatonic bytones will appear
in the chapter on cadences.

16. The truth that a tone's specific harmonic
form is caused by its specific combined relation in
time and space has been and will continue to be
demonstrated. Thus far each of the seven diatonics
(original tones) ifas appeared as a regnant tone and
as a bytone, and has reported one of the five original
harmonic percepts 1 or 3 or 5 or 7 or 9. Thus far
each of the seven has appeared in the following
harmonic relations: do as 1 of I and as 5 of IV; mi
as 3 of I; sol as 5 of I and as 1 of V; ti as 3 of V;
re as 5 of V; fa as 7 of V and 1 of IV; la as 9 of V and
3 of IV. This summary shows that four diatonics
(do, sol, fa and la) have appeared each in two har-
monies, while the remaining three (mi, re, ti) have
appeared only in one harmony. The former are
bond-tones or connecting links between two har-
monies. Of these sol is the first and the nexus
between I and V, I and V,, I and V9 as follows: —
1 3 5^^^ 13 5^9

I Do — mi — 5oZ I V

I V,

V9

The next bond-tone is do, the nexus between I

and IV.

1 3 5^.-^l 3 5

Fa — la — do Do — mi — sol

Sol — ti — re \—fa

— la

IV I

Sol, being the original bond-tone and first connect-
ing link between two harmonies, was the first of the

ACCENT AND REGNANT HARMONY 123

seven diatonics to undergo a change of relation,
namely, from 5 to 1. Next to follow was do, chang-
ing its relation from 1 to 5. These bond-tones plainly
indicate that the roots of the two harmonies which
each connects lie sl fifth apart. Thus I — V connected
by sol and I — IV connected by do are called fifth-
related harmonies. These fifth-related harmonies are
not only the first of their kind, but are the first of any
kind. This explains why fifth-related harmonies are
nearest related harmonies, why fifth-related keys are
nearest related keys. These fifth-relations also dis-
close the origin of the authentic closing-cadence V — I,
of the plagal closing-cadence IV — I and of the fifth-
cycle of keys. In these diatonic-Major relations the
bond-tones sol and do are in repose and stable, and
this is true of all bond-tones of fifth-related harmonies.
The case is otherwise with the bond-tones fa and la
which in all the relations thus far presented main-
tain their unstable character, which is explained by
the fact that they belong to the genus dissonance.
Whether as bytones to I or as regnant tones in V9
and IV or as bond-tones connecting V9 — ^IV and
IV — ^V9, both fa and la manifest this unstable char-
acter, and they do not gain repose and stability until
they appear in Minor as we shall see in the next
chapter. Meanwhile I present them as connecting
links between V9 and IV.

124 THE NATURE OF MUSIC

17. As defined on a previous page, a harmony
is diatonic when all its components are diatonics.
The test of the pure diatonic harmonies of melody,
in fact of all the harmonic forms and relations of
melody, lies in the common reports of original har-
mony in one voice. In one voice a diatonic in certain
relations generates a thread of harmony in which all
the concomitants are diatonics, while in certain
other relations the same diatonic generates a thread
of harmony among whose components there are
chromatics and even enharmonics mingling with
diatonics, as we shall see in the sequel. Here we are
concerned with pure diatonic harmonies. I, V, V^,
V9 and IV are diatonic harmonies and the only ones
in the Major mode. All forms of harmony are con-
sonances or dissonances. Each specific form of conso-
nance and dissonance had its genesis on a specific
tone in a specific relation, and each such original form
is a prototype. Once generated and differentiated
each prototype is reproduced and repeated on other
tones also in specific relations. The harmonies thus
far generated will serve as an illustration. I, V and
IV are major consonances : I is the prototype of this
specific form and it first arose on do 1; V and IV are
reproductions and replicates, the former arose on re 5,
the latter on la 3. Again, V^ and V9 are major dis-
sonances, and both are prototypes of their respective
forms of which all like forms are replicates. This
concludes the summary of the diatonic harmonies of
the Major mode. In the next chapter, the subject of
which is the origin of the Minor harmony and mode,
we shall encounter three other diatonic harmonies and

ACCENT AND REGNANT HARMONY 125

new forms of consonance and dissonance, all of which
are minor,

18. The operation of the principle of harmonic
genesis and regnant harmony, the efficient accent,
has now been exemplified. We shall resume these
subjects later on, but before dismissing them here
it may be well to pause and observe the operation
of this principle with greater scrutiny. We have
noted that alternating rhythm-periods make for
rhythmic equilibrium, that alternating tone-rhythmic
periods make for combined rhythmo - harmonic
equilibrium, in short, that the connection between
harmonic equilibrium and rhythmic equilibrium is
indissoluble, and that rhythm has transmuted chaos of
sound into perfect tone-equilibrium or harmony. The
shortest rhythm contains two periods. The shortest
melody contains two tones each occupying a rhythm
period, one light, one heavy. Thus the combined
form and equilibrium of composite rhythm and
harmony is conditioned by recurrence of these alter-
nating light and heavy periods. Let the following
wave-lines indicate these alternating periods, first,
in the order light-heavy; next, in the order heavy-
light, and let the repetition marks indicate recurrence.

1 .\ light / heavy^ : 1 1 2. / heavy\ light /: 1 1

r r r r

The notes indicate respectively short-Zongr, long-
short; the dynamic =^ indicates the efficient accent.
Now sing each diatonic whole step and half step in
accordance with these two forms of rhythm and note

126

THE NATURE OF MUSIC

the operation of the ejBSeient accent as it generates and
reports the regnant harmony and determines which
of the two tones is regnant and which is a bytone.
The general result will be as follows: The tone that
falls on the light and short accent is the bytone and
component of the byharmony, while the tone that
falls on the heavy and long accent (efficient accent)
is the regnant tone reporting the regnant harmony
of which it is a component. I first present the
ascending steps.

a) 15 15 6) 53 53 c) 31

VI IV IV

4)

V
5

0 5

m

^^

5 3 /) 9 3

IV

3 g)3 I

IV
3 1

^ J UP .|uJ=^:J|r ■Irn-ti

I N.B. V IV

Next follow the descending steps,
a) 13 1 3 6)3 I

i

fir^I^dSL^t^m

e)

V I

3 5 3 5 d)5 1

IV V N.B.

O 7 e) 7 O

m

^

IV

IV

ACCENT AND REGNANT HARMONY

127

1 3 /) 3 5

a

g)

5 1

^m

5 1

^

w

i

IV

t

At N.B. in both above groups of examples we
again encounter la 9 playing the part of a bytone
during the regnancy of the harmony of which it is
a component. Attention is called to the fact that
except at N.B. the form of all the above regnant
harmonies is that of a consonance. Here we observe
the general truth that the efficient accent everywhere
makes for the stable equilibrium of consonance except
in cases like N.B. where specific relations of specific
tones cause the regnant harmony to take the form
of a dissonance. The above examples illustrate
another series of facts. First, we observe that in
certain relations a regnant consonance is generated
by the efficient accent on a single component as indi-
cated by the tones reporting I, V and IV; second, a
regnant dissonance (see N.B.) is not generated unless
at least two of its components occupy successive
rhythm-periods. We will first take up the conso-
nances I, V, IV. All the components of I possess
this individual power to generate its regnancy, do
by itself, mi when preceded by IV or V, sol when
preceded by IV, as shown below at a). Two com-
ponents of V have this individual power; they are re
and ti; see below at b). Two components of IV
have this individual power, namely, la and /a; see
below at c).

128

a)

THE NATURE OF MUSIC
5 3 5 3 13 5

i

f

6)

IV_

3 5

IV

1 3

J V_

c)l 5

i

i

I V I

5 11 8 11

I IV

5 13 5

i

I

^

^

^

-gi — -»

L

IV

IV L

IV

In its diatonic relations sol cannot report itself as 1
of V except in conjunction with another component of
V. The same is true of do as 5 of IV. This explains
why in their diatonic relations sol individually cannot
generate regnant V and do individually cannot gen-
erate regnant IV.

The regnant dissonances V^ and V9 next claim
our attention. Both of these regnant dissonances
require a succession of at least two components to
generate them, and in generating regnant V^ fa must
be one of the two, while in generating regnant V9
la must be one of the two. Examples of both are
given below, regnant V^ at a), regnant V9 at 6).

a)

5 3

i

V.

ACCENT AND REGNANT HARMONY

129

^m

*)

I V^ I Vv I

95535 95393 1

i

^

^

-#—

g

V9.

I

V9.

V9.

I

3 9 5 1 ,5913 35 931

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s

I

V9.

V9.

V9.

Alternating rhythmic periods are the elements of
rhythmic form; a rhythmic form is therefore a
succession of elements. Harmonic components are
the elements of harmonic form; a harmonic form is
therefore a concurrence of elements. Every such con-
currence occupies a rhythm-period: thus when we
relate one such concurrence to another we are moving
from one rhythmic period to another, and this con-
currence (harmony, form and relation in space) and
succession (rhythm, form and relation in time) are
indissolubly combined. It is therefore perfectly nat-
ural that regularly alternating rhythm-periods of
cadence and repose should have caused corresponding
concomitant alternations of regnant harmonies in
cadence and repose, since both in rhythm and in har-
mony cadence is tend and repose is end of tend. One
illustration will suffice.

3135151353531

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i

IV

^

I

130

THE NATURE OF MUSIC

Such examples of concurrent alternations of rhythmic
and harmonic cadence and repose manifest the direct
influence of rhythm upon the harmonic structure of
melody, while on the other hand the direct influence
of harmony upon the rhythmic structure of melody
is manifested in the lengthening of the rhythmic
periods of alternating cadence and repose from beats
to measures. These reciprocal influences of the two
elements, now of rhythm on harmony, now of harmony
on rhythm, the two always inseparably combined yet
acting and reacting each upon the other in obedience
to the inherent shaping principle of equilibrium, these
are the chief shaping forces in the evolution of the
musical phrase and thence of the larger forms of
music. I will pause here a moment to point out
how harmony may contract and expand the rhythmic
form. In contractions secondary eflScient accents
appear within the limits of one measure (see below at
a)) while in expansions the regnant harmonies may
extend indefinitely and cause the rhythmic forms to
be either perfectly regular (see b)) or irregular
(see c)).

o)

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IV

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etc. or

etc. or

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— I 1—

3^

i

ACCENT AND REGNANT HARMONY 131
5) 3135 3 13 5

^

etc. or

0)

I V

8 13 5

^

?

etc.

513

3 5

^

i

:^=Sia!

f^^4

^

etc. or

V.

5

_IV
5 3 5

Fq^rap^

i

I

i

IV

The next examples illustrate the prolongation of
harmonic cadence in the progressions V — IV and
IV— V at a), IV— V, at h).

I

\

.IV

IV.

«

359315 35

1 3

i

Hir nN

I

P

t

V9

IV.

At a) as we move from <i 3 to /a 3 and vice versa
the concomitant harmonies report progressions in
parallel fifths and octaves which though unseen are
there and are heard. Such parallels are unavoidable.

A general survey of the foregoing analysis of
regnant harmony and the eflBcient accent enables us

132

THE NATURE OF MUSIC

to ask and answer a comprehensive question. Under
what conditions does the change from one regnant
harmony to another take place ? This change takes
place when a hytone of the momentary harmony
falls on the efficient accent. The following examples
present these bytone-changes on single diatonics, and
a few chromatics are also introduced in anticipation
of their subsequent explanation.

i

3 5 3

5313 1353

J=^=T^

lY I

3 15

-Bh — I 0-

II

13 5 1

'-t^

eS:

\]

-IV

etc

This change also takes place when certain single
bond-tones fall on the efficient accent. The first of
these bond-tone changes of regnant harmony is
reported by the single diatonic sol as follows: —

5 9 15

5 5^5915

i

m

i=F-

i

-j|) ^^^5^

V9

In this melody from Beethoven's E flat concerto
the bond-tone sol instantaneously changes from 1 of
V to 5 of I. In such bond- tone changes of regnant
harmony two secondary causes cooperate with the

ACCENT AND REGNANT HARMONY 133

efficient accent, first the tendency to resolve disso-
nance, next the regular alternation of harmonic
cadence and repose, both of which I have already
explained.

The foregoing analyses demonstrate that original
harmony in one voice reports the exact number of
components in a harmonic thread; three components
in I, V and IV, four in V7, five in V9. They demon-
strate that whenever and wherever it is potential in
a relation the efficient accent makes for a regnant
consonance, that is, for stable equilibrium. They
demonstrate that the form of regnant harmony
generated by the efficient accent, be it consonance or
dissonance, is always a question of the momentary
relation and is always the equilibrium of the moment,
consonance being stable, dissonance being unstable
or relative equilibrium.

39. Chords Derived from the Original Consonance
and Dissonance in One Voice

From the prototype consonance I are derived the
diatonic-Major triads I, V, IV known as the three
primary chords.

i

s^i^

W=w^&^^^^

I Y IV IV I V

The common reports of original harmony in one
voice for the first time demonstrate and prove the
truth that these triads may be represented by single
components as well as by any two or by all three.
Every conceivable combination of two or three tones

134

THE NATURE OF MUSIC

lies in these harmonic threads and may represent
each of these triads. Of the many possible repre-
sentations of the triad I, I present the following: —

i

-<2;t-

i

I

I

I

4

etc.

m.

t

jO.-

'J21

-^-

etc.

The triad V may be represented by the single com-
ponents re 5 and ti 3, the triad IV by the single
components la 3 and fa 1. Both triads V and IV
may appear in any of the above two-tone and three-
tone forms.

From the prototype dissonances in one voice, V9
and Vy, are derived the corresponding chords of the
ninth and seventh, also the chord vii^^. Besides these,
the dissonance V9 breaks up into three triads. All
are given below in the order of their mention.

m

^-

3 5

e

1. Chord Roots. V9

2. Original Root. V9

V9

V
V

V9

ACCENT AND REGNANT HARMONY 135

Like the harmonic report of a single tone so also
that of a chord is determined by the relation in which
it appears and varies as the relation varies. All the
above chords in their diatonic-Major relations claim
sol as their common harmonic root. Hence the above
distinctions and discrepancies between chord-roots
and original harmonic roots. Any tone may be taken
as a chord-root. Thus a chord-root may be an
original harmonic root as in V9, V^ and V, or it may
be a harmonic third as vii^y and vii° or a harmonic
fifth as II. The important fact to be observed here
is that certain chord-forms of harmony are detached
from their original harmonic roots. To regard the
roots of the chords vii^^, vii° and ii as harmonic
roots and to symbolize them as i is to create the
greatest possible confusion in the mind owing to the
irreconcilable conflict and utter discord between a
thing and its symbol, between what we really hear
and feel and know to be true and what we are con-
strained arbitrarily to think and what we know to be
false. Hence this truth: No given chord in a given
relation is perfectly comprehended unless we subject
it to the common reports of common harmonic feel-
ing and perception. Hence the necessary distinction
between harmonic analysis with true reports and
chord-analysis with false reports. We shall meet all
the above chords in transmuted relations when we
take up the Minor mode. Here attention is called
to the important chord vii^^, which is composed of the
four original cadence-tones and which I name the
Major-cadence-seventh-chord. In resolution its two
lower tones rise, its two upper tones fall as below

136 THE NATURE OF MUSIC

at a). Chords whose components simultaneously rise
and fall have double cadences. Chords whose cadences
rise only or fall only have single cadences. Below at
b) and c) the double cadence of vii% is separated
into single cadences. At 6) sol is added to the two
lower tones of vii^^, thus forming the triad V
and becoming the bond-tone of the original rising
chord-cadence V — I, the authentic ending. At c)
do is added to the two upper tones of vii^^, thus
forming the triad IV and becoming the bond-tone
of the original falling cadence IV — I, the plagal
ending.

7

5 5 1 5 5 3 5
533533 13

a) 3 1 ^)1 3 1 c)i 5 1

vii^ I V V— I IV lY— I

In this separation of the original cadence-tones in
the triads V and IV, re and ti retain their original
relations as 5 and 3 respectively while the relations
of la and /a are changed, la from 9 to 3, /a from
7 to 1. HarTnonic intervals are indicated by numbers
specifying the exact relation of a tone to its har-
monic root: such are the numbers over the above
chords. C/iord-intervals are computed from chord-
roots. Since any tone, that is, any component of a
harmony may be a chord-root it follows that chord-
roots and chord-intervals are sometimes harmonic
roots and harmonic intervals and sometimes not,

ACCENT AND REGNANT HARMONY 137

wherefore no chord can be understood except through
harmonic analysis. Above at a) the chord-intervals
of vii°7 are root, minor third, diminished fifth, minor
seventh, while the harmonic intervals of the same
tones are respectively major third, pure fifth, minor
seventh, major ninth. These chord-intervals generate
discord between feeling and thought while the har-
monic numbers unite feeling and thought in complete
concord : the former are arbitrary and false, the latter
are self-asserted, unalterable and true. At h) and
c) the chord-intervals and harmonic intervals agree,
but this agreement becomes less and less frequent
the further we penetrate into the domain of chords,
and therefore the call for exact harmonic analysis will
grow correspondingly more and more frequent.

Intervals are further to be distinguished under two
heads: 1. Intervals of concurrence. 2. Intervals of
succession. To the first belong the intervals formed
by the concurring components of a tone's harmonic
thread and of a chord. To the second belong all
steps from one tone's harmonic thread to another
and from one chord to another; in short, all steps in
one voice and in combined voices. Here is an exam-
ple in one voice : —

351535513 ^31

i

IV I v^

In moving from one of these tones to another the
steps are major second, major second, pure fourth,
major second, minor third, and so on. Thus we

138

THE NATURE OF MUSIC

observe the above intervals in the ordinary sense of
length of steps, to perceive and know which is to
perceive and know very little since such interval-
steps give us no intelligence whatever of what is most
essential, namely, the inherent harmony of each of
the two tones in such a step. The essential thing to
perceive and know is that in moving from the first to
the second tone we are stepping from mi the third
of one harmony to re the fifth of another harmony, for
this includes the perception of the whole step or
major second from mi to re and the knowledge of the
length of this step is but secondary and supplementary
to that of the two harmonies. This is true of all steps
in one voice, true likewise of the steps of each chord-
voice as we move from chord to chord. Equally if
not more important is the necessity to discriminate
between the intervals formed by any two tones in
a given chord and the harmonic report of each of the
two tones. Two voices will suffice to illustrate this
point as follows: —

S*^ 55 1311515
153''3''353'^3

^i

^

B

r
I

v^ I V7 I Y^ I V I y^ I

The intervals of these combinations or chords are
as follows: major third, minor third, minor third,
major sixth, minor sixth, augmented fourth, minor
sixth, pure fourth, minor third, major second, minor
third. With these intervals compare the superscribed
harmonic reports and note that the first chord is the

ACCENT AND REGNANT HARMONY 139

only one in which the interval-numbers and the har-
monic report do not conflict. Numbers are used for
so many and various purposes in music that we cannot
wonder that students are so easily confused. Since
the harmonic numbers alone accord with the common
feeling and perception of relations they should bring
some order out of this confusion. The term minor
appears over and over again in the above description
of intervals notwithstanding the fact that the entire
example does not contain a single minor harmony,
percept and concept. Why not like the Germans
use the terms major and minor exclusively in connec-
tion with modes and harmonies? Why not, as they
do, describe major intervals as great (gross), minor
intervals as small (klein) f How much simpler,
clearer, more sensible and practical to describe the
above intervals thus: great third, small third, small
third, great sixth, small sixth, and so on. This
German custom will henceforth be adopted in these
pages.

We have seen that one-voice harmony is self-asser-
tive, that in one voice the harmonies are always com-
plete, that is, single tones give rise to harmonic threads
of three, four and five components. Chords are selec-
tive combinations of tones and may represent a har-
mony incompletely as well as completely : thus a triad
may be represented by a combination of two or all
three of its components ; a seventh-chord by two, three
or all four of its components; a ninth-chord by two,
three, four or all five of its components. Briefly, one-
voice harmony is assertive and its harmonic forms
are complete; chord-forms are selective and may be

140 THE NATURE OF MUSIC

complete or incomplete. A second voice always
implies a first voice to which a second voice is added
and this second or added voice is always selective.
The original guide in the selection of one or more
added voices is the concomitant harmony or harmonic
thread of each tone in the first voice, and this first
voice is always the dominating voice* or melody to
which all added voices are subordinate. In short, the
dominating voice is the melody the concomitant
harmonies of which in every concrete case are this
or that series as generated by the specific relations of
its tones. When Wagner states that his melodies and
their harmonies arise in his mind simultaneously he
calls our attention to a great truth, namely, the
indissoluble unity of melody and harmony. Had
Wagner developed this idea theoretically his psycho-
logy would doubtless have led him to discover original
self-assertive harmony in one voice. The influence
of the dominating voice not alone on the selection of
harmony, but also upon conception and expression,
will be more fully dealt with in the chapters on poly-
phony and chords. The three one-voice harmonies
I, Vy and V9 have given us the complete triad, com-
plete seventh-chord and complete ninth-chord. These ,
three are the prototypes of all like chords. From
common feeling of harmony in one voice we have
derived the principle of chord-building which is to
superadd a third, fifth, seventh and ninth to a
fundamental tone which is the chord-root. We have
seen that I, V and IV are the only three-tone diatonic
harmonies which assert themselves in one voice in
Major. But in chord-building, triads, seventh-chords

ACCENT AND REGNANT HARMONY 141

and ninth-chords may be and are produced on each
of the seven diatonics and are incorporated in the
Major mode. All these chords also appear in the
Minor mode in completely changed relations and
with completely transmuted harmonic reports of their
components directly caused by the changed relations.
In short, a given chord is one thing in Major and
quite another thing in Minor, as we shall see. Mean-
while we here note that chords like one-voice har-
monies fall into two divisions: consonances and
dissonances. Each of these two divisions of chords
subdivides into two varieties, namely, simple and
compound chords. A simple chord is built of the
components of one harmony: such are all the chords
thus far derived and presented on a previous page.
A compound chord is built of the components of two
or more harmonies: this variety of chord will be
explained in the proper place. In chorded music
regnant harmony and byharmony become regnant
chord and by chord. The subject of chords is resumed
in the next chapter.

40. The Tone-Region, Its Diatonic Scales

Each of music's seven octaves repeats the same
series or scale of tones, and forms the nucleus of a
tone-region. The tones of all regions are connected
by their harmonic threads, and the relative pitch of
each tone is due to harmonic relation. The seven
diatonics constitute the first group of tones that was
discovered, expressed and exploited, and the causes
and order of their genesis have been explained. The
tone-region shows the natural juxtaposition of tones.

142 THE NATURE OF MUSIC

Regnant I being the first harmony, do being the root
of this harmony and the original meloharmonie point
of repose which we call the Tonic, it follows that do
is the original centre of the tone-region, as follows : —

sol — la — ti ^ Do — re — mi ^ f a

V I IV

Here the seven diatonics form a scale of two
conjunct tetrachords. The Tonic do is the common
tone and common centre of the two. A tetrachord
is a scale of four tones. The above dashes ( — ) and
curves (w) indicate respectively whole steps and
half steps, and show that the two above tetrachords

have the same form, namely, ^-^. This scale of

seven tones and conjunct tetrachords I have named
the septonate.* The septonate is the nucleus of the
tone-region. What evidence is there that do the
Tonic is the original centre of the tone-region ? The
incontrovertible evidence is adduced from harmony
briefly as follows: —

The cadence of V rises or resolves upward into I;
the cadence of IV resolves downward into I: ergo, I
lies between V and IV. This septonal nucleus of the
tone-region besides being the index of meloharmonie
resolution is also the index of progression. For
example, from V to IV progress upward, from IV to
V progress downward. What is true of these har-
monies is true of the corresponding chords. From
the intuitive feeling of these one-voice self-assertive
resolutions and progressions the rules for treating the
corresponding chords in corresponding relations and

ACCENT AND REGNANT HARMONY 143

for treating all other chords in similar relations in
the same way have been derived by induction.

The diatonics form a scale of eight tones in which
the same two tetrachords are disjunct. This scale
proceeds from the Tonic-centre of one tone-region to
the Tonic-centre of a contiguous region; in it the
two Tonics form lower and upper terminals. This
our familiar Major scale is as follows : —

Do — re — mi -^fa — sol — la — ti Do

I IV V I

A consonant thread of harmony extends throughout
the range of pitch and connects all its components in
all regions. Of these threads I is the genus and
original, V and IV are relative. In the following
illustration the arrows indicate the whole range of
pitch.

I— ^1 — ^iV

i

i

The thread of the dissonant genus V9 extends from
one region into the next, and in each octave one such
thread intersects another thus: —

144 THE NATURE OF MUSIC

At each intersection four components of V9 form
the tetrachord of three consecutive whole steps known
as the tritonus, as follows : —

•^ 1 9 3

fa — sol — la — ti
— ^^

A few of the dissonant chords formed by combining
these tones are next given in close and open positions.

9

3 3

1 -^ 9 1 9 3 9 9 '^

119 19 3 11

7 -g?-

i

i

s?^ f> i-g^

25^

-^^ ^-

^^ TSr

V, V9

Here observe in passing that the tri tonus is the
only tetrachord whose four tones are components of
one harmony and together form a simple chord of
the dissonant type.

A septonate is named by its central tone: thus the
above septonate is the Tonic-septonate. A diatonic
scale of eight tones is named by its terminal: the
above octonal scale is likewise a Tonic-scale. Each
of the seven diatonics may appear as a septonal
centre of two conjunct tetrachords and the octonal
terminal of two disjunct tetrachords, and each such
scale like that of the Tonic is named by its septonal
centre and octonal terminal. Thus sol the Dominant,
fa the Subdominant, mi the Mediant, la the Sub-
mediant, re the Supertonic, ti the Subtonic, each of
these may be the septonal centre and the octonal
terminal and, as these syllables and names imply, all

ACCENT AND REGNANT HARMONY 145

these scales are related to the original scales of the
Tonic. In these scales there are four forms of tetra-
chords as the subjoined groups of symbols of whole
and half steps show.

1. 2. 3. 4.

I---I I---I I---I I---I

I here present the septonal conjunct forms of these

scales.

'' -^-^ "-^

do —re —mi ^s^ Fa — sol — la — ti

ti^do —re — Mi ^^fa — sol —la

la — ti v_^ do — Re — mi -^^fa — sol

Sol—La — Ti^^ Do —Re —Mi v^ Fa

fa — sol — la — Ti s.^ do — re — mi

mi ^^fa — sol — La — ti >w^ do — re

re — mi -^^^ fa — Sol — la — ti s»^ do

The above capitalized syllables of the central
Tonic-septonate and those marking the centre of each
individual septonate form a Greek cross which ap-
positely suggests the Greek modes, which I next pre-
sent in their octonal form of disjunct tetrachords.

^ — & — P5

-^2 ^

La to La Sd \o Sd

Fa to Fa Mi to Mi

i

146

THE NATURE OF MUSIC

g

■Z7-

W

^ sr

-^—TSr

SL

tS* Z?-^

■^—z^-

Be

to

iJe Do

to

2)0

i

Ti

^ — ^ — ^
to

Ti

In three of these septonal and corresponding
octonal scales the two tetrachords in each have the
same form: in both Tonic-scales both tetrachords

have this form, ^^i in both Supertonic-scales

they have this form, — -^ — : in both Mediant-scales

they have this form, ^^ . In each of the other

septonal and octonal scales the forms of the two
tetrachords differ, as the examples show. The appear-
ance of these tetrachords in all music is most common.
For illustrations the reader is referred to Bach's first
** Invention" in two voices and the principal theme
of Wagner's "Meistersinger." All the above tetra-
chords will be found in the following quotation from
Beethoven's E flat Concerto: —

In his book on "The Music of Antiquity" Gevaert
has extricated the Greek modes, their identity and

ACCENT AND REGNANT HARMONY 147

names and their true connection with the church-
modes from a state of greatest confusion. My chief
purpose in bringing forward these ancient modes at
this juncture is to point out the fact that they all lie
in and form part and parcel of our modern tone-
system. Thus far the attempts to harmonize the few
extant specimens of Greek melodies in accordance
with the arbitrary rules of chord-harmony appear
not to have been successful or satisfactory. The
same may be said of the harmonizations of Gregorian
and Ambrosian melodies. Indeed, the consensus of
opinion seems to be that the addition of chords
distorts and destroys the inherent character, power
and simple beauty of such melodies, and that they
should therefore be left unharmonized. This dis-
approval of adding chords to such music, which
originated in one voice, gains significance when we
consider on the one hand that this disapproval
springs directly from the common harmonic sense and
is therefore a common report of common music-
feeling while on the other hand it is natural that no
two investigators should agree on any one series of
chords for a given melody. And why.? Simply
because chord-harmony is purely selective and always
the expression of personal judgment and taste. But
original harmony in one voice and its common reports
place the subject of the music of antiquity and its
harmonization on a new basis and in a new light.
The Greeks had no multi-voice harmony, but they
had one-voice harmony although they did not know
it; they had no idea of harmony in our sense of
chords, but they had the harmonic sense and applied

148 THE NATURE OF MUSIC

the term harmonies to the tones composing their
modes. Their possession of the common harmonic
sense is proved by the fact that on one hand they
perceived that certain tones tended to others (sense
of dissonance), and on the other hand that a certain
tone was final, the tone to stop on (sense of conso-
nance). When Aristoxenus describes the sudden
transition from the pitch of one tone to that of another
as ** the topical motion from the repose of one tone
to that of another" he is unconsciously expressing
his intuitive sense of one-voice harmony. His defini-
tion of rhythm would indeed be a credit to twentieth-
century text-books and encyclopaedias.* If not his
intuitive harmonic sense, what was it that caused
Aristides, pupil of Aristotle, to make these queries,
** Why is it that when I change the mese (middle tone)
all the other tones are wrong; why when I change one
of the other tones, that one alone is wrong.?" Such
evidence that the Greeks possessed the harmonic
sense might be multiplied indefinitely. Books which
shall embody the common reports of original harmony
on Greek, ecclesiastical, in short, on all one-voice
music, remain to be written, a life-work not for one,
but for many. In another place analyses of several
Greek melodies and Gregorian chants will be pre-
sented. Certain types of music are spoken of by
historians and theorists as music without harmony
and music without rhythm. As I have said and
shall reiterate over and over again, melody without
harmony and melody without rhythm never existed.
The concomitant harmony of melody being self-
assertive and its reports being common it follows

ACCENT AND REGNANT HARMONY 149

that every melody ancient or modern is the messen-
ger of common harmonic reports. The rhythm of
ancient melodies may be traced in all cases where the
melody is accompanied by a text, for the alternating
syllabic accents of the text discover the heavy recur-
ring accents which are at once the measure-accents
and the efficient accents of regnant harmony. In
harmonizing the melodies of antiquity the selection
of chords should be made to conform with the
concomitant harmonies which each such melody itself
asserts. Harmonizations so selected would emphasize
and enhance rather than distort and destroy the true
nature, beauty and effect of such melodies, would
strengthen rather than weaken them, and would cir-
cumvent the personal equation. Original harmony
in one voice therefore not only empowers us to per-
ceive the concomitant harmonies of a Greek melody
and Gregorian chant, but empowers us to feel a Greek
melody as the Greeks felt it, to feel a Gregorian chant
as Gregory himself felt it.

41. Musical Moments. Power and Originality
of Music

While thinking, expressing or listening to music
as we proceed rhythmically from tone to tone, from
moment to moment, the inner consciousness unites
with, our whole being is merged in the flight of time
itself; self-consciousness is annihilated, the spirit is
liberated, our self-surrender is complete. During
these musical moments we are dominated and swept
onward by music's elemental forces and shaping
principle; we are ever in the present, now — here^

150 THE NATURE OF MUSIC

now — here. Now denotes time (rhythm), here denotes
space (harmony) : now — here connotes composite form
and relation in time and space, the united harmonies
of rhythm and tone, the musical moment. This
complete obliteration from consciousness of all other
ideas and mental processes, this enthralling concen-
tration of the attending inner consciousness upon
the musical moment, the ever present, is the secret
of music's great, perhaps greatest, power. Whatever
else this power may be, at bottom it is elemental, it
inheres in the elements and principles of music, a
field of investigation far from being exhausted, the
only field free from speculation and open to scientific
accuracy of observation. The true and the beautiful
are rooted in, spring from and are shaped by these
elements and principles, their power is primarily due
to this elemental power, they are vague and myste-
rious in themselves yet nothing could be more real
and potent. At least we know that our knowledge
of the aesthetic power of music must ever remain
limited to what we can learn from its elemental
power. Alike spell-bound, liberated and uplifted by
this great power of the musical moment are the
producing composer, the reproducing artist and the
contemplating listener. The psychology of the pro-
ducing composer is eloquently set forth by Wagner
in his essay on Beethoven. The musical moment
of the artist and listener will be considered pres-
ently.

In the universe of one rhythm struggling for and
maintaining one equilibrium or harmony each motion
and moment are parts of a correlated and equili-

ACCENT AND REGNANT HARMONY 151

brating whole. Each moment in the short space of
a single human life is a rhythmic moment accentuat-
ing the individual struggle for physical, mental, social
and spiritual equilibrium or harmony. When we
consider that music is the direct language of equili-
brium or harmony, and that it directly presents the
universal message of all the arts, we can no longer
regard its universal power as a mystery not to be
penetrated and wholly insoluble. What choice or
will has man to resist universal energy, rhythm and
equilibrium, universal form and principle of form,
all of which underlie, are blended and idealized in
music .^^ I have pronounced music to be the only
universal and only purely spiritual language, but it
is more; it is the language of liberty and freedo^n, it
is a complete whole to which nothing can be added,
from which nothing can be taken away. Can you
add anything to or take anything from a tone, is not
a tone complete in itself.^ Music's elemental power
to absorb the whole attention and to annul all the
ordinary conscious activities of thought and volition
is due more to tone than to rhythm. Musical
rhythm 'per se does not possess this power. Why?
Because we are so pervaded with this law of motion
that we spontaneously take up an initial rhythm,
remember it, repeat it, and therefore anticipate it
without conscious effort of attention, in a word, with-
out knowing it. With tap of hand or foot we often
unconsciously take up any pronounced rhythm in
our environment and sharply mark the recurring
accents to which we sometimes hum an improvised
air. So fixed is the innate rhythmic habit of pre-

152 THE NATURE OF MUSIC

serving the equilibrium from moment to moment,
so keen the sense of keeping time or balance that our
anticipation of the recurring periods of music is per-
fectly definite; because we feel what is coming we do
not stop to think about it. This is why rhythm per se
has not the power of concentrating the whole atten-
tion and does not necessarily even attract the attention.
However, all this is changed when tone, the living and
original voice of music, unites with rhythm; it is
then that the elemental power asserts itself and holds
the attention. Each tone in a musical series com-
mands the entire attention; not one progression or
resolution if unperceived that does not break the
thread of connection, that does not mar our sense of
the whole.. Let the music be familiar or unfamiliar,
in either case absolute attention upon each tone is a
necessity; the momentary relation of each tone must
be felt by the artist else he cannot express it, by the
listener else he loses the connection. In unfamiliar
music it is obvious that the listener cannot anticipate
progressions or even resolutions, but even in familiar
music where he does anticipate them, and where he
anticipates whole phrases, sentences and paragraphs,
nevertheless, he is compelled to rivet his attention
upon each tone -moment, now — ^here, now — ^here.
This rapt attention upon the musical moment is not
the result of any conscious or voluntary effort, it is the
direct effect of music's elemental power, the power
of tone-rhythm. The artist expresses the musical
moment as he feels it then and there. He has grouped
the series of moments in a composition into motives,
phrases, sentences, paragraphs; he has correlated and

ACCENT AND REGNANT HARMONY 153

unified all these parts into a great whole : yet when he
produces his work his consciousness is concentrated
upon each tone-moment, now — here, now — here. It
is precisely because the artist has conceived the whole
in all its parts, precisely because he knows and
anticipates each motive, phrase, sentence and para-
graph, that he is able to concentrate his attention
upon each moment, that he can express then and
there what he feels then and there. Certainly the
artist cannot express now when he is thinking of by
and by. Observe your pupil who while playing on
page 1 is disturbed by the consciousness of an
approaching difficulty on page 2. It is plain that
the thought of by and by is effectually musicidal to
the momentary expression of now. In each tone of
a melody there is a balance of the united harmonies
of time (rhythm) and space (tone) to be perceived,
which if unperceived then and there are lost forever.
Common music-feeling in which this union of har-
monies originated, whence it emanates, to which
it alone appeals and is directed, is therefore at once
the originator, the transmitter and receiver of the
rhythmo-harmonic voice of music, melody. The
psychology of music's elemental power presents an-
other chapter, the subject of which is the operation
of the law of gravitation in the domain of feeling and
thought. Light rhythm-periods tend and resolve into
heavy rhythm-periods, which are rhythmic centres
of gravity; dissonances tend and resolve into conso-
nances, which are harmonic centres of gravity : in both,
this tendency to resolve is attraction into equilibrium.
Having thus roughly explained music's elemental

154 THE NATURE OF MUSIC

power as concentrated in the musical moment we will
next briefly consider music's originality and unique
position as an art.

Tone has just been described as a complete whole
to which nothing can be added, from which nothing
can be taken away. Tone is unique, therefore
original; there is nothing like it or comparable to it
in the entire realm of expression in which it has but
one rival, speech. But the spoken word describes,
defines, voices something not itself and is a means
to an end, while tone directly voices itself, only itself,
and is at once both means and end. Again, the
spoken word has a specific meaning, a meaning put
into it, while tone has a universal meaning, a meaning
not put in but inherent, which is harmony. Tone is
directly presentative ; tone-language ^presents itself and
nothing else; it does not and cannot represent or
misrepresent, nor can it be represented in artificial
substances or forms. Music is idea in tones, no
more, no less. Tone-rhythm embodies and presents
the music-idea, nothing else. When we contem-
plate music we contemplate the reality, the thing
itself, music. A statue or portrait of a man is a
statue or a portrait, but not the reality, the thing
itself, a man. Tone-rhythm is substance and form
in one. Substance and form of what.? Of the
music-idea, which is melody, the composite of rhythm
and harmony. Unlike the substances which the
other arts change from their original form into some-
thing else, into a building, a statue, a painting, the
substance of music permanently preserves its original
form, is immutable, cannot be shaped into anything

ACCENT AND REGNANT HARMONY 155

but music. The subject of music or the music-idea
is always melody, the substance and form of music
is always tone-rhythm, therefore in music the subject
and the substance are not only always united, but
neither exists independently of the other, the two
cannot be sundered. Great and greatest music re-
quires no fuller titles than Melody in A, Sonata in B,
Symphony in C. This perfect union and insepara-
bility of subject, substance and form in the music-idea
or melody which directly presents itself and which
cannot present something not itself, at once points
out the originality of music, its unique position as an
art and distinguishes music from the other arts. I
have just defined music as idea in tone. More wide-
spread than one might suppose is the narrow view
which limits the idea to that which can be expressed
in words. Were this true the inner psychical world
of ideas would be deprived of much besides music.
An idea is that which conveys complete sense to the
mind no matter what its peculiar form or vehicle may
be, no matter what sense or combination of senses it
appeals to. The mind's wealth of ideas is limited
only by the number of forms or vehicles in which to
embody and express ideas, and no one form of idea
has a perfect equivalent in any other form. There
is no equivalent in words for an idea in tones and vice
versa. A beautiful melody is a perfect idea in tones
just as a beautiful poem is a perfect idea in words.
Each is perfect of its kind, the one no more so than
the other, perfection being absolute and not relative.
We may compare the psychology of the two ideas and
their relative power, not their truth and beauty, for

156 THE NATURE OF MUSIC

the true and the beautiful are ever perfect. How
vain, hopeless, even absurd is the seeking of equivalent
ideas in words for ideas in tones.

The language of tones alone completely voices and
harmonizes the composite inner experience; it is the
inner world of harmony governed by the same laws
as the outer world which it mirrors, it is therefore a
whole; universal harmony is its essential message,
universal harmonization of mankind is its essential
purpose and function. The composite inner experi-
ence with its infinitesimal number of elements is
summed up in the momentary mood (Stimmung), and
the most we can say of the ever changing mood is that
it is now brighter, now darker, or now lighter, now
heavier; that it varies in the individual and is not
the same in any two individuals. Music attunes the
momentary mood of one, of all; here lies its power,
the power of the musical moment. All the other arts
share in the universal message and purpose, but no
one or combination of them so pervade the inner life,
exert so great a power or occupy so unique a position
in the art-hierarchy as does music. In the drama we
note that the other arts merge into, aid and strengthen
each other in accomplishing the essential purpose of
the drama which first of all is pure illusion. But
music being a whole and complete in itself does not
and cannot merge with, be aided and strengthened by
the other arts. The drama is illusion, music is reality;
the drama represents, music presents. Drama and
music are therefore antitheses, each is most potent by
itself, each antagonizes and disturbs the other when
the two are associated, as in the music-drama. For

ACCENT AND REGNANT HARMONY 157

these reasons in the main the music-drama is a work of
hybrid not of pure art. Whenever and wherever music
presents itself it attracts and dominates the attention.
In all its associations with other arts music refuses to
play a second part and never does. The composers
of songs, cantatas and operas are great and greatest
only when and where their music is great and greatest.
Music-contemplation is disturbed in the opera by the
presence of scene and action, in the cantata by the
implied scene and action which the imagination must
supply. Words expressive of pure sentiment alone
blend harmoniously with music, and when distinctly
rendered do not disturb music-contemplation, where-
fore as a work of art the song is purer than either
cantata or opera. Such hybrid art-creations, while
they are justifiable, exert immense power and may
even be called great, nevertheless as works of art
they are not pure. As a matter of course absolute
music is the most pure and potent music. Pure
enjoyment in music-contemplation is grounded and
dependent on anticipation, that is, on familiarity with a
composition. The greater this familiarity the greater
our enjoyment, the keener our anticipation of each
musical moment; it is then that we yield ourselves
completely to the power of the musical moment. The
unfamiliar conduces to another species of enjoyment
during which the mind maintains the attitude of
interrogation as what next.^ but this is not the true
mental attitude of complete receptivity and pure
enjoyment. Every public performance demonstrates
that the familiar is most enjoyed, wherefore two thirds
of a programme should be made up of familiar com-

158 THE NATURE OF MUSIC

positions. Great music and the great scenes of
nature affect us similarly. Both stir us to the core
and pervade us with the sense of infinity. In the
contemplation of either we enjoy, absorb and are
benefited, each according to individual capacity and
receptivity, just so much, no more, no less.

Owing to its peculiar elemental power, its complete-
ness in and by itself, the universality of its message
and function, the indissoluble unity of its subject,
substance and form in melody, it is futile to compare
music with the other arts. Architecture is often
chosen for this purpose of comparison because like
music it is a presentative art, and certain analogies are
traced in its static rhythms and harmonies and the
mobile rhythms and harmonies of music. *' Archi-
tecture is frozen music," is a frequent quotation. If
there must be comparisons let them be sought in the
myriad recorded and mobile rhythms and harmonies
of nature and not in the other arts, whose subjects
are too specific and definite and fix the attention
upon the same single idea or group of ideas, thus
directing thought and feeling into the same definite
channels. There is however a broad common ground
which music shares with all the arts. Each art, music
included, has its peculiar form or vehicle of expression
in which each in its own way embodies human thought
and feeling. All art is self-expression, and every art-
work springs from the imagination. But the building,
statue, painting which we behold are finished per-
formances; each stands before us in its entirety; each
has been produced once for all time; each time we
look at it we behold the same performance; each such

ACCENT AND REGNANT HARMONY 159

work may be contemplated at leisure; we may-
observe its points in any order we please and may
discuss them with a companion without disturbing
the moments of contemplation. None of these par-
ticulars apply to music. The composer's original and
finished creation is a book of symbols comparable with
the plans and specifications of the architect. True
the musician may read the book and hear the music
in the way that Carlyle preferred to see plays, "in
the theatre under my hat." But the music- work to
be contemplated by the listener must be performed,
not reproduced, but actually and audibly produced;
each and every hearing involves a fresh and indepen-
dent production. No artist, no conductor can exactly
duplicate a previous production; each is new, indi-
vidual. A music-work is produced then and there
and contemplated then and there on the spot; now
it begins, now it is ended and ended forever, it has
passed into eternity along with the moments during
which it held artist and listener united by its magical
spell, a mere evanescing memory to look back upon
and talk about. Not only are the moments of pro-
duction and contemplation concurrent, not only do
they begin and end together, but they concentrate the
attention of both artist and listener upon one and the
same idea; their duration is prescribed and limited;
there is no looking backward until the final harmony
has ceased to vibrate. Artist, it is difficult to determine
which is the greatest, your responsibility, your power,
or your privilege. Your responsibility is great, stand-
ing as you do between the masters whose creations it
is your power and privilege to recreate and your

leo THE NATUEE OF MUSIC

fellow man to whom you interpret these creations.
Your responsibility to the master-genius is twofold:
first of all, because the message of music is universal;
next, because the universal message embodied in
great music is the quintessence of an integral portion
of its creator's inner life, of his experience of universal
experience, for which he demands a corresponding
integral portion of your inner life and experience, — ■
life for life, heart-beat for heart-beat, a whole for a
whole, and all this for each and every performance.
Your responsibility is not lessened in that your
performance is not handed down to posterity like
a building, statue and painting for deliberate con-
templation and for critical essay and assay. Yours is
but a moment, a unique moment in infinite time;
yours is a unique power and privilege exerted at the
musical moment when your heart-beat is merged
with the heart-beat of hundreds, even thousands of
your fellow men in one harmonious rhythm, **im
Ganzen, Guten, Schoenen." Worthy are those who
do not shirk the responsibility, who do not abuse the
power and the privilege.

42. Subrhythm and Rhythm-Expansion. Music's
Classic Form

The term period here used only in connection with
rhythm applies to rhythm-waves of every form and
length. There are beat-periods, subbeat-periods,
measure-periods, periods of two and four measures, of
three and six, of eight and twelve measures, and so on.
A beat-period may be divided and subdivided into
shorter and shorter waves or periods; a measure-

ACCENT AND REGNANT HARMONY 161

period may be expanded into longer and longer waves
or periods and the form of a wave or period may be
regular or irregular while every form is reducible into
the elementary rhythm-numbers 2 and 3. Equili-
brium, the shaping principle, requires a wave of one
length to be followed and balanced by another wave
of the same length. A long period or great wave is a
balanced composite of successively shorter and shorter
balanced periods or waves whose relative lengths and
intensities are equal divisions and subdivisions of the
whole, the balance of each being relative to that of
all the others in the balanced whole in accordance
with the inherent principle of form. Among all these
waves or periods there is one which is at once the
characteristic and fundamental rhythm inherent in
and reported by every phrase of melody. This
foundation-period, the predominating and character-
istic pulse of music-thought and feeling I name the
suhrhythm. The symbol of the subrhythm is the
measure. When two-pulse the subrhythm is written
in dual measure; when three-pulse, in triple measure.
The subrhythm is the thing itself, the basic rhythm-
idea, while the measure is only its symbol. Since
the names of things and those of their symbols are not
interchangeable, and since we possess no term for
what is here designated as subrhythm, I do not hesitate
to add this term to our overstocked nomenclature.
Periods shorter than the subrhythm play upon the
subrhythm, they present the play of rhythm upon
rhythm. Periods longer than the subrhythm are ex-
pansions of the subrhythm first into phrases, next
into groups of phrases, next into groups of groups of

162

THE NATURE OF MUSIC

phrases. In the following illustration the forms of
all the periods are dual.

3 13 913 13 91313 515 13

^jfM-'Mf-^^-nf-htj; r iJ f If Ji

IV IV I IV VI

In their relative order from shorter to longer the
above wave-lines indicate respectively beat-periods,
measure-periods (subrhythm), two-measure periods,
four-measure periods, lastly the whole or eight-meas-
ure period. Just as each shorter period is balanced
by another of the same length, just so the larger eight-
measure period requires another eight-measure period
in order to effect a balance. Thus the repetition of
the eight-measure period produces a still greater wave
or period of sixteen measures. The possibilities of
rhythmic expansion are alone limited by the percep-
tive and conceptive faculties. Although our example
presents the simplest form of rhythm it suffices to
illustrate the subrhythm and its expansion. On the
line of least resistance the repetition of an initial
subrhythm is spontaneous; however, it is an error to
speak of repetition as a principle of form, since it but
superficially describes the operation of the actual prin-
ciple, equilibrium. The regular alternations and repe-
titions of periods long and short are plainly due to the
cardinal shaping principle, equilibrium, which is the
vera causa of balanced motion and rhythmic unity.

Appearing in the above example are the numbers

ACCENT AND REGNANT HARMONY 163

2, 4, 8 and 16, namely, groups of two beats, and of
2, 4, 8 and 16 measures. All these numbers reappear
in the potential divisions and subdivisions of one or
both of the subrhythmic periods or beats as fol-
lows : —

2

r r i; ; I :? :5 II ^ I e^

Thus we observe on one hand the expansion, on
the other the division and subdivision of the sub-
rhythm, the latter being illustrative of what I have
just called the play of rhythm upon the subrhythm.
This play of rhythmic thought upon the subrhythmic
periods is further illustrated by the following list of
rhythms potential in a single period of the subrhythm.

1. r

y

2.

1/ or -• 5 or J 1

3.

e^ o. q ^ or g^

4.

f fL^* or U ^ or -> y

5.

UJ <" ^U - t^'

6.

LUS or q IJI,' or ' q r f •

7.

L/ o' L=b'

8.

gj- or gj q or q f or

Students after working out this list resulting from
the division of a quarter-note will find it profitable
to work out other lists headed by notes of other
denominations, as ^ , T , J . Each of the four result-

164 THE NATURE OF MUSIC

ing lists will present the same series of rhythms and
each individual rhythm will appear in another set of
symbols thus : —

1. °

r

r

2. r r

r r

r r

3. r r r

LJ r

f-r '

etc. etc. etc. etc.

This work may be supplemented by four other
lists in which the unit is divided into three parts as
follows : —

1. ^- f f f

2. r r r r r r lji^ £±/

3. r r r r un ^uj ^'^ r

etc etc. ete. etc

Such rhythmic work will cultivate alertness of obser-
vation and is stimulating to the imagination. How
to pursue and apply such work will readily suggest
itself to teacher and student.

In its diversity of rhythmic forms, its play of
rhythm upon rhythm, its inexhaustible combina-
tions, mixtures and groupings of the most diverse
rhythms, music has only one rival, nature. Although
from the view-point of evolution mensural music is
but a thing of yesterday, although our historians
speak of much of the ante-metrical music as music
without rhythm, nevertheless when we consider that
all motion is rhythm, and that all form is rhythmic
form shaped by equilibrium, it follows that rhythm-

ACCENT AND REGNANT HARMONY 165

less music is inconceivable and never existed. That
it never did exist, and that tone and rhythm have
never been separated in music, has been demon-
strated and proved in precedent chapters of this
book by the truth that the original form and rela-
tion of tone, namely, consonance and dissonance in
one voice, had their genesis in the stable and unstable
equilibrating periods of rhythm. This indissoluble
union of rhythm and tone took place not by any
voluntary effort of man, but under the impulse of
inherent laws. The high degree of rhythmic com-
plexity attained in primitive music is a familiar fact
of history. The rhythm of primitive chants and songs
unaccompanied by instruments was emphasized by
words or gestures or both together, and when accom-
panied by instruments the rhythmic emphasis was
further intensified by drum, pipe and string. In all
this musical exercise, the results of which must have
been very crude in its early stages, common feeling of
rhythmic sound was its common guide, while pleasure
in and love of rhythmic sound were its common
stimuli. Moreover, this exercise in its early stages
was marked by an instinctive and unconscious
obedience to inherent and unwritten laws, not so
difficult to be sure as conscious obedience to written
laws. The effect of this pleasure-gratifying and un-
conscious law-abiding exercise of the music-sense was
the slow dawning and developing of that keen and
accurate perception which is the source of all our
knowledge of music, the evolution of perception
being the road upon which all knowledge has been
gained. This pleasure-gratifying and law-abiding

166 THE NATURE OF MUSIC

exercise in rhythmic sound on the road to true per-
ception is traceable throughout music's development.
The story of the development of pure instrumental
music is not long in telling. The primitive woods-
man beat upon a hollow tree-trunk and the sound
pleased him; the primitive shepherd blew into a
reed and the sound pleased him; the primitive war-
rior twanged his bowstring and the sound pleased
him. Because the sound pleased woodsman, shep-
herd and warrior they kept on beating, blowing and
twanging, man has kept on beating, blowing and
twanging ever since, does so to-day, and promises to do
so in the future. In the hollow tree-trunk the prime-
val woodsman discovered the principle of the drum,
in the reed the shepherd that of the wind-instrument,
in the bowstring the warrior that of the stringed instru-
ment. All sorts of drums, pipes and stringed instru-
ments in all sorts of shapes were fashioned out of all
sorts of materials favoring the principle of each class.
Steadily advancing perception, selection, craft and
art gradually employed and combined the best mate-
rials, discovered and produced new materials, modified
and improved shapes, added new principles such as
stroke of bow and blow of hammer on string, im-
proved and perfected many old instruments, discarded
many others and invented new ones. And all this was
accomplished under the impulse of steadily evolving
music-feeling and music-art in fulfilment of inherent
laws and principles. Result: the modern orchestra
with its choirs of perfected instruments, the great
organ, the pianoforte and their respective literatures.
The basic group-numbers of rhythms being 2 and 3,

ACCENT AND REGNANT HARMONY 167

it follows that the forms of music-rhythms are as diverse
as are the regular and irregular combinations of these
elementary group-numbers, first in the subrhy thm, next
in the potential subdivisions and expansions of all the
potential subrhythms, which is to say that the diver-
sity of music-rhythms is limitless. The classification
of music-rhythms is roughly outlined under the four
following heads: —

I. Simple groups of 2. Simple groups of 3.
II. Compound groups of 2. Compound groups
of 3.

III. Mixed groups of 2 and 3, as 5, 7, 10, 11, etc.

IV. Simultaneous groups of 2 and 3, and of their

compounds and mixtures.
The forms of I and II are regular; those of III
and IV irregular. It is possible, though rare, that the
subrhythmic periods and all the shorter and longer
periods resulting from the division and expansion of
the subrhythm may be regular throughout. But what
should be emphasized here is the fact that while a
subrhythm may be regular its shorter and longer
periods may present many irregular forms, and con-
versely, while the subrhythm may be irregular its
shorter and longer periods may present many regular
forms. This great variety of potential subrhythmic
forms, the limitless possibilities of their division and
expansion, the commingling and concurrence of regu-
lar and irregular forms, the infinite possibilities in
multi-voice music of the interplay of rhythms, not
only of one rhythm on another but of rhythms upon
rhythms, all this plainly intimates the inexhaustible
wealth of music-rhythm.

168 THE NATURE OF MUSIC

The subrhythm, the written form of which is the
measure, is named by the number and length of its
periods, therefore by its measure or metre. The sub-
rhythmic period is a beat of the measure. The
measure of subrhythms may be simple dual or triple,
compound dual or triple, mixed dual or mixed triple,
that is to say, the measure may contain 2 or 3 or 4 or 5
or 6 or 7 beats. The measure of five beats is mixed
dual because 5 is divisible into two parts, namely,

2 + 3 or 3 + 2. The measure of 7 beats is mixed
triple because 7 is divisible into three parts, namely,

3 + 2 + 2, 2 + 3 + 2, or 2 + 2+ 3. The length
of a subrhythmic period is named by that of the beat
of a measure and may be a I or J or ^ or I^ ; it may

also be a 1 , I , JJn or j^. Hence the various

indices of the measure of subrhythms as |, |, |, |, and
so on. The above dotted notes are suggested as
measure units and may be marked in the measure-
index by a corresponding dot after the number
indicating the unit as 1. instead of %, I instead of
I, I instead of |, |, instead of |, I, instead of ^^, etc.
All this but suggests the possibilities of diverse sub-
rhythmic forms, while those of the subdivisions and
expansions of those subrhythms must needs be left
to the suggestion and imagination of readers and
composers.

Music has another resource for variety of rhythms
in another mode of division peculiar to itself. I allude
to the division of a unit into three parts or triplets as

a . . 3

G> into p p p , p into m f 9y m into # ^ # , and so

ACCENT AND REGNANT HARMONY

169

on. There are yet other resources arising in the
play of the imagination upon the subrhythm; for
example, the play of a 3 on a subrhythmic 2, of a 5
and 6 on a subrhythmic 4, and so on, not to mention
the possibilities of new forms arising by subdivision
and expansion of these play-rhythms.

a) I r r

1 I

r r

Li' r r

etc.

b)t r

3
f F P ^

fill

r r r rr

t^n^n^

Also the play of 2, 4 and 5 on a subrhythmic 3,
not to mention possible subdivisions and expansions,
as follows : —

ir

r

4

r r

r

r r r r r

etc.

Next, an example (Chopin Op. 42) where the
melody sings a 2 to the subrhythmic 3, the former
dividing the accompanying figure into 2x3, the latter
dividing it into 3x2, as follows: —

hfhr h_d

r r r

P P

r r

etc.

Next, an example (Schumann "Des Abends")
where the melody sings 3 to the subrhythmic 2 (a))
and later continues the same thing in syncopation as
at 6).

«) 2

8

£j/^f..^.^^d^.^

etc.

170

THE NATURE OF MUSIC

Our next example illustrates two concurrent melo-
dies, the subrhythm of one of which is I or 1., while
that of the other is |.

J N r-r-i

J-^JJ F.

r u

N 1 H 1
1 1 1^

etc.

W^f^fi' ^

'^t ^^»

• ^^ « _

r r

r f

r- f

To sum up : Below are the five forms of elementary

periods.

TWOS

^ '^^—^ ^^

light heavy heavy light

THREES

light light heavy

light heavy light

heavy light light

Any of these forms may be the subrhythmic period
of, may appear in the smaller and larger periods of
the subrhythmic divisions and expansions. In any
period the above forms may be simple, compound or
mixed. In simultaneous rhythms the possible concur-
rences of twos and threes, their compounds and mix-
tures are simply endless. A single larger period of
simultaneous rhythms may combine the greatest vari-
ety of regular and irregular forms. No single music-
work is so rich in variety of rhythms as Bach's " Well-
tempered Clavichord." Mozart and Beethoven, the
former notably in the subdivisions of the subrhythm,
the latter in both the subdivision and expansion of the

ACCENT AND REGNANT HARMONY 171

subrhythm, present a great diversity of forms. More
complex rhythms of the classes III and IV appear
in profusion in the works of Berlioz, Liszt and
Wagner, of Chopin, Schumann and Brahms, of
Tschaikowsky, Strauss and others. Music's struc-
tural development has followed the natural law by
which forms proceed from simple to complex, from
regular to irregular, from homogeneity to hetero-
geneity. Music-rhythms are boundless as thought,
imagination and expression; they are however the
shapes of music-thought itself and are not to be
viewed and treated as moulds into which composers
shape music-thoughts as caterers shape cakes and ices.
Music-thought and imagination shape tone-rhythm
and necessarily obey and fulfil the law of being inher-
ent in tone-rhythm. Melody, the composite of the
two elements rhythm and harmony, the flower of
music and the essential form of the music-muse, has
undergone great structural changes and will undergo
other changes as the evolving music-muse may require.
Greatly as old and modern melodies differ in structure
yet they all obey and fulfil the shaping principle of
tone-rhythm and they are all based upon a common
structural unit, namely, the phrase. The phrase
appears everywhere, in bird-song, in folk-song, in
the melodies of all composers. Differences in struc-
ture lie first of all in the form and next in the treat-
ment of the phrase. The phrase as presented by
self -developed melody in a state of nature is one thing
while the phrase as developed in the creations of
music-art is quite another matter, although both are
links in a chain of continuous evolution. In fulfil-

172 THE NATURE OF MUSIC

merit of the shaping principle of equilibrium the first
great end and aim in melody's self-development was
perfect symmetry, and this meant perfect simplicity
of form. In a state of nature and under conditions
of complete freedom to bud and blossom into perfect
form in conformity with the laws of its being, melody
attained this end and aim in the folk-dance and
folk-song in which it directly and spontaneously voiced
the soul of the people. This perfect form of ideal
beauty attained by melody in a state of nature is
nothing short of wonderful. In melody's structural
development its two elements rhythm and harmony
have acted and reacted upon each other and have
played an equipollent part. The simple symmetrical
melody arose under the predominating influence of
rhythm at a time when harmony was little developed
and the chord unknown. On the other hand, the
more complex structures of modern melodies have
arisen under the predominating influence of melody's
rapidly developing element of harmony. But nothing
could be wider of the truth than the view that in
modern music melody has been supplanted and super-
seded by harmony. Melody being the raison d'etre
of harmony could not be supplanted by one of its
elements. I repeat: no melody, no harmony; no
melody, no idea ; no melody, no music. From first to
last music is melody and all composers are melodists.
In fulfilment of the shaping principle of equili-
brium short and simple tone-rhythms expanded into
symmetrical phrases, and these phrases then ex-
panded into the symmetrical folk-melody. This reg-
ular expansion of the subrhythm into larger and

ACCENT AND REGNANT HARMONY 173

larger symmetrical periods lay in the rhythmic nature
of things. Melody in a state of nature could develop
no further and was ripe for greater things, was ready
to enter the realm of fine art, *'the paradise and play-
ground of the human spirit." Melody did enter into
this domain of constructive thought and imagination
and the classic form of music took root. Regular
symmetries in smaller parts and wholes naturally led
to regular symmetries in larger parts and wholes.
Hence the classic sonata and symphony, in creating
which the old masters simply felt, obeyed and fulfilled
the shaping principles of tone-rhythmic thought, leav-
ing it to others to define these principles. Genius was
their guide and law, art and its universal message was
their absorbing end and aim. Nothing could have
been more natural than these regular symmetries and
the prominence of the group-numbers 2 and 4 both in
the germinal melodies and larger structures. Are
not nature's most obvious rhythms dual and regular,
has not nature produced bipeds and quadrupeds in
fulfilment of equilibrium, do we not walk on two feet
and group our steps in twos and fours .? True our
modern composers have profited by nature's further
teaching that there are countless irregular symmetries
both in minute forms and in large aggregates and
masses, all of which are pervaded and ruled by har-
mony. But regular symmetries which in music corre-
spond w4th perfect simplicity of form had to come first
and did come through the influence of rhythm, while
through the influence of harmony have appeared those
irregular symmetries in the phrases, melodies and
larger structures of modern music which have been so

174 THE NATURE OF MUSIC

unjustly condemned as unsymmetrical because they do
not square with the regular symmetries of the classic
form. However, such criticisms as well as the concep-
tion of the classic forms as conventions and models to
be strictly adhered to have their origin in the minds
of analyst and theorist, who necessarily follow "limp-
ing" in the wake of genius. In a previous chapter
a distinction was drawn between rhythmic time and
mathematical time or clock-time: the former has the
group-pulse or accent which the latter lacks. The
same distinction holds between rhythmic and mathe-
matical symmetry. The regular symmetries of the
classic form are rhythmic, not mathematical, and
therefore the classic sonata and symphony are not
to be likened to the geometrical patterns of French
gardens and the regular squares of a modern city.
Symmetry in music, be it regular or irregular, is always
rhythmic. When we consider that rhythm pervades
body and soul and that we spontaneously express the
group-pulse or accent in our ordinary bodily move-
ments and speech, it is strange, to say the least, that
so large a proportion of performers seem not to know
what the rhythmic group-pulse is and in their per-
formances so often remind us of clock-time.

The folk-melody is the bloom of ages upon ages of
evolution, and its perfect form of ideal beauty is one
of the countless wonders of nature. The thought
and imagination which developed this free-born
melody into the perfect rhythmic balance and unity
of the classic form, and which is so simple and naive
in Haydn, so pure and balanced in Mozart, so great
and potent in Bach and Beethoven, constitute the

ACCENT AND REGNANT HARMONY 175

record of music's first great wave of development as
an art. The classic form is not only to be regarded
as the necessary culmination of a wave of psychical
development, but is an ideal and spiritual achievement,
an eternal glory, which no extravagance of language
can overestimate. In it, all that has followed is
rooted, for music-art is a continuous evolution, the old
and the new being one in kind and links of one chain.
In music, as in all the arts, the classic constitutes the
firm rock of its school, it is the basic school of music-
culture for composers, performers and listeners.
Composers and performers thus schooled are quickly
detected. "Learning to know the best that has been
thought, said and done," this, Matthew Arnold tells
us, is culture. For music-culture we should therefore
turn first of all to the old masters whose works
clearly reveal the fundamental principles of tone-art.
We may then turn to the modern masters not for the
purpose of learning as some think how they have
violated laws, but to continue our culture. Genius
enforces, does not violate, laws. Its ideal and spiritual
content, the potency and universality of its message,
not its specific form, constitute its justification and
greatness before the tribunal of beauty, the art-deity.
This message and greatness like beauty itself are
mysteries, yet in the presence of a great work of art
they are realities: the beauty of the work is unmis-
takable, es packt

CHAPTER V

ORIGIN AND NATURE OF MINOR

43. Origin of the Minor Consonance

With the subject before us we resume our study of
the evolution of harmony in one voice, which is the
self-asserting harmony of melody. Music began with
one voice, that is, with melody, wherefore origins are
to be sought in one voice or melody. Our study is
centred in melody, our facts are the common har-
monic reports of melody, our test of truth is common
feeling and perception of the self-reports of melody.
This confirmed by common experience and observa-
tion is the truth of our theses, namely, that melody is
the indissoluble composite of rhythm and harmony
and not an element; that melody apart from mode,
that mode apart from harmony do not and never did
exist; that in one voice the harmonic reports of
melody are common reports and are not mutable
except through arbitrary personal selection; that the
efiicient accent on an isolated tone always generates
the major consonance, in other words, that the
natural harmony of a tone is major. Independently
the last thesis suffices to establish the priority of the
major consonance and mode. But overwhelming
and conclusive evidence of the priority of major is
furnished by bird-songs and primitive melodies most
of which are in major while the proportion of those

ORIGIN AND NATURE OF MINOR 177

in minor is exceedingly small. The major mode arose
when the major consonance arose; the minor mode
arose when the minor consonance arose: the ques-
tion of the origin of the mode therefore resolves
itself into that of the origin of the consonance with
which it sprang into being and in which it is rooted.
How melody brought forth major has been fully
explained. How melody brought forth minor is the
study confronting us.

An isolated tone never generates and reports the
minor consonance. It is true that on an isolated
tone we may think and hear the minor chord as we
may any one of a hundred other chords, but in so
doing we think and hear what we select, not what a
tone itself asserts and reports. Now in this our study
of one voice or melody everything hinges upon our
power to discriminate between the self-report of a
tone and personal selection. The former alone is
free from bias and has value ; the latter is all bias and
valueless. Whether discrimination between the two
be easy or difficult, in no way affects the truth of our
thesis that an isolated tone never reports the minor
consonance, nor does it affect any of our data and
theses.

In evolution a new something springs from a previ-
ously existing something. Since major came before
minor it follows that minor sprang from elements
previously existing in major. We have explained
how melody began by intoning the rhythmic relation
of cadence and repose and thus brought forth the
major consonance and its cadences, that is, the major
mode. Hence our thesis: the form of harmony is

178 THE NATURE OF MUSIC

due to relation. Later we demonstrated that certain
changes in relation generate new forms of harmony.
Hence our thesis : new forms of harmony spring from
previously existing tones in new or transmuted rela-
tions. This thesis points out the solution of the
centuries-old puzzle as to the origin and nature of the
minor consonance and mode. It required at least
two tones and a specific relation potential in those two
tones to generate the minor consonance in feeling and
perception. The two tones in which that specific
relation was potential previously existed in major.
What are the two tones, what the specific relation.?
The tones are do and la, the relation is a small third.
The downward step do to la with the efficient accent
on la generates the harmonic thread of the minor
consonance as follows: —

i

^^^3

I

¥

^^

do la do la /

This I claim to be the origin of the minor conso-
nance and mode in one voice. Our example illustrates
the self-assertion of the minor consonance and demon-
strates that this specific form of harmony springs
from the repose or stable equilibrium inherent in the
specific relation of the small third formed by do and
la. Apart from two tones in the above relation of
a small third the minor consonance cannot be felt,
heard, thought or expressed, and therefore could not
have been generated and asserted by melody. On
the other hand, apart from this consonance which we

ORIGIN AND NATURE OF MINOR 179

all recognize and therefore relate as the minor Tonic-
harmony it is impossible to feel, perceive or conceive
the minor mode.

In one voice, specific relations of specific tones give
rise to and report specific forms of stable and unstable
harmonies, that is, of consonances and dissonances.
Just what these specific relations, tones and forms of
harmony are we learn from our common feeling and
perception of the self-reports of melody. In observ-
ing and verifying the common reports in one voice we
stand on common intellectual ground, for when that
which we think, fully and faithfully interprets the
common feeling and percept then only shall we agree
as to the facts or common reports. I repeat: our
concepts in one voice are false when they conflict,
and true when they completely accord with our
common feeling and percept, that is, with the common
report of melody. Now the small third is the only
relation that gives rise to and reports the minor
consonance. I next present three theses based upon
common reports.

1. Any isolated combination of two tones in the
relation of a small third generates and reports the
minor consonance which we all involuntarily recog-
nize and relate as the minor Tonic-harmony.

2. An isolated major consonance invariably reports
its root to be do, its third to be mi, its fifth to be soL

3. An isolated minor consonance invariably reports
its root to be la, its third to be do, its fifth to be mi.

The three components of the major consonance are
major harmonic percepts which I mark with larger
numbers. The three components of the minor con-

180 THE NATURE OF MUSIC

sonance are minor harmonic 'percepts which I indicate
by smaller numbers. Both consonances and their
symbols are given below for comparison and correla-
tion.

1 3 5

1. Major Tonic-harmony : do — mi — sol

18 6

2. Minor Tonic-harmony : la — do — mi

Upon the priority of major we base our thesis that
minor has been derived from elements previously
existing in major. Thus major supplied the original
tones named diatonics which in minor reappear in
new and transmuted relations. Note do and la in
the above example. Do, the major Tonic and the
original root (1), of the genus consonance, reappears
in minor as small third (3) of the minor consonance.
La, the original ninth (9) of the genus dissonance, in
which it is the highest tone, reappears in minor as
the original minor Tonic and root (1) of the original
minor consonance. Thus again, major supplied the
original forms of consonance and dissonance, each of
which assumes a new and transmuted form in minor.
Our example presents the original and transmuted
forms of consonance. Thus again, major supplied the
basic relations of rising cadence, falling cadence and
repose which characterize and underlie tone-relation
in general and mode-relation in particular and which
in minor are directly imitated. Minor is therefore
not only derived but is purely imitative; it is derived
from material provided by the prototype major, and
it imitates the relations of cadence and repose ori-

ORIGIN AND NATURE OF MINOR 181

ginally derived from rhythm and first intoned by
melody in the prototype major mode. Here we note
in passing that imitation is not alone a principle of
music-structure as demonstrated in round-song, anti-
phonal chant, sequence, canon and fugue, but, what
is even more important, imitation is a principle of
harmonic genesis closely allied to that of potential
harmony, the subject of a later chapter. Again re-
ferring to our example we note that do is the origi-
nal major Tonic, that c^o-major is the original major
mode; next, that la is the original minor Tonic, that
Za-minor is the original minor mode and corresponds
with what is known as relative minor. The almost
universal adoption of relative minor as the true minor
amounts to a tacit acknowledgment of the priority
of major, and presents but one of thousands of cases
in which our great thinkers draw their conclusions
from facts reported by common feeling and perception.
In all books on music, be they historic, biographical,
aesthetic, theoretic or didactic, we everywhere find
the direct appeal to music-feeling for every hidden
and ultimate truth. It is safe to say that every truth
that came to stay in the books came by way and
sanction of music-feeling. The conflict between an
abstract theory and concrete feeling waxes strong in
every case where the two are irreconcilable owing to
the unconquerable protest and revolt of music-feeling.
One of a number of cases in point is the Zarlino-
Riemann theory of pendant minor with harmonic
roots in air upon which we will later on present the
common harmonic self-reports of one voice or melody.
The concept of minor as la minor (relative minor)

182 THE NATURE OF MUSIC

completely harmonizes with our common feeling and
percept of minor, and its validity is demonstrated and
confirmed by the self-reports of melody.

Reverting to our theses on page 179 it may be asked,
why fix upon the specific tones do and la for the origin
of minor? Among previously extant diatonics are
there no other combinations of two tones in which the
requisite relation of a small third is potential ? Ages
upon ages before there was any conscious perception
of harmony, melody had brought forth both the major
mode and minor mode in one voice. In connection
with this early formative period of melody when feel-
ing of harmony was in its incipient stages of develop-
ment we could not confidently speak of specific tones
or of specific relations generating specific forms of har-
mony, in short, we could not answer the above ques-
tions, were it not for harmony in one voice, its definite
self-reports and its demonstrable principles. Admit-
tedly the refined harmonic sense of to-day is connected
with, rooted in, and the evolutionary product of, the
harmonic sense of the entire past, or briefly, of yester-
day, and it follows that the harmonic percepts of
to-day spring from the harmonic feelings of yesterday,
that the common self -reports of melody so clearly per-
ceived to-day are the same which yesterday were but
dimly felt. Thus harmony in one voice is the connect-
ing link between the harmony of the present and that
of the entire past, and by means of its self-reports we
can trace the genesis of tone upon tone, relation upon
relation, harmonic form upon harmonic form; and
because these self-reports are common and apply to all
music in one voice it matters little whether our illustra-

ORIGIN AND NATURE OF MINOR 183

tions are drawn from modern or primitive melodies, or
whether we devise them as we proceed, so long as they
are in one voice and exemplify the special case under
consideration. We may now answer the above ques-
tions beginning with the second. Yes, there are three
other combinations of diatonics which frequently ap-
pear in primitive melodies in the relation of small
thirds. One is sol down to mi, which like do to la
dates back as far as the pentatonic period, and which
insistently reports the major Tonic-harmony (I), sol
asserting itself as 5, mi as 3. Later on when the down-
leader /a and the upleader ti had made their appear-
ance, melody introduced two other combinations,
namely, /a down to re, re down to ti. During the ante-
minor stage of music when melody had evolved but a
scant web of harmonic threads and had generated at
most three regnant harmonies, namely, I, V and IV,
not one of these combinations in small thirds could
have generated the minor consonance. Why not?
Simply and obviously because these original har-
monies of melody necessarily and always appear in
correlation, as demonstrated by primitive melodies of
birds and men. Because of this necessary correlation
the combinations /a to re and re to ti insistently report
the major Dominant-harmony (V),/a asserting itself
as 7, r^ as 5, ti as 3. Indeed, the original relations of
original tones are so deeply rooted in harmonic feeling
that even to-day we cannot change them except
through deliberate reflection and a voluntary effort of
selection which in every such case results in a modula-
tion. Needless to say it would be the height of ab-
surdity to accuse man of such refined intellectual

184 THE NATURE OF MUSIC

powers of abstraction at a time when his melodies were
the simple, naive and spontaneous intonations of con-
crete feelings. Of these primitive melodies and of the
beautiful folk-melodies and of the immortal melodies
of our masters two things are equally true: not one
was ever produced through deliberate reflection, and
no one can t6ll whence they came. Of all the seven
diatonics do and la are the only two tones through
which melody could have brought forth the minor con-
sonance, and this paragraph may be concluded by
restating our thesis.

Any isolated combination of two tones in the rela-
tion of a small third generates in feeling the minor con-
sonance, and in every such case the two specific tones
are do and la.

44. Original and Duplicate Forms of Harmony

Each specific form of harmony in one voice arose on
a specific tone in a specific relation: every such form
being the first of its kind is classed as the original, and
every repetition of such an original on other tones is
classed as a duplicate.

In the whole realm of harmony there are but two
forms of consonances, the major form with its distinc-
tive and characteristic large third (3), the minor form
with its distinctive and characteristic small third (a).
Of the two consonances the major form is the proto-
type, the minor form is the derived and modified type.
Their distinctive thirds at once mark the structural
difference between the two forms and the individual-
ity and essential character of each. The major Tonic-
harmony based on do is the original major form: the

ORIGIN AND NATURE OF MINOR 185

minor Tonic-harmony based on la is the original
minor form. In evolution these forms are repeated
on other tones, and all such repetitions for lack of a
better name are here called duplicates. Duplicates
of the major form on V and IV have already been pre-
sented and explained and others will follow. Dupli-
cates of the minor form will appear presently.

Roman numbers are employed for the double pur-
pose of indicating the root and the specific form of a
harmony; in larger type they indicate major, in
smaller type, minor harmonies. I shall strictly adhere
to this universal custom save in one particular, namely,
the numbers indicating minor harmonies will be
printed in italics for reasons which will become obvious
as we proceed.

45. Origin in One Voice of the Minor Form of
Dissonance. Original Cadences of the Minor
Mode

In minor the diatonics owing to their reappearance
in new and transmuted relations undergo a redistribu-
tion and regrouping. The prototype modal relations
of cadence and repose in precedent major are directly
imitated in minor, and these imitative relations consti-
tute the vera causa of the genesis of the minor forms of
consonance and dissonance which are the counterparts
in minor of the two major prototypes. For the group
of tones and relations which we have named the reg-
nant major Tonic and its cadences there is a corre-
sponding minor group, the regnant minor Tonic and
its cadences ; for each specific tone and relation in the
precedent major group there is a corresponding tone

186

THE NATURE OF MUSIC

and relation in the derived and imitative minor group.
In short, everything in major has its parallel and
counterpart in minor. Major provided the material
by means of which melody produced minor, and minor
in its turn has added new material. Just as in major
so in minor, the cadence-tones arose over and under
and tend up and down into the regnant Tonic-har-
mony. Because of these corresponding tones, relations
and harmonies in the two modes, parallel examples
in major and minor will be given in all cases where
they will add to the clearness of our exposition. Our
first example presents a pentatonic melody, in which
note the common harmonic self -reports and corre-
sponding tones, relations and harmonies in the two
modes. The pitch of these and other examples is
chosen for convenience of presentation and should be
thought an octave lower.

Major

i

g

sol

mi

I-

do mi

sol

^

la

sol

I

Minor

i

m

e^

mt

do
I

la

do

fa

n

Carefully compare these parallel examples. The
syllables and harmonic numbers show the new and
transmuted relations of the diatonics in minor. Ob-
serve that each mode is represented by the three com-

ORIGIN AND NATURE OF MINOR 187

ponents of the Tonic-harmony, by one component of
its Dominant, by one component of its Subdominant.
Observe the parallel regnant harmonies, / in minor,
the counterpart of I in major. Tone upon tone com-
pare the corresponding tones and harmonic percepts of
the two modes as follows : mi s in minor is the counter-
part of sol 5 in major, do a of mi 3, ti 5 of re 5, la i of
do 1, and so on. The essentially imitative character
and nature of the minor mode is plainly manifest not
only in the whole meloharmonic phrase, but in each
tone and interval, each progression and cadence, each
harmonic percept. Observe the parallel falling ca-
dences : ti 5 to la 1 in minor corresponds with re 5 to
do 1 in major, /a s to mis in minor with la 3 to sol 5 in
major. Observe that the cadence-tone ti 5 in minor
reports its concomitant third to be a large third and a
chromatic, namely, si (gjlj! in our example), and that
this chromatic is the minor upleader which corre-
sponds with the major upleader ti 3. Observe in the
falling cadence/a to mi (f to e) in minor how unnatural
it would be to substitute fjjl for f. These observations
will have an important bearing on the sequel.

The major Dominant (V) was first announced and
represented in melody by its fifth re and first appeared
in cadence, that is, as a byharmony. The same is
true (see above example) of the corresponding minor
Dominant (V) which was first announced and repre-
sented by its fifth ti (counterpart in minor of the major
re) and likewise first appeared in cadence as a by-
harmony. Again, the major Subdominant (IV) was
first reported by its third la, the parallel minor Sub-
dominant (as in example) by its third /a. Thus the

188

THE NATURE OF MUSIC

part played by re and la in major is repeated in minor
by its corresponding tones ti and fa. Thus, as we
have seen, the efficient accent on re generated the reg-
nant Dominant (V) in major; hkewise the efficient
accent on ti generated the regnant Dominant (F) in
minor. Again, the efficient accent on la caused the
genesis of the regnant Subdominant (IV) in major, on
fa the corresponding regnant Subdominant {iv) in
minor. In the parallel examples below compare
these corresponding regnant harmonies and note the
harmonic reports upon their genesis as just ex-
plained.

Major

m

g

I

IV

Minor

m

^i

IV

Our next consideration is the minor form of dis-
sonance and how it arose. The entire harmonic
thread (comprising five components) of the genus dis-
sonance (prototype major form) was and is latent in
the major cadence-tone re. Likewise the entire har-
monic thread (comprising five components) of the
derived and transmuted form of dissonance in minor
was and is latent in the corresponding minor cadence-
tone ti. Compare the two in the following example : —

Major

ORIGIN AND NATURE OF MINOR 189

5 3135^53135, 9^5 31

:^=¥

H — i — m — I — H

T' I i-f m

re

V V^ V9

5 3136,53135, », 531

Minor

^

^%^f^^ttf-^=^t^

r V, n

The two forms are again presented in syllables and
harmonic numbers for further observations.

13 5 7 9

1. Major V9 : sol — ti — re — fa — la

1 O O 7 o

2. Minor VqI mi — si — ti — re — fa

Compare corresponding tones and harmonic per-
cepts as follows: sol is root of major Dominant, mi
is root of minor Dominant, and so on. Observe that
the two dissonances differ only in their ninths, all the
other intervals being the same; the ninth in major is
large and was first reported by /a, the ninth in minor
is small and was first reported by /a. The distinctive
individuality of each of the two types of consonances
is due to its characteristic third, 3 in major, s in minor,
while that of each of the two original types of disso-
nances is due to its characteristic ninth, 9 in major,
9 in minor. Both types of dissonances confirm the
truth of our thesis that the ninth is the highest har-
monic component of a harmonic root and therefore the
genetic limit of harmony.

190

THE NATURE OF MUSIC

Sol is the bond-tone connecting the cadence and
repose groups of harmony V9 — I in major, appearing
first as 5 of I, thereafter as 1 of V. Likewise mi is
the bond-tone of the corresponding groups of har-
monies Fg — I in minor and Hkewise mi appeared as
6 of z before appearing as 1 of F. Both bond-tones
are next presented.

Major

$

I-

-<5>-

V-

I

Minor

i

w=

13 5

f

^^

Just as the major dissonance arose in relation to the
major consonance just so the minor dissonance arose
in relation to the minor consonance. The remaining
four components of the two dissonances are cadence-
tones which lie directly over and under, and which
tend and resolve up and down into the components
or repose-tones of the two consonances. Of the four
in major all are diatonics and had their genesis in
relation to the major consonance. Of the four in
minor three are previously existing diatonics in trans-
muted relations while one {si, the chromatic) is a
newly derived tone the genesis of which we have just
explained. The four in minor directly imitate the

ORIGIN AND NATURE OF MINOR

191

four in major. Compare below the four cadence-
tones and three repose-tones in each of the two modes.

Major

Cadence-Tones

3 5

i

^

9

Repose-Tones

1 3

I

Minor

$

3 6

kt

^

I

In this relation the four cadence-tones present an
aggregate of five cadences in each mode since ti in
minor resolves both up and down like its prototype
re in major. Each cadence in minor imitates and
is the counterpart of its corresponding cadence in
major. Compare the five parallel cadences below.

3 15 15 3

1. Major: ti do re do re mi

fa mi

9 5

la sol

3 ^
2. Minor: si la

5 X

ti la

" 8

ti do

7 3

re do

e 5

fa mi

The resolutions of these cadences are next presented
in the form of chords as follows: —

Major Minor

\

V9 I

192 THE NATURE OF MUSIC

The addition of a terminal Tonic to each of the
above groups of four cadence-tones and three repose-
tones completes the scales known as diatonic major
and relative minor. They are presented below both
ascending and descending for the purpose of exhibiting
their parallel progressions and resolutions or cadences,
the latter marked by slurs.

Major

Minor

I

9=fS

m-^

-^L

do

^- ^^ " ' ^ TTl^

la

In all the preceding illustrations of parallel cadences
we note how each cadence in minor has arisen by
imitating its major prototype. Thus the upleader
si 3 in minor corresponds with the upleader ti 3 in
major, the downleader re ? in minor with the down-
leader fa 7 in major, the double cadence of ti 5 with
that of its prototype re 5, the cadence of /a q with that
of its prototype la 9. In short, each tone and relation
in major is offset by a corresponding tone and rela-
tion in minor. Hence the close relationship of major
and minor. Each mode has its own specific form of
consonance and specific form of dissonance at its
foundation, and let us remember that in one voice,
melody generated all these forms in obedience to the
inherent and uniform laws of causation which we
have already defined.

The above minor group of tones is as noteworthy
for the absence of sol, the only diatonic which does

ORIGIN AND NATURE OF MINOR 193

not appear, as it is for the presence of the newly
generated tone si. As regards si, which arose as a
concomitant in the harmonic thread generated hjti5,
we pause here to observe first, that chromatics first
arose as concomitants and were generated by diatonics
in transmuted or new relations; next, that all newly
generated tones like si pass through three consecu-
tive stages of psychological evolution which mark the
progressive development of melody. Indeed, with
the exception of the components of one harmony, all
tones have passed through these three evolutionary
stages. The one exception is the major Tonic-har-
mony which was at once a regnant harmony and the
first harmony generated by melody and whose com-
ponents do 1, mi 3, sol 5 therefore made their first
appearance in melody as regnant tones. The three
consecutive psychological stages are as follows: —

First Stage : in which a tone had its genesis as an
elementary harmonic or concomitant in a thread of
harmony generated by a previously existing tone in a
new relation. This is a tone's lowest or elementary
stage.

Second Stage : in which a tone has been differen-
tiated and has appeared in melody as a bytone, that
is, in the relation of cadence on a light rhythm-period.
In this stage a tone has become an individual con-
stituent of melody and of the tone-system. This
stage may be called briefly the bytone stage.

Third Stage : in which a tone has appeared in
melody as a regnant tone. In this stage a tone first
appears on light rhythm-periods after or between
other co-harmonics of the regnant harmony, but does

194

THE NATURE OF MUSIC

not attain its highest development in one voice until
it appears on the eflSlcient accent (heavy rhythm-
period), when it generates the regnant harmony of
the moment. This highest stage of a tone in one
voice or homophony is named briefly, the regnant
stage.

These three stages apply exclusively to music in
one voice or homophony. Next let us follow si 3 in
minor and its major prototype ti 3 through these
three stages. Our parallel examples illustrate their
lowest stage as concomitants. In minor, si is present
as concomitant 3 in the harmony generated hj ti 5;
in major, ti is present as concomitant 3 in the har-
mony of r^ 5. See below at the places marked by an
asterisk.

Minor

^

Major

$

-(2-

Next the two tones appear as bytones in their
second stage.

Jfinor^

^

j-XJ m

i

-z^

ORIGIN AND NATURE OF MINOR
131 153513 1

195

Major

t

w=^i-r~cj^s.

Next in their third and regnant stage.

5 3, .531

Minor

^

M

^

t

m

3

Y * i Y

, 3 5 1.

i

^

S

^

^^

- F
3 1

J

3 5

*
V

Major

m

e

5 3

■* a-

5 1 5 3 13

I

11

-V

V

Everywhere in all the above and previous examples
the common harmonic self-reports demonstrate the
fundamental implication of rhythm, therefore the
operation of the shaping principle of equilibrium, in
short, the uniform laws of psychological causation in
homophony.

The absence of the diatonic sol in the minor group
of seven tones thus far presented raises this question :

196

THE NATURE OF MUSIC

Does sol ever appear as a constituent tone of the
minor mode and if so, how ? Presently we shall see
that sol does appear in minor melodies, and plays
a most significant part in the minor mode. The
succeeding parallel examples present all seven tones
of both modes in all their tonic and dominant rela-
tions.

Major

Minor

3 9 1

3 5 15 3 1 5

i

a:

iM=t

m

T=p:

^m

V9

3 8 1

I

5

E3a

I

^ These seven tones of the minor group appear in
all their tonic and dominant relations in each of the
following fugue-themes of Bach.

3 3 3 1 5 s

y^-l=

^m

mi la

78 "87 »1 78"1&S

H 1 ! 1 ! 1 I I , I »r

5

5

p^-7

i

etc

ORIGIN AND NATURE OF MINOR 197

mi do la
/

V,

m

-=i — s^

-=i ^

W

5 6

' 1 , . 5

* ±

££

t£

6 7

-^i 5 ,

etc.

-f^^^^^

^m

V.

*^

^

, 5 1

t

§te*

^

-^— =^

etc.

The study of Bach more than that of any other
one master quickens our perception of melohar-
mony and its common self-reports and teaches us
to appreciate the essential and fundamental impor-
tance of meloharmonic discrimination to an intelligent
interpretation and expression not alone of polyphonic
music, but of all music. In the study of the rhythms
and harmonies first of one melody and next of com-
bined melodies we gradually realize that there are
principles of expression inherent in music itself and
therefore in common feeling of music. What these
principles are is considered in a later chapter. That

198 THE NATURE OF MUSIC

Bach had a profound and vivid sense of these inherent
principles and expected as much from his inter-
preters may be inferred from the fact that he left
us his monumental piano work "The Well-tempered
Clavichord" without a single mark of expression.

We have explained the origin in one voice of the
minor form of dissonance, have defined its five com-
ponents and their correlations. We have accounted
for seven tones of the minor group and have encoun-
tered these seven tones in the following nine minor
relations : Za as i of /, do as 3 of /, mi as 6 of / and 1 of
V, si as 3 of F, ti as 5 of F, re as 7 of F, fa as » of F
and 8 of IV, All these tones and relations appear in
the subjoined fugue-theme of Bach.

i3i6 siSiSsiSiStIo It*

I JV I TTT 7

46. Three Regnant Minor Harmonies and Their
Bytones and Cadences

Having explained the subject of regnant harmony
in the preceding chapter we may proceed without
needless repetitions to study the bytones and cadences
of the minor tonic, dominant and subdominant har-
monies. In a given melody the leading question is:
What is the regnant harmony or series of regnant har-
monies ? Every tone in a melody relates to a regnant
harmony, and if a component, is classed a regnant tone,
if not, a bytone. Such are the essential points to be
borne in mind.

ORIGIN AND NATURE OF MINOR

199

1. Regnant Minor Tonic, Its regnant tones are
lay do, mi, its bytones are si, ti, re, fa. In future
examples each bytone is marked by a star. During
the regnancy of this harmony, si, ti and re report them-
selves respectively as 3, 5 and 7 of V, while /a reports
itself as s of iv. See below and compare with the
parallel major example.

Major

i

5 3

5 1

5 1

3 1

^

^m

W

■X-

Minor

$

t^

5

5 1 — 3

t^

B

H

M

■X-

While there are other bytones to this regnant our
examples are strictly confined to the tone-material
thus far accounted for. This material includes the
diatonic sol and evokes the question: Does sol ever
appear as a bytone to this regnant.^ Our questions

200

THE NATURE OF MUSIC

are addressed not to abstract theory, but to concrete
melody and its governing principles. Melody could
and did, can and does introduce sol in this relation
as shown below. Sol arises on the line of least resist-
ance in the descending tetrachord which starts on the
octave and terminates on the fifth of the regnant
minor tonic. See last two measures [but one]. Com-
parison with the parallel example in major again
recalls our attention to the imitative nature of minor
and shows that each harmonic percept and step in
minor are the direct counterparts of their respective
major prototypes.

135 3535 335 3

Major

m

p^

^ J. Ai^T-.^

* »

51335 351 335,35 1

i

mm

3==p:

1

*

* *

* ^

*

Minor

8 5

^^

^

8 3 6

±=Mz

* -3^

^^

S 1 8 8

g

^

8 8 5 7 8

^^

W§

I

tr-#-

^—^

■X- ^

^ *

In the minor example sol appears in the last three
measures [but one], and reports itself as small third of
the dominant, thus demonstrating that the minor domi-

ORIGIN AND NATURE OF MINOR 201

nant in this instance assumes the form of a minor con-
sonance, the index of which is v. The data to be
observed in this connection are first, that F is a pure
diatonic harmony since all its components are dia-
tonics; next, that V arises spontaneously in one voice;
next, that the minor dominant F is a chromatic har-
mony owing to its large third si, which is a chromatic.
Presently we shall see that the diatonic minor domi-
nant (y) asserts itself in one voice as a regnant har-
mony. Further observations are these : The asterisks
in our examples show a series of two bytones, the first
resolving into the second, the second resolving into a
repose-tone of the regnant /. Bytones which resolve
into the regnant harmony are classed as bytones of
the first degree: bytones of the second degree resolve
into those of the first degree. We shall meet with
bytones of the third degree which resolve into those
of the second. In the descending tetrachord from
la 1 down to mi s we recognize the upper half of the
descending melodic minor scale as follows : —

i

1

3 3 5

I

la sol fa mi re do ti la

/

All the above tones are dia tonics, yet the scale-
melody is not diatonic. Why not ? Simply because
all the harmonies are not diatonic. To be diatonic all
the components of a harmony must be dia tonics. This
is the case with all the tones of the first of the above
two tetrachords, which is pure diatonic minor. Not so

202 THE NATURE OF MUSIC

in the second tetrachord, in which the harmonies both
of re 7 and ti 5 report the presence of the chromatic si
(git) as a concomitant and component 3, for which
reason they are classed as chromatic harmonies.
These common harmonic reports in one voice there-
fore plainly and conclusively demonstrate and prove
that even though a melody be entirely composed of
diatonics, yet that melody may not be diatonic. The
test as to whether a melody is or is not diatonic lies in
its concomitant harmony, which in one voice asserts
and reports itself, and this test and new view-point will
greatly modify the facts and conclusions which in the
past have been recorded by music-archaeologists in
their studies of homophony. But is there such a
thing as a pure diatonic minor melody.^ Such a
melody might easily be conceived and represented by
selecting diatonic chords as an accompaniment, but
this would be but an arbitrary conception void of any
archaeological value. On the other hand, if such a
melody is conceivable in one voice and itself generates
and reports only diatonic harmonies which we all per-
ceive in common, then indeed would we gain a fact of
considerable value to music-archseology and psycho-
logy. The common self-reports in the next illustration
answer our question in the affirmative, and conclusively
demonstrate that such melodies do arise in one voice,
and from this we may infer that they may have arisen
in the remote homophonic past.

1 Sfi 36 8 1 81 6 1888

umi^

•x- ^

ORIGIN AND NATURE OF MINOR

203

This is a "pure minor melody, each tone reports a
diatonic harmony, each harmony is a minor conso-
nance. In the first measure the by tone /a reports itself
3 of IV, in the second measure sol reports itself s of F,
in the third measure both bytones make the same re-
ports. Thus through sol the minor dominant assumes
the form of a minor consonance. Thanks to self-
asserting harmony in one voice we are able to aflSrm
that there is such a thing as "pure diatonic minor which
is the perfect counterpart of jmre diatonic major. The
subject of pure minor melodies will again be reverted
to when we shall study sol in other relations.

Does melody ever ascend on the upper half of the
descending melodic minor scale ? Yes, there are many
examples, especially in modern music. We cite one
from Liszt, Rhapsody II.

Si;

etc.

m^

mi fa sol

The ascending upper half or tetrachord of the
melodic minor scale has been derived through imita-
tion from the same tetrachord of the major scale, thus
introducing another chromatic, namely, fi (f jlf in A
minor) as follows: —

Major

c±r

1

5

3

7
\ —

5

H—

3 3 1

3

— # —

-W-

1— J —

P —

— n^ —

* *

I 1

204

THE NATURE OF MUSIC

^ ^

Minor

$

B:

3 3

f-pf

m

* *

3 3

3 3

i^zt^j-^-^BE^^^tJ^^-^^

Here the chromatic fi (ijjf) arises as a bytone to
regnant / ; it is a bytone of the second degree and
resolves into si, a bytone of the first degree ; its report
of 3 announces the subdominant in the form of a major
consonance. Our examples show that the minor
dominant in one voice assumes the forms of both con-
sonances, the major form through si 3, the minor form
through sol a. See below.

13 5 a . .

mi — si — ti I mi — sol

V \n

Next we note that in one voice the minor subdomi-
nant assumes both forms, the minor through /a s, the
major through fi 3.

8

-fa
IV

3 5

-fi — la

Iv

ORIGIN AND NATURE OF MINOR 205

We have met all these forms as byharmonies to reg-
nant / and are presently to see how they arise as reg-
nants. All these harmonies are nearest related to the
minor tonic, and arose at an early period of melody's
exploitation of the minor mode in one voice ; and since
they assume both the major and minor forms and
appear both as diatonic and chromatic harmonies,
they plainly reveal the mixed or hybrid composition of
the minor mode, and add further conclusive testimony
to the derived and imitative nature of minor. Our
examples and analyses clearly point out that there is
but one source of light and truth on homophonic prob-
lems, that there is but one true and responsible reporter
on those fundamental homophonic harmonies in
which all harmonies are rooted, the one and only re-
porter into whose testimony the personal equation
cannot enter. This one source, this one reporter is
melody, the composite of rhythm and harmony, the
free, untrammeled and universal rhythmo-harmonic
voice of music. The growth of the scale of tones from
its incomplete to its complete diatonic form, thence to
its chromatic form and thence to its present enhar-
monic form, means the gradual growth of the tone-
system from its first beginnings up to the present time.
However, the efficient cause of all this growth is
rhythmo-harmonic melody. Under the guidance and
government of its inherent laws of development
melody discovered and exploited tone upon tone, re-
lation upon relation, harmony upon harmony, thus
gradually expanding the scale and system of tones and
keys. Beginning by intoning the relation of cadence
and repose and generating consonance and dissonance,

£06

THE NATURE OF MUSIC

melody has continued to cadence and repose on this
tone, on that tone, on any tone in the ever widening
tone-realm, the difference between to-day and yester-
day being a difference in the extent of the tone-realm,
a difference between simpler and more complex melo-
dies. Like yesterday, so to-day melody reports now a
consonance, now a dissonance, no more, no less.

2. Regnant Minor Dominant, Like its major pro-
totype this regnant has three forms: a three-tone
form F, a four-tone form F^, a five- tone form Fg. This
harmony was first reported in melody by its fifth ti.
The concomitants of ti 5 are mi 1 and si 3. The
efficient accent on ti or si generates regnant F thus : —

i

i

I

p^

Through its accession of this regnant, melody was
enriched first by all the possible steps from one compo-
nent to another, next by the bytones and cadences
playing upon its components. The former are too
obvious and require no illustration. As to the latter
we will first consider the bytones of regnant F. Reg-
nant F has but two diatonic bytones, namely, la and
do, which cadence into the third (si) and fifth (ti) of
this regnant. See below and compare with parallel
example in major.

3 13131535151311

Major

ORIGIN AND NATURE OF MINOR
8 1 3i3i SaSi 5i31i

207

Minor

F*

There are no diatonic bytones to the root (mi) of
this regnant. Re and fa, which lie respectively under
and over this root, are not bytones of the regnant domi-
nant ; they are components and regnant tones. During
the regnancy of the dominant, re reports itself as i and
gives rise to the four-tone form V^ while fa reports
itself as o giving rise to the five-tone form Fg. See
below and compare with corresponding tones and
relations in major.

«) 5 31357 5313579

^

V9

Major

t 1^ u

Minor

b)

5 3 1 357 531357 »

1 5

Uajor Jf I I

C)7

V9

9 5 13

i

6)

1 5

e),

5 1

i

208

THE NATURE OF MUSIC

The seventh (re) of V^ has but one diatonic bytone,
which lies under it and is do. The diatonic lying over
re 7 is mi the regnant root. See below and compare
with parallel major.

5 31 7 3 5 S 7 B 7 1 S

i

:^

Major

B^

I

h^

V, *

•X-

Minor

i

m

E3

tEEEEi

' 7

1

Next let us study the ninth (fa) of Vq. In the first
place this small ninth like its prototype la 9 in major,
cadences into the regnant harmony of which it is a
component. In other words, the regnant tone fa o
resolves into its co-harmonic the regnant tone mi, as
shown below. Again compare with example in major.

7 5 3 9 13 5-^ ^

Major

13 5

g

Minor

3

fcfti

During the regnancy of the dominant, melody also
resolves the ninth upward into the upleader, which is
the third of that harmony. Compare the next parallel
illustrations. This rising cadence is keenly felt in

ORIGIN AND NATURE OF MINOR

209

stepping from the large ninth to the upleader {la to ti
in major, /z to si in minor as at b) in the minor example
below), but is not perceptible in stepping from the small
ninth /a to the upleader si as at a) in the minor ex-
ample.

Major

i

5 3 1

IS^^

5 V 9 3 1

— 0

?

^-

I

6)5

9 3

^^

Minor

s

tm

■z?-

V

^U

At a) in the above minor example, fa and the other
components of regnant V are the counterparts in
minor of the corresponding components of regnant V
in the major example. But at 6) in the minor
example the melody during the regnancy of V exactly
imitates and duplicates the steps of the major melody
in the corresponding measure thus introducing the
chromatic fi (/jlf), which reports itself as large ninth
and a component of the regnant harmony, thereby
causing the regnant minor dominant to assume the
original major form of dissonance. This inherent
tendency of both the large and small ninths to resolve
each into the harmony of which it is a component has
led some music-theorists to class the ninth as a bytone
to the chord of the dominant. But here we are not
dealing with chords, we are dealing with the antece-
dents of chords, with harmony in one voice the com-
mon self-reports of which for the first time enable

210

THE NATURE OF MUSIC

us to discriminate positively between regnant tones
and by tones, and they clearly and conclusively demon-
strate in the case of the two ninths that a tone may be
at once a regnant tone and in cadence to its own
harmony. A regnant tone is not a bytone, a bytone
is not a regnant tone: by carefully and strictly ad-
hering to the necessary distinction between the two
we shall avoid what else would be inextricable con-
fusion.

Are there any diatonic bytones to either of the
two ninths during the regnancy of either of the two
dominants? No, the tones thus far accounted for
which lie over and under the ninth are, like the
ninth, components of the regnant dominant in both
modes. The tone under the ninth is the root, the
tone over the ninth is the third of the dominant,
during the regnancy of which both tones are of
course regnant tones. We are now to see that the
ninth is not the only cadencing regnant tone as shown
at N.B. in the next parallel examples, in which the
melody cadences from the regnant third to the regnant
ninth.

35739 1 91391357399 1

^ Y-^ N.B. N.B. ~^

Major

V-A-

3 5

7 3 9

l8ol3578 9 0 1

^^^^^^M

Minor

N.B.

N.B.

N.B.

ORIGIN AND NATURE OF MINOR 211

The diatonic sol at each N.B. in the above minor
melody calls for a series of observations. Through
sol in the above relation, original harmony in one
voice discloses a curious and interesting fact which
throws a strong and clear light upon consequent
complex chord-formations so numerous in modern
music. The above minor melody is the exact coun-
terpart in minor of the parallel melody in major, and
sol arises in the minor melody on the line of least
resistance. Previously we met sol as small third but
as a by tone to regnant /. Now we meet sol again as
a small third, but this time as a regnant tone and,
what is more, as a regnant tone in cadence. Observe
that the cadence-tend of sol in this relation is much
stronger than that of the parallel tone ti in the major
melody. And why ? Because of the presence of the
large third si in the concomitant harmony of sol.
That is to say, this sol a reports si 3 in its concomitant
harmony, it means that we feel and hear the small
third and the large third of the same root simulta-
neously. Hence the stronger cadence- tend of sol s to
fa 9 than that of the parallel major ti 3 to la 9. Hence
the important fact reported by harmony in one voice
that there are harmonies containing double thirds^
that is, two thirds of one root. Hence the inference
that there may be other double harmonics as double
fifths and the like, an inference to be verified later.
From this important fact adduced from and verified
by harmony in one voice we naturally draw the
logical conclusion that chords may be compounded
of double harmonics, that is, of double thirds and the
like. Such chords may be named double chords.

212

THE NATURE OF MUSIC

They are a true reality, since modern music has intro-
duced them frequently. I present a double chord
containing double thirds, choosing for my subject sol s
in the above relation, which tone and relation are
responsible for the genesis of this double harmony
and consequent double chord.

1 1

This cadence of sol z into fa © during the regnancy
of V is often found in the melodies of Chopin. Here
is a familiar example from the prelude in E minor.

1 sDoloOsols

i

^

w

il

'^^=¥

N.B.

etc.

5*

I

lEI

*-^

17

Such excerpts from compositions might be multi-
plied indefinitely. For my last illustration of sol •
in this relation I give the principal theme of the
allegro of Beethoven's sonata op. 111. Although this
opening theme presents sol s but once, it is given in its
entirety, it being so fine an example of harmony in

ORIGIN AND NATURE OF MINOR

213

one voice, a form of writing in which Beethoven so
frequently expressed himself.

sSSl 8 3 fioSl 8 3 O

assi

'TTA0rT^

m

I7 8 5 STsSl ol

7 8 O 8 7 8

1 » 1

7 8 7 8

5 8 7 8 5

15 7

^i

^J * J

hj. J J. J. i ^ -i -J- :;^

T "•*

^

. 5

5 1 3

S^

^

^

^ ' ^ ^

T*— •^

T-

8 5

5 1

1 6

3 9 1 5 1 3

7 8

:^3

^

5=rf

^m

s^

-JK

t=t:

iF

§a

J ^'' /J F

5 o It 5i37a5ol75i3

fe£

i=?

tr*

t^it

s

•— #

tK

5 1

* — • — wr

1

'- etc.

214 THE NATURE OF MUSIC

The above harmonic numbers indicate the self-
report of each tone and speak for themselves. This
theme presents certain regnant harmonies which
hitherto have not appeared in our examples, and
comment upon which at this juncture of our exposi-
tion would be premature and is therefore deferred.
In connection with the above example we call atten-
tion to this law. Relation of tones and harmonies is
always forward. Rhythm-relation being forward all
relation is forward. Observe the triplet in each of
the two motives with which the theme opens. This
premeasural triplet relates forward and therefore
relates to and plays upon the regnant tonic-harmony.
Observe fa (a^) at the end of the third and fourth
measures: it likewise relates forward and therefore
reports itself 9 of F.

One more remark remains to be made regarding
sol 8 as a cadencing regnant tone. It is an original
product of the minor mode and is distinctively a
minor harmonic percept. We have seen how melody
evolved the minor mode out of tone-material and
relations previously extant in major, thus generating
the new and individual minor forms of consonance
and dissonance by imitating the cadence and repose
relations of the prototype major mode. Through
the same process of imitation, melody has reversed
the process by reproducing and imitating in major
many of the melodic steps and harmonic forms which
first arose in minor. Just as melody adopted the
major tetrachord in minor (below at a)) just so
melody adopted two minor tetrachords in major, as
at b) and c).

ORIGIN AND NATURE OF MINOR 215

o) h) e)

Major

a)

Minor

This introduction by melody of the products of one
mode into the other at once exhibits the union in
melody of perfect freedom with perfect adherence to
law and order, but in modern music has assumed such
proportions and created such an apparent modal
muddle that each of the two modes seems well-nigh
to have lost its identity. The modal identity is how-
ever always asserted and reported by the modal
major or minor tonic-consonances. This self-report
so obvious and definite in simple homophonic melo-
dies is less obvious but not less definite in the com-
plex melodies of polyphony and chorded music with
their intricate chromatic harmonies and manifold
modulations. As we progress in tracing the evolution
of melody and the consequent concurrent evolution
of tonality and of the tone-system, it will become
increasingly clear that our conceptions of mode,
tonality and scale or system require considerable
modification. In order to maintain our clearness of
view as we gradually enter into these apparent com-
plexities we will continue to focus our attention upon
melody, the voice which has gradually discovered and
exploited the wide realm of tones as represented by
the enharmonic scale with its boundless potential
relations and harmonies, our only source and reporter

216

THE NATURE OF MUSIC

of truth. I repeat, melody, perfectly free because
perfectly self-governed, raay repose or cadence here,
there, anywhere in the tone-realm. Melody exercised
this freedom yesterday in a narrow, exercises it to-day
in a wide realm of tones.

One more form of the regnant minor dominant
remains to be presented. This form is a minor con-
sonance generated by melody through the diatonic
sol. We have met this consonance, due to the report
of sol as small third, in the paragraph on the minor
tonic, where sol appeared as a bytone. In the follow-
ing melody sol a is a regnant tone and announces the
regnant minor dominant in the form of a minor
consonance.

m

5 1

~N

1 8

^

i^

3 6

8 5

^^

-^

it=i=!t=iiz^

IV

Here sol a reports regnant v in the second, third
and fourth measures and appears as a bytone in the
fifth and last measures. This melody reports three
diatonic harmonies, namely, 7, V and iv ; all of its tones
and their concomitant harmonics are diatonics, all
its harmonic percepts are minor, in short, this
example presents a jpure diatonic minor melody.
This proof by the above harmonic self-reports that
a pure minor melody is not only conceivable and
self-assertive in one voice, but is an absolute reality.

ORIGIN AND NATURE OF MINOR

217

confirms our thesis that melody and not a scale is the
real object of study and source of true knowledge
regarding music. No conceivable rhythmic arrange-
ment in one voice of the scale of diatonics from la to
la will generate and report exclusively diatonic har-
monies and minor consonances. To be sure this is
easily effected with chords arbitrarily selected for the
purpose, but such selective representation of harmony
is no test.

The form of a minor consonance cannot be gener-
ated by the other two components, namely, the root
(mi) and the fifth (ti), save when both or either of
the two is associated in the same rhythmic period
with sol 3. This is shown in our next example from
the fifth measure onward. Ti alone (see second
measure) or ti supported by mi (see third measure)
always announces the minor dominant in the form
of the major consonance.

1 5

6 S 1

^Efe^

§^

F-

The mixed or hybrid nature of the harmonies gen-
erated by the diatonics of the minor mode is next
exemplified, and may suggest the rich and varied har-
monic potentiality of the minor mode to the tone-muse
of young composers.

218

THE NATURE OF MUSIC

"5V

-*-

— F-

•

5

-ft-

-^

6 8

-a— f-

1

s

ft

7 5

-s — h-

-^ K

L

1

. i^

=r+-

-h

._iL

=1=

+-^

8 18 1

5ll 81585 i

9

9fc?=?

^^^

During the regnancy of F, sol the generator of this
harmony has one diatonic by tone, namely, la^ as

follows : —

1=1

3 18

S 1

I

#-1^

8 15 18 1 1

^^§

1=0:

rt:

e

The summary of the forms of the regnant minor
dominant which we have thus far generated and ex-
plained is as follows: Fg, F9, F,, F, v,

3. Regnant Minor Subdominant Like its major
prototype this regnant was first generated and an-
nounced in melody by its third which is fa. The effi-
cient accent on fa and also on re when supported by /a
generates this regnant minor consonance and diatonic
harmony as follows : —

^ffif iff^if fife-J4

18 5

^

^#

ir

JV

IV

Our present tone-material contains five bytones to
this regnant. Four of these bytones are diatonics,

ORIGIN AND NATURE OF MINOR

219

namely, do, mi, sol, ti. The other by tone is the chro-
matic si. The next example includes all of them and
indicates the harmonic self-report of each in this
specific relation.

IV-

f^-^

S S t 1 5 1

5 8 5 S 1

a 1

^

i

=9fc^3

^

^

f

•"sflt-

The efficient accent onfi (f^ in A minor) causes the
regnant minor subdominant to assume the form of a
major consonance. Owing to the chromatic^ (f|t)
this regnant IV is classed as a chromatic harmony
which, as the next example shows, enters most natu-
rally after regnant / and is most naturally succeeded by
regnant V or regnant iv.

^=M

^S

^

IV

5^

£=t

3 3 3 3 9 3

^S=:j^» # ■ P

I n L I

IV ,y
5

IV
3 3 3 5

6 ,. .8,8858 1

^>^j=£^^ftf^^?^#^^^^^

IV *

ir

220 THE NATURE OF MUSIC

Here we note that regnant IV enters after / and is
succeeded twice by V and twice by iv. A bytone to
regnant IV, namely, si (gjjf), appears in the triplets and
is marked by an asterisk. Our present tone-material
contains other bytones to this major form of the sub-
dominant, and even though all these bytones are dia-
tonics they all have a modulatory tendency, that is,
they shift the key-centre and change the mode from
minor to major. We have demonstrated that even
though a melody be composed entirely of diatonics it
may contain and report chromatic harmonies, and we
are presently to show how diatonics among themselves
may effect and definitely report modulations. Mean-
while, let us observe that the fact that a melody con-
tains only diatonics by no means proves a melody to
be diatonic. To the eye such melodies on paper ap-
pear to be diatonic and have been thus erroneously
judged and classified. Thanks to common harmonic
reports in one voice such errors are no longer possible.
The statement that music is heard, not seen, ought to
be supererogatory. An Indian chief after having in-
vited a group of men to squat with him in his wigwam
proceeded to ask what was the vocation of each guest.
Fixing his eyes upon one who was pointed out as a
musician the chief placed a finger on his ear and
winked. That much he knew.

We have now presented the regnant harmonies of
the minor tonic, dominant and subdominant, and have
studied the bytones and cadences of each. The rela-
tions and combinations of regnant harmonies among
themselves, their progressions and resolutions (ca-
dences), were analyzed in the preceding chapter where

ORIGIN AND NATURE OF MINOR

221

we treated the regnant harmonies in major. Those
in minor being very similar in their relations and suc-
cessions, we need not pause here to consider them in-
dividually since their relations and connections are
exemplified in our illustrations of minor melodies. To
summarize. The tone-material which has thus far
appeared in our minor melodies aggregates nine tones,
namely, the seven diatonics and the two chromatics
si and fi (^ and fjj! in A minor). Our next example
introduces all of these tones.

^

7

Ui

^-

^

3 9

=9i§:

^=W

V

^'

4- I

t=t

*i

*f-fyi'

I

:P=1=

-•— s>-

Next we summarize the forms of harmonies thus
far reported by our melodies in minor.

1. Minor consonances: /, iv, v. i is the original,
IV and V are duplicates.

2. Major consonances: F, IV. Both are dupli-
cates of the original I or major tonic.

3. Four-tone dissonances: F^, which is a dupli-
cate of the major prototype V^.

4. Five-tone dissonances: F^, F9. The latter is a
duplicate of the original major V9.

All the above forms resolve themselves into two
which had their origin in the minor mode and which
are distinctively minor, namely, the minor form of

222 THE NATURE OF MUSIC

consonance, that based on la being the original; the
minor form of dissonance, that based on mi being the
original.

47. Harmonic Percepts of Minor Origin

The minor forms of consonance and dissonance
comprise five harmonic percepts which correspond to
the five major percepts derived from the major forms
of consonance and dissonance. Both groups are
given below for comparison, and each harmonic per-
cept is indicated over the tone on which melody first
generated and reported it.

13 5 7 9

1. Percepts in Major: do mi sol fa la

2. Percepts in Minor: I la do mi re fa

^ V

Among these percepts we observe one duplicate,
the small seventh, which originated in major on fa
and which was reproduced in minor on re. Thus
only four of these percepts had their origin in minor
and are therefore distinctively minor harmonic per-
cepts. They are : —

I860

la do mi fa

The whole number of harmonic percepts thus far
generated by melody and explained is nine, as follows :

1, i; 3, 3; 5, 5; 7; 9, 9.

ORIGIN AND NATURE OF MINOR 223

The meaning and use of these numbers we have
defined. Over the notes of a melody they are read
thus: large root, small root; large third, small third;
large fifth, small fifth; small seventh; large ninth,
small ninth.

The self-reports of melodies in minor like those in
major confirm the truth of our theses, namely, that in
one voice each tone is felt, heard and expressed in
cadence or repose as root or third or fifth or seventh
or ninth ; that specific relations generate specific forms
of harmony, and that the two are linked as cause and
effect; that no form of harmony contains more than
five components. These nine percepts derived from
the major and minor forms of consonance and dis-
sonance, and which are the harmonic products of
homophonic melody far back in the ages, constitute
the connecting link between homophony on one hand
and polyphonic and chorded music on the other, and
therefore the harmonic basis of all music. However
simple the one or complex the other, one thing is
always true of and reported by all one-voice music
and all multi-voice music. It is this. Now the reg-
nant harmony is a consonance, now it is a dissonance,
one or the other. This was so in the yesterday, is so
in the to-day, and, we may assume, will be so in the
to-morrow of music's evolution. Homophonic mel-
ody produced the only two forms of consonances in
music and the two original major and minor forms of
dissonances. All the above nine harmonic percepts
are therefore distinctively homophonic products. As
we shall see, homophonic melody may have continued
to produce even other harmonic percepts of the dis-

224 THE NATURE OF MUSIC

sonant order, to which belong all the myriad new
harmonic percepts and forms which are distinctively
the products of polyphonic and chorded music. All
the new harmonic percepts derived from multi-voice
music are inseparably linked to and rooted in the
above nine and, as we shall find, are either combina-
tions, compounds or modifications of the nine. Hence
the importance of the nine. In pursuing this study of
melody's evolution of harmony which we trace in its
common self-reports two things should be borne in
mind : first, the harmonic percept, important because
it comprises a complete harmonic thread ; next, the
regnant harmony, important because it determines
the exact relations of tones.

48. A Tone's Harmonic Pedigree

Observe that each of the above nine percepts arose
on a specific tone; next, that these percepts are repro-
duced on other tones ; next, that certain percepts when
thus reproduced on certain tones generate new tones
in the concomitant harmony. For example, sol was
the first large fifth, namely, 5 of I in major. When
this large fifth was reproduced on ti in minor a new
tone, the chromatic si, was generated in the concomi-
tant harmony, in which it reported itself as large third.
This fact, in conjunction with the thesis that all the
nine percepts are potential in all tones and with the
rhythmo-harmonic laws of causation which we have
set forth, throws light upon the processes by which
melody gradually expanded the tone-system and tonal-
ity and evolved so much out of so little. But the fact
that a harmonic percept originated on a specific tone

ORIGIN AND NATURE OF MINOR 225

and thereafter was reproduced on other tones points
to the interesting inference that each tone has a har-
monic pedigree. By this I mean that melody first in-
troduced a tone in a specific relation, and next pro-
ceeded to introduce that tone in another relation and
then in another, and so on. Such a sequence of rela-
tions would trace the tone's harmonic evolution or
line of descent. Aside from its immediate interest
and value to psychology, the harmonic pedigree if as-
certained would enable the archseologist to determine
approximately the chronological order and relative
ages of primitive melodies. To be explicit. What is
a specific tone's line of descent or harmonic pedigree ?
It is that tone's evolutionary sequence of harmonic
relations. Where is this evolutionary sequence to
be traced? In melody, where it was produced.
All harmonic percepts being potential in all tones,
melody has carried each tone through a sequence
of percepts. To illustrate all this we will here pre-
sent the harmonic pedigrees of the seven original
tones (diatonics) so far as ascertained at this junc-
ture of our study.

1. Do first arose as 1 of I in major, then appeared
as 5 of IV in major, then as s of / in minor. So far as
already ascertained the pedigree of do is briefly 1, 5, 3.

2. Sol first arose as 5 of I in major, next appeared
as 1 of V in major, then as a of r in minor. This
pedigree of sol is briefly 5, 1, s.

3. Mi first arose as 3 of I in major, next appeared
as 5 of /, 1 of F and i of F in minor. This pedigree is
briefly 3, s, 1, i.

4. Re began as 5 of V in major, next appeared as i

226 THE NATURE OF MUSIC

of V in minor, then as i of IV and 1 of IV in minor.
This pedigree is 5, ?, i, 1.

5. La began as 3 of IV in major, next appeared as
9 of V in major, then as i of /, 5 of iv and 5 oi IV in
minor. This pedigree is 3, 9, 1, s, 5.

6. Fa began as 7 of V in major, next appeared as
1 of IV in major, then as 3 of iv and © of F in minor.
This harmonic pedigree is 7, 1, a, 9.

7. Ti began as 3 of V in major, next appeared as 5
of V and 5 of v in minor. This pedigree is 3, 5, s.

In these pedigrees we observe that of the nine per-
cepts thus far accounted for do has reported three and
has still to appear as 1, 3, 6, 7, 9, 9; sol has reported
three and has still to appear as 1, 3, s, 7, 9, 9; mi has
reported four and has still to appear as s, 5, 7, 9, 9;
re has reported four and has still to appear as 3, 3, s,
9, 9; la has reported five and still has to appear as 1,
8, 7, 9; fa has reported four and has still to appear as
1, 3, 5, 6, 9; ti has reported three and has still to
appear as 1, 1, 3, 7, 9, 9. Of all these relations still
remaining to be reported by diatonics both the rela-
tions and the harmonies are either chromatic or
enharmonic. The above pedigrees of seven tones
present an aggregate of twenty-six harmonic relations
each of which is distinct and individual. Thus we
observe that the multiplication of harmonic relations
is very rapid while that of harmonic percepts is very
slow. This is true not only of homophony, but of
multi-voice music as well. Further back the Zarlino-
Riemann theory of pendant minor was alluded to as
an example of irreconcilable conflict between music-
thinking and music-feeling. This conflict becomes

ORIGIN AND NATURE OF MINOR 227

evident when we subject the foundation of the theory
to the test of harmonic self-reports in one voice, a test
which we are now prepared to apply having just
summed up the original harmonic percepts of homo-
phonic melody and having finished our explanations
of the origins both of major and minor. The theory
in question is based on acoustics, and postulates that
the minor chord springs from a descending acoustic
series of undertones generated by a root on the top
just as the major chord springs from the ascending
acoustic series of overtones generated by a root at the
bottom, that the minor chord is the exact inverse of
the major chord in that the relative intervals and
ratios of vibration in both acoustic series are identical,
as shown below by the familiar acoustic numbers
1;2;3;4;5;6;8;. Thus at 6) the minor chord is as
4; 5; 6; 8; going down, and the major is the same
going up. In short, minor is inverted major.

h)

a)

Minor
Series

Major
Series

5^!f^^3^

i=

It is assumed that C is the root of both the major
and minor triads at 6). In other words, the sup-
posed C-minor triad hangs suspended from its aerial
root C just as the C-major triad rests upon its ground-
root C. The inverted acoustic series forming the
above minor triad is a purely arbitrary conception,

228 THE NATURE OF MUSIC

since the existence of such a series of undertones has
never been demonstrated, nor has it ever been heard
by the musical ear. It cannot be gainsaid that from a
mathematical point of view this hypothetical series of
undertones is both charming and fascinating, since to
the eye its explanation of the minor chord appears
both logical and satisfactory. This probably explains
why the theory has won so many adherents. But mu-
sical hearing, feeling and perception refuse thus to be
deceived. The common harmonic self-report of the
minor triad at h) is this : F is the root, Al? the third,
C the fifth. The triad is F-minor, not C-minor. One
might as well try to invert one's self and walk on the
ceiling as try to perceive C as the root of this triad.
The test of harmonic self-reports on the above hypo-
thetical minor series is as follows: 1; or C = 6. 2; or
C= 6. 3; or F= 1. 4; or C= «. 5; or A>= s.
6; or F= i. 8;or C= s.

Next I present the Zarlino-Riemann minor scale,
the tones of which are arbitrarily conceived as the
components of three pendant primary minor triads
supposed to hang suspended from the aerial roots C,
F and G. Below compare this pendant minor scale
with the ascending major scale and observe the per-
fect correspondence of the whole and half steps. Just
as in the case of the triad so also here in the case of the
scales the minor is the exact inverse of the major.

-iS^

Majai
Scale

iE=E^=,=^.=^ '• - ±J

ORIGIN AND NATURE OF MINOR 229

The test of harmonic self-reports in one voice when
applied to this hypothetical minor scale at once dis-
closes the fact that the scale is major, not minor. In
whatever rhythm we may ascend or descend on this
scale the resultant melody will always report itself as
major, each individual tone will report a major har-
monic percept, in short, we feel and perceive in com-
mon that this scale starts and ends on mi, the large
third of the major tonic-harmony upon which it is
based. Our next example presents the scale in its
descending form, each tone is named by a syllable,
each harmonic percept is marked by its specific num-
ber.

3 5 13 3 5^3

mi — re — do ^^^ ti — la — sol — fa s,.^ mi

Not only is this Zarlino-Riemann scale major, but it
is also identical with the ancient Dorian scale of the
Greeks. In the terms of our notation the tonic of
this scale is Ai? and not C ; the basic harmony of the
scale is that of AKmajor and not the supposititious
pendant minor chord of C.

On the line of least resistance, upon which homo-
phonic harmonies assert themselves, this scale abso-
lutely refuses to report the minor mode. However,
there are two ways in which in one voice this scale
may be induced to report itself as minor. First, by a
prelude in which we establish the feeling of the minor
consonance as below at a); next, by arbitrarily con-
ceiving the scale as minor. In the first case the minor
harmonic percepts owing to the prelude arise on the
homophonic line of least resistance, while in the second
case they are premeditated and therefore selective.

230 THE NATURE OF MUSIC

In both cases the result as to harmonic reports is the
same and as follows : —

Prelude Scale

^'^^^^J^^^^gd-r^'Mj^l^

F/.

Now that we have transmuted the scale from major
to minor thereby demonstrating that it may report
itself as minor in homophonic melody or one voice,
this question arises : Does this scale of minor harmonic
percepts in any way support the theory of pendant
minor? The above common harmonic self -reports
based on common harmonic feeling and perception
answer in the negative. These self -reports plainly
testify as follows : the scale, now minor, starts and ends
on mi (C), which is the fifth of the minor tonic-har-
mony based on la (F) ; its tonic or point of complete
repose is F and not C; its tonic-harmony is erect
F-minor and not pendant C-minor. Homophonic
harmony and its common self-reports being subjects
new to music-theory the same is necessarily true of
the facts here adduced as well as of the conclusions to
which they point. In conclusion it remains to be
said that besides being an acoustic theory of harmony
based on an acoustic hypothesis, the Zarlino-Riemann
theory is specifically a chord-theory. Having demon-
strated in preceding chapters of this book that chord-
harmony is selective harmony it is difficult to see how
the chord-theories of harmony could possibly have
escaped the bias of personal selection and therefore
of the personal equation.

ORIGIN AND NATURE OF MINOR

231

49. Chords Derived from the Minor Forms oj Con-
sonance and Dissonance in One Voice

From the original minor form of consonance / is
derived the original minor triad /. All other minor
triads like iv and v are duplicates. Below are the
triads /, iv, v.

i

^

IV

I

Like its major prototype the minor form of disso-
nance presents six chords, namely, the small ninth-
chord Fj, the two seventh-chords V^ and ra°y, the
three triads F, F77°, 77°, as follows: —

i

7

5 ?
3 5

-19-

1

^

^^^

<5?-

N.B.

vir

7

N.B.

r/yc

Jt

Of all these chords only two forms are of minor
origin. They are the small ninth-chord Fg and the
diminished seventh-chord F77°^, both marked N.B. in
our example. Each of these forms is the first of its
kind, all like forms being duplicates of these originals.
The remaining four chords are duplicates of forms
which originated in major and have been presented
in § 39. The first, second and fourth of the above
chords are based on the harmonic root mi, the third

232 THE NATURE OF MUSIC

and fifth omit the harmonic root, the sixth omits
both the harmonic root and third. The superposed
harmonic numbers show that mi is the harmonic
root of all of the six chords. In § 39 we pointed
out and explained by means of the harmonic self-
reports of homophony the necessary distinctions be-
tween harmonic roots and chord-roots, between har-
monic intervals and chord-intervals and by the same
means demonstrated that chords are often incom-
pletely represented by one or two components, some-
times appearing detached from their harmonic roots,
sometimes from their harmonic roots and thirds, some-
times even from their chord-roots. These distinctions
and facts being exemplified in the above groups of
chords and having previously been explained it is
enough here to call attention to them.

By comparing the above minor group of consonant
and dissonant chords with the corresponding major
group in § 39 the reader will observe that two chords
identical both as to form and component tones appear
in both groups. They are: li in major and iv in
minor; vii° in major and //° in minor. Despite their
identity in form and component tones these triads
make one report in major and a very different report
in minor, as shown below.

5 7 9 3 5 7

1. Major:

2. Minor:

re

— fa-

-la

n

1

3

5

re-

-fa-

la

ti-

-re —

-fa

VII°

5

7

9

ti-

-re —

-fa

IV ir

ORIGIN AND NATURE OF MINOR 233

Obviously this difference in harmonic report is
caused by difference in relation. Just as in homo-
phony the self-report of a specific tone varies as its
relation varies just so in multi-voice music the self-
reports of certain specific chords vary as their rela-
tions vary. No words can therefore overstate the
importance of relation, it is everything. Have we not
demonstrated in the genesis and evolution of harmony
that harmonic form to relation is as effect to cause ?
We have demonstrated that homophonic melody by
means of relation has produced the original forms of
harmony and the original tones of the tone-system.
Let us be explicit on this question of form and relation.
The two are inseparable in concrete music. So long
as we are contemplating and investigating tones or
chords in relation so long only are we contemplating
and investigating concrete music. But the moment
we leave out relation we leave out music and are then
contemplating and investigating only the mere mate-
rial of music. Thus abstracted from relation, a spe-
cific tone is simply a constituent of the tone-system
distinguishable from the other constituents as they
from it by relative pitch. A specific chord thus ab-
stracted from relation is simply one of the innumer-
able chords of music's chord-material distinguishable
from other chords as they from it by difference in
structure. Briefly, a tone or a chord out of relation
is out of music. The physical, physiological and psy-
chological views, analyses and theories of music's raw
material, that is, of tones and chords out of their dis-
tinctively musical relations, have not discovered a
single truth about music, have added nothing to our

234 THE NATURE OF MUSIC

intelligence and appreciation of music, and are ut-
terly valueless to music-theory and music-education.
Music itself presents its own peculiar forms and rela-
tions, in short, its own peculiar problems to the inves-
tigator. However, in his quest for truth the investi-
gator is in reality seeking he knows not what unless
he equip himself with the first essential requisite to
music-research, namely, with an adequate knowledge
of what the peculiar forms, relations and problems of
music are. After all, the great leading question is :
What is music ? And the answer to this question has
to be worked out independently by musicians. Music
isy and it is futile for physicists to tell us that music is
all wrong and should be otherwise.

The harmonic reports of the chords thus far de-
rived plainly show that a chord-root may be a har-
monic root or third or fifth; that a chord-third may
be a harmonic third or fifth or seventh ; that a chord-
fifth may be a harmonic fifth or seventh or ninth: in
short, that the self-report of a chord is determined by
its relation and is ascertained by harmonic analysis
as here set forth. No one, for example, hears the
component tones of the diminished seventh-chord
{yn^^ in minor) as root, small third, diminished fifth
and diminished seventh : we all hear them as 3, 5, 7, 9.
All other chords not based on harmonic roots furnish
similar examples. Chords are therefore more than
mere combinations of tones differing in structure.
Each component tone in a chord reports a harmonic
percept. Therefore correctly defined, a chord is at
once a combination of tones and a combination of
harmonic percepts, Homophony produced the origi-

ORIGIN AND NATURE OF MINOR 235

nal tones and the original harmonic percepts ; in poly-
phony and chorded music these tones and percepts
have been combined in well-nigh every conceivable
way.

In parallel examples I next present the major and
minor subtonic-seventh-chords. Each of these chords
is composed of the four cadence-tones of the mode in
which it arose. At a) the chords present double
cadences, that is, simultaneously rising and falling
cadences. At b) and c) the cadence-tones are sep-
arated and the cadences become single, that is, at b)
they rise, at c) they fall.

Major

Minor

T=^^ — ■ ^ :? ■ y

i^

At b) the bond-tones sol in major and mi in minor
combine with the two rising cadence-tones thus form-
ing the major and minor dominant-triads. At c) the
bond-tones do in major and la in minor combine with
the two falling cadence-tones thus forming the major
and minor subdominant-triads. The resolutions at
b) present the authentic ending, at c) the plagal
ending. The next example illustrates these single
cadences and two endings in pure diatonic minor,
all the triads being minor and composed of dia-
tonics.

236

THE NATURE OF MUSIC

i

f

-s*-

±=i^

p

IV

The above example may call forth this question:
Are not the above triads /, v and iv identical with the
secondary triads of the major mode known respec-
tively as VI, III and ii ? The question is premature at
this juncture, but may be answered provisionally in
the affirmative. As chords they are identical both in
major and minor, but their relations in major and
minor differ. Their relations in the above example
are in minor, and each triad is a combination of the
minor harmonic percepts i — s — 5. Concisely stated,
triads which are primary in minor are secondary in
major and vice versa.

CHAPTER VI

CHORDS IN THE LIGHT OF THEIR ORIGIN

50. Description and Summary of Chords Thus Far

Derived

At present our list of triads aggregates five in major
and six in minor as follows : —

In
Major

fe^^^^^

f II IV V

VII

In

Minor

iz^II^ZZ^EE^^iE^

11° IV V V Vjf

This summary presents only three distinct types of
triads, the major, the minor, the diminished. The
originals of the three types are respectively I in major,
/ in minor, vii^ in major. All other triad-types are
either modifications of the three originals or com-
pound chords.

The structure of a triad is described when we name
the exact interval relations of its third and fifth. We
describe the major triad as root, large third, pure
fifth: the minor triad as root, small third, pure fifth:
the diminished triad as root, small third, diminished
fifth. When we describe the structure of chord-types
we treat each type as chord-material and compute the
intervals of components from the chord-root without
considering whether or not the chord-root is a har-

238 THE NATURE OF MUSIC

monic root. But in the harmonic analysis of a con-
crete case we first name the type of a specific chord
and then proceed to describe the chord's specific rela-
tion which gives us the harmonic report we are in
search of.

There are three triad-positions. In its first posi-
tion, the triad is named the ground-triad, the chord-
root being its lowest tone. In its second position
with the chord-third as lowest tone, the triad is named
the sixth-chord and may also be called the terce-
form. In its third position with the chord-fifth as
lowest tone, the triad is named the fourth-sixth chord
and may also be called the quint-form. The posi-
tions of triads are further distinguished as close and
oj>en : close when the components are in closest prox-
imity, as below at a), o'pen when the components are
spread apart as at 6).

a) Close h) Open

sr

M /Q ,<3 IJ

I la I| I la Is

As everybody knows, all thorough-bass numbers
like 6 and | in our example indicate intervals as com-
puted from the lowest tone or bass.

Seventh-Chords, We have thus far presented four,
two in major, two in minor. They are: —

In Major In Minor

N.B. N.B. N.B.

CHORDS IN THE LIGHT OF THEIR ORIGIN 239

This summary presents three types, each marked
N.B. Each of these types is the original; the chord-
root of the first is the major dominant, that of the
second is the major upleader, that of the third is the
minor upleader. Every type of chord should have a
name in terms descriptive of its structure like the three
triad-types just considered. Since any chord-type
may appear on any tone in any key it would simplify
analysis were we able to refer to each specific type by
its structural name before proceeding to report on its
specific relation in any special concrete case. The
first of the above types of seventh-chords is known as
the dominant-seventh-chord, the second as the major
subtonic seventh-chord, the third as the minor sub-
tonic seventh-chord and also as the diminished seventh-
chord. All these names except the last are relation-
names. The first type is also known as the primary
and also as the main (Haupt) seventh-chord, and these
names also describe relation instead of structure. Be-
fore proceeding to give each of the above seventh-
chords its structural name we will first explain how
the form of such a chord is described. A seventh-
chord is a combination of a triad and a superadded
seventh. Its description requires two terms, the first
defining the triad, the second defining the seventh.
The two terms joined by a hyphen will give the exact
structural name of the specific type. The first of the
three types (N.B. in our example) comprises a major
triad and a small seventh ; the structural name of this
type is therefore the major-small seventh-chord; the
first of the hyphened words describes the triad, the
second describes the seventh. Accordingly the sec-

240 THE NATURE OF MUSIC

ond type (second N.B. in example) is named the
diminished-small seventh-chord. The third type (last
N.B. in example) is named the diminished-diminished
seventh-chord, or briefly, the diminished seventh-
chord. All other types of seventh-chords are either
modifications of these or compound chords.

Next we exemplify the four positions or forms of a
seventh-chord. They are: 1. the ground-form with
chord-root as lowest tone; 2. the terce-form with
chord-third as lowest tone; 3. the quint-form with
chord-fifth as lowest tone; 4. the sept-form with
chord-seventh as lowest tone. The four are known
respectively as the ground-seventh-chord, chord of the
fifth-sixth, chord of the third-fourth, chord of the sec-
ond. All appear below in close and open positions.

Close Open

js. -^

^ jsL _ J2. =: ^.

^-. — ^ ^fe' — g^ gy^ \—^. &^ ^ —^ H

V. V| Vj V, V, V| V| V,

Ninth-Chords, We have thus far derived two, the
large ninth-chord in major, the small ninth-chord in
minor: both are based on the dominant, and each is
the original of its peculiar type.

In Major In Minor

i^^

V9

The description of a ninth-chord requires three
terms, one for the basic triad, one for the superadded

CHORDS IN THE LIGHT OF THEIR ORIGIN 241

seventh, one for the superadded ninth. Thus the
large ninth-chord is described as major-small-large,
the small ninth-chord as major-small-small.

Owing to the fact that the chord of the ninth ex-
tends beyond one octave the customary inversion-idea
cannot be applied to this chord. In truth the idea
though universally practiced cannot logically apply to
any chord, since the inversion of a chord, like that of a
tone, is simply an impossibility. A triad has three
positions close and open, a seventh-chord has four
positions close and open, and each individual position
is an individual form distinguished from other posi-
tions and forms by its lowest tone or bass. Thus the
ninth-chord falls in line with the triad and seventh-
chord. Having five components the ninth-chord may
appear in five positions close and open. They are
presented in the next example. The first position
is the ground-form with chord-root as bass and is
marked ©; the second with chord-third as bass is the
terce-form and is marked 1; the third with chord-
fifth as bass is the quint-form, marked §; the fourth
with chord-seventh as bass is the sept-form, marked ?;
the fifth with chord-ninth as bass is the none-form,
marked 9.

or

jO-

^

or

V9.

242

THE NATURE OF MUSIC

i

-(2-

sSzs:?:

or ^ or ^

.^_ or or .a.

" a.

-<s^

^SL

Qr ^ or

9i=i^

-(2-

.gi2 ^(S2-

V?.

vg

The open positions after the close position of each
of the above forms are easily multiplied by conceiving
other combinations of the five chord-components.
When viewed as abstract material, the close posi-
tions of the above forms from the second onward
strike both ear and eye as amorphous and repulsive.
But in the concrete when each component reports a
clear and definite harmonic percept these chords at
once gain a definite shape and suggest many conjunc-
tions with other chords, some preceding, others suc-
ceeding them. For the time being we are summariz-
ing and describing the structure of chords the origin
of which we have explained in previous chapters. On
the other hand, the treatment of chords in concrete
music is the special subject of another part of this
work. But a word in the latter connection may be
said here. As harmonies we have seen that the large
and small ninth-chords appear sometimes with the
root, at other times without the root. With the har-
monic root the two above types are classed as ninth-
chords ; without the harmonic root the resultant chords
are classed as seventh-chords. By omitting the har-
monic root in the above example all the chords would
become seventh-chords.

CHORDS IN THE LIGHT OF THEIR ORIGIN 243

I next present the two original types of ninth-
chords in a series of ground-forms very commonly em-
ployed, especially in instrumental music. It will be
observed in these illustrations that while the chord-
root is retained throughout, the upper four tones ap-
pear successively in four positions first close, then open.

Large Ninth-Chord

l-p ,

/o 1

'X

^ ^ 1

-fr\ ■

o

c>

^-^

%]) I

ej

e>

if

■f-^

^

JSL

(or„)

o

^

c

^^

^

^

— ^—

— ^

f5>

^^-

^ 1

— & —

(S> —

— <& — i

L-^

&

& —

(S" —

— & ■

V9.

^maU. Ninth-Chord

^ — = 1

— 1 ^ fr"^

-^-^i »

fl^- s^ -s>- -s>-

S-^ -^- -&- -^- -&-

All other types of ninth-chords are either modifica-
tions of the original two or compound chords.

51. Simple and Compound Chords Defined

1. A simple chord is a combination of components
of a single harmony.

2. A compound chord is a combination of compo-
nents of two or more harmonies.

In the above summary all the chords are simple and
all the types there presented are types of simple chords.
Their sole guide having been harmonic feeling and

244 THE NATURE OF MUSIC

perception, the first builders of chords worked induc-
tively and were not troubled by laws of acoustics.
Moritz Hauptmann* tells us that treatises on harmony
usually open with a learned chapter on acoustics the
half-truths in which have little if any influence on the
chapters that follow. The truth is that the com-
monly adopted rules for building chords were formu-
lated in accordance with the dictates of harmonic
feeling and perception. The rules are: for building
triads, superadd third and fifth to root; for seventh-
chords, superadd seventh to triad; for ninth-chords,
superadd seventh and ninth to triad. The validity of
these rules as applied to simple chords has been con-
firmed by the three -tone, four -tone and five -tone
threads of original harmony in one voice. This prin-
ciple of chord-building by superadding third upon
third has been extended beyond the ninth to the
eleventh and thirteenth. The resultant chords, all of
which are compound, are known as chords of the
eleventh and thirteenth. The above rules apply ex-
clusively to simple chords. Their application to
chords in general is a purely arbitrary procedure and
has caused much gratuitous confusion in heads and
books. For when our intellectual or conceptual re-
port on a specific chord in a specific relation does not
agree with and is in truth utterly refuted by our con-
crete perception of that chord's harmonic report, how
can we help feeling confused! Theories that present
such conceptions are certainly false. Viewed in the
abstract a chord is musically dead; we have done
with it when we describe its structure and classify it.
Viewed in the concrete a chord is alive, each of its

CHORDS IN THE LIGHT OF THEIR ORIGIN 245

components is alive with its harmonic self-report, for
the chord is musically related. We are here con-
cerned with chords that are alive. We have seen
that in concrete music, harmonies may be completely
and incompletely represented by chords; completely
when the chord presents all the harmonic components,
incompletely when certain components are omitted.
Whatever their number, when the components of a
chord report a common root then the chord is simple,
and when they report two or more roots then the chord
is compound. The largest number of chords in use are
compound. The subject of compound chords belongs
to Part II of this work, but a few examples at this junc-
ture will suffice to show what they are. To the two
definitions of chords at the opening of this section we
now add a third which is general.

3. Chords are selective combinations of two or
three or four or five or more individual tones. They
are classed under the following heads : I. Consonant
or Dissonant. II. Simple or Compound. In the fol-
lowing parallel examples in major and minor all the
combinations marked by asterisks, with the exception
of the second, are compound chords. In these com-
pound biads ^ (two-tone-chords) the two tones are
components of different harmonies; one reports one
root, the other another root.

133 915 353135 1
131 531 139577 3

In

Major

mi:

uiU-jMeU^

fVCTr- r

r-rrf=f

* The writer coined the word biad by analogy with triad and tetrad. L. E. K.

246

THE NATUEE OF MUSIC

513 133 5553391
551 111 33317 7 7

i

Ui I J J J I J j

^

f

f

r

r r

r r

3 3 15 3 3 3
3 5 1 113 5

^

^-J-J-fj-^L^

3 5 7 3 5 3
13 3 113 1

^dd

Jc=^=?t

i

fT^TT

CTT

^ -X- -X- -Jt

iSs 9 Ifi SOSlsSl

1 8

5 3

1 8 O 6 7

Minor

^^^^^^

ife*3

ft^ !»rf rr ^n^

5 I 3 1 3 s

5 5 1 a 1 X

6 5 6 8
8 8 8 1

3 6 1

7 7 7

m

¥=i^ii-ni

r r

8 0 10 8 8 8

8 5 1 1 1 8 6

8 6 7 8 5 8

1 8 3 1 1 3 1

rri*

^

Uf

* *

The above superposed percept-numbers, large and
small, register our common perception of the concrete
harmonic self-report of each tone in each biad and

CHORDS IN THE LIGHT OF THEIR ORIGIN 247

therefore of each biad's harmonic relation. Relation,
being the immediate cause of a tone's and chord's
specific self-report, is first of all a question of mode:
Is the mode major or is it minor? This becomes
plain when we compare the corresponding relations
and consequent self-reports in these parallel examples.
The two examples present a number of the same biads,
but the reader will observe that the same biad makes
one report in major and quite another report in minor.
In addition to the question of mode one of three other
questions enters into this self-report-determining rela-
tion of every tone or chord. The three questions are:
Whither.? Whence.? Whence and whither.? The
first pertains to an initial tone or chord, whose self-
reports are influenced by what follows. The second
pertains to a terminal tone or chord whose self-
reports are influenced by what precedes. The third
pertains to an intermediate tone or chord whose self-
reports are influenced both by what precedes and
follows. By concretely thinking and carefully com-
paring these two examples of biads the reader will
appreciate the influences of this whither, whence
and whence-whither of relation. One more remark.
All biads are incomplete forms either of triads or
seventh-chords or ninth-chords. In a series of para-
graphs, each devoted to a measure of the above
parallel examples, we will now take up the explana-
tion of the biads marked by asterisks, first explaining
the biad in major and then the corresponding biad
in minor.

First Measure, This biad (with asterisk) simul-
taneously reports 3 of I and 3 of V, is therefore a

248

THE NATURE OF MUSIC

compound chord and represents the major mediant-
triad the symbol of which is iii. The corresponding
biad in minor is a compound of a of / and 3 of F and
represents the minor mediant-triad known by the
symbol HJ[, Thus the major mediant-triad is a com-
pound of the harmonies I and V: the minor mediant-
triad is a compound of the harmonies I and V, I next
present the full triads with harmonic report of each
component.

1. Major Mediant-Triad:

3

mi -
E

5-1

-sol-
G

3

-ti
B

marked III.

2. Minor Mediant-Triad:

8

do-

1"

6-1

-mi —
E

3

- si

marked Hi

The three tones in these triads are known as the
chord-root, chord-third, chord-fifth respectively. The
middle tone (chord-third) in each of the triads simul-
taneously reports itself as a component of two har-
monies. A tone presenting such a double report is
named a double harmonic. Every compound chord
contains at least one double harmonic. Primary
chords are simple : secondary chords, like those above,
are compound. Therefore secondary chords are com-
pounds of primary or simple chords. Before and after
the simple chords of which they are compounds, the
two above triads appear in third-relations and are
heard as compound in accordance with the above
analysis. They are given below in these third-rela-
tions and are marked N.B.

CHORDS IN THE LIGHT OF THEIR ORIGIN 249
In Major In Minor

$

^

Ǥ-

-(&-

W^

III I

V '" V

' TH. '

VNi

N.B.

N.B.

N.B.

N.B.

In short, these triads are heard as compound in all
relations excepting ffth-relations, in which case they
are heard as simple chords, that is, chords whose com-
ponents all report a common root. The structural
description of the two triads is as follows: the major
mediant (iii) is a minor triad its chord-intervals being
root, small third, pure fifth; the minor mediant (Hi)
is an augmented triad its chord-intervals being root,
large third, augmented fifth. This type of augmented
triad is supposed by Richter and others to have arisen
in minor on the third degree of the scale. This would
mean that our example presents the original aug-
mented chord. We shall see that this is not so, since
the harmonic percept of the augmented fifth first
arose in homophony on the major dominant, and we
shall further see that the augmented triad of the
major dominant is a simple chord.

Since the above mediant-triads are compounds of
the tonic and dominant harmonies of their respective
modes it follows that there are other secondary triads,
namely, those which are compounds of tonic and sub-
dominant and those which are compounds of domi-
nant and subdominant. These are the submediant-
triads vi in major and VI in minor, and the super-

250

THE NATURE OF MUSIC

1. Major:

la-
A

— do — mi
C E

2. Minor:

8

fa-
F

6-1 S

— la — do
A C

tonic-triads ii in major and //° in minor. Thus in
each mode there are three primary and three secon-
dary triads. We first present the harmonic analysis
of the major and minor submediant-triads.

3 5-13

VI.

= VI.

It is only in certain relations that these triads make
the above self-reports. They do so when they appear
as bychords on light rhythm-periods each before and
after the primary triads of which they are compounds.
See below: —

^ Major

^m

^

-Zir

-7^

sr

IV ^i IV

N.B.

VI

NJB.

f\

Minor

-(5>

.. 1 1

— Bj Z} —

— 25 ■

^^-7^ — f—

-*—

— 1 i9

V

J ^

IV

ri jy I VI I

N.B. N.B.

* This example and those on pp. 251 and 252, not found in the MS., were
supplied by Miss Luise Haessler. L. E. K.

CHORDS IN THE LIGHT OF THEIR ORIGIN 251

In most other relations these secondaries are heard
as simple chords. Surprising and noteworthy are the
facts first, that the triad vi is at once a minor triad
and a compound of two primary major triads ; second,
that the triad VI is at once a major triad and a com-
pound of two primary minor triads. The two asterisk-
biads in the ninth and tenth measures of our parallel
examples represent the triads in question and report
them as compound.

Next follows the analysis of the supertonic triads
II in major and ii^ in minor.

1. Major

5 7-1 9-3

re — fa — la

D F A

5 7- «-t

2. Minor:

ti — re — fa

B D F

= n.

IV

These compounds of V and IV in major, V and IV
in minor, make the above self-reports as bychords in
connection with their respective modal subdominant-
triads as follows : —

Major

\

i!^

¥

=2:

-&-

» See footnote, p. 250.

252

THE NATURE OF MUSIC

Minor

li

9t

IV

3

-#-

7/0

N.B.

'K

-&-

-^-

IV

The asterisk-biads in the seventh measure, page
246, represent these supertonic-triads and are heard
as compound. Before the dominant these triads are
heard as simple chords.

f Major '

i

^i

l^E&

11 V

N.B.

Minor

11

-»■

^

-"s:

no
N.B.

The books agree that this downward progression
from II to V and from //° to V is most natural and
correct, but do not satisfactorily explain why. The

* See footnote, p. 250.

CHORDS IN THE LIGHT OF THEIR ORIGIN 253

supertonic-triad is based on the fifth of the dominant
and therefore lies over it. Besides this, the fifth of
the supertonic-triad is the original ninth of the domi-
nant and its natural tendency is downward. Hence
these natural progressions.

Second Measure, The supertonic-triads as simple
chords and as just described are represented by the
asterisk-biads in this measure which precede the domi-
nant. Their analysis in this relation is as follows:
II = 5, 7, 9; If = 5, 7, o.

Third Measure, This biad is a compound of I
and V, and represents the secondary seventh-chord of
the major mediant 11I7. The corresponding biad in
minor, a compound of / and F, represents the corre-
sponding chord 7M7 in minor. Below are the full
harmonic reports on these chords.

3 5-1 3 5 I

1. Major : mi — sol — ti — re [ = Illy.

E G B D )

3 6-13 5 ]

2. Minor : do — mi — si — ti \ = IrJJl'

C E Gif B I

The remaining secondary seventh-chords (except-
ing those of the major and minor sub tonics which we
have already analyzed and found to be simple chords)
are compounds of primary harmonies. They are
those of the two tonics 1 7 and 1 7; those of the two sub-
dominants IV7 and iv^; those of the two submediants
VI7 and VI 7; those of the two supertonics 1I7 and 11%.
These chords are next analyzed in the order of their
mention. 1 7 is a compound of the primaries I and V;
/ 7 is a compound of / and F, as follows : —

254.

THE NATURE OF MUSIC

1. Major :

2. Minor

1

3

5-1 3

(fo.

— mi-

- sol — ti

c

E

G B

1

s

6-1 3

la -

-do-

-mi — si

A

C

E Git

= 17.

z7.

Next follow the major subdominant seventh-chord
which is a compound of I and IV and the correspond-
ing chord in minor which is a compound of / and iv.

1 3 5-13

1; Major : fa — la — do — mi . = IV 7.

2. Minor

F

A

C E

1

8

8-1 8

re

-fa-

— la — do

D

F

A C

= /r.

h

C E

G

2. Minor :

8

fa
F

6-1 8

— la — do
A C

6

— mi
E

^ The submediant seventh-chord in major is a com-
pound of IV and I ; in minor it is a compound of IV
and /, as follows: —

3 5-13 5

1, Major : la — do — mi — sol I = vi7«

= FI7.

The supertonic seventh-chord in major is a com-
pound of V and IV, while in minor it is a compound
of V and iv^ as follows: —

* This paragraph omitted in MS. was supplied by Miss Luise Haess-
ler. L.E.K.

CHORDS IN THE LIGHT OF THEIR ORIGIN 255

1. Major:

2. Minor:

5 7-1 9-3 5 1

re — fa — la — do
D F A C

5 ''-^

0-8 6

ti — re -

-fa -la

B D

F A

= Ilr.

= IV

While in certain relations there are variations in
the reports of these secondary seventh-chords they
nevertheless always report themselves as compound.
These compound triads and seventh chords call forth
many observations which however belong to Part II
on chords. My purpose here is fulfilled by introduc-
ing the subject of compound chords, by showing that
they really exist and what they are. Interested read-
ers will observe the differences in major and minor of
the self-reports of certain chords which are identical
in both modes.

Fourth Measure. The asterisk-biad is a compound
of I and V differing from the compounds thus far con-
sidered. The regnant harmony is that of the domi-
nant and is represented by its seventh in the lower
tone and therefore the upper tone is a bytone. In
short, this is a compound of regnant tone and bytone,
examples of which are very common. All this is true
of the corresponding biad in minor.

Fifth Measure. The parallel asterisk-biads present
similar compounds of regnant tone and bytone.

Sixth Measure. These compound biads represent
the major and minor tonic-seventh-chords which we
analyzed a moment ago.

Seventh Measure. These parallel biads represent

256 THE NATURE OF MUSIC

the major and minor supertonic-triads in relations in
which they are heard as compound chords. They
were analyzed in the paragraph on the first measure.

Eighth Measure. Compare this second biad with
the last biad in the preceding measure and observe
how the self -report of a specific combination may vary
even in the same mode. Also compare the same
biads in minor.

Ninth and Tenth Measures, Both measures pre-
sent the same biad in different positions. This biad
represents the submediant-triad in a relation in which
it reports itself a compound chord. The same applies
to the corresponding biads in minor. The analysis of
these submediant triads has already been given.

Eleventh Measure. These parallel compound biads
represent respectively the major and minor subme-
diant-seventh-chords which were analyzed on a pre-
vious page.

Last Measure. Both of these biads are based on
the regnant dominant, and are therefore compounds
of a regnant tone and a bytone. In the first biad the
bytone is below, in the second it is above. The same
is true of the corresponding biads in minor. This
concludes the analysis of the parallel examples on
pages 245-246.

The only secondary triads and seventh-chords not
included in the above analyses are those of the major
and minor subtonics, which are simple chords, since
the components of each report a common root. It
may also be stated here that all secondary ninth-
chords are compounds either of two or of three pri-
mary harmonies. In another chapter we shall con-

CHORDS IN THE LIGHT OF THEIR ORIGIN 257

sider the conclusions to be drawn from the facts
adduced from these analyses.

Our tone-material thus far accounted for admits of
a brief presentation of two other groups of compound
chord-structures both of which are very common and
have proved puzzling and difficult to account for and
explain by means of the arbitrary principle of super-
added thirds, a principle which in no way applies to
them. The first of these groups of chords are com-
pounds of repose-tones and cadence-tones, that is, of
stable and unstable tones. The second group com-
prises chords with superfix- tones, infix-tones and sub-
fix-tones, that is to say, chords with a tone added
above, between or below. Our next parallel exam-
ples present compound chords of the first group.

53 5,3 353 3
a)^ 1 1 1 6)1 1 1 c)l 1 1 1

In
Major

i

^m

T r

iis

3

*

^

3

9-3

9-3

, 9-3

7-1

7-1

5

5

\ 5

5

5

9-3

9-3

1 1-5

^)l-5

/)l-5

S)7-l

/>)*-!

258

In

Minor

«)

E

THE NATURE OF MUSIC

h) c)

iS;

1

5

^^S? ($'■

A

-<5» -^-

JL^^

All the above combinations marked by asterisks are
compounds either of the two primaries I — V in major
and / — V in minor, or of the three primaries I — V — IV
in major and / — V — iv in minor.

The chords in a), 6), c), d), e) and /) are com-
pounds of one stable tone plus one, two, three and
four unstable tones respectively. The stable tone
do \ (C) is the chord-root of each of these compound
chords. Why? First, because being the tone to
which the other tones are added and being stable it is

CHORDS IN THE LIGHT OF THEIR ORIGIN 259

the principal tone in each chord ; second, because it is
the harmonic root of the chord into which each of
these compound chords resolves. The chords in g)
and h) are compounds of two stable tones plus three
and four unstable tones respectively. Both of these
stable tones do (C) and sol (G) are harmonic roots, but
for the reasons just given do (C) is the chord-root of
these compounds. The harmonic root /a (F) which
appears in these chords is in every case an unstable
tone. The chord-root of these compounds may
appear below, between or above the other chord-
components, but the ground-form or fundamental posi-
tion of these and like chords is that form or position
in which the chord-root is lowest tone or bass. In all
cases the structure of these chords is described in
accordance with the ground-form and in the inter-
val-terminology of thorough bass. On the other
hand, the harmonic reports of these chords are deter-
mined by the concrete relations in which they appear.
While this species of compound chord may arise on
any tone their occurrence is most frequent on the
major and minor tonics and dominants. There are
so many types of this species of chord that we now
present only a few others and defer their harmonic
analysis owing to the fact that they introduce har-
monic percepts not yet accounted for.

i»^^^=^

jS^

CA-i <g^v.^<« g2>x^

:^

260

THE NATURE OF MUSIC

jC«==-

(2-^ — L, , ^_ gy-,_ «22J==» (2.

The above ties for stable tones, and cadence-marks
for unstable tones plainly indicate the resolutions of
these compound chords into the major tonic-harmony.
To the eye the first three chords appear to be nothing
but fourth positions of the diminished seventh-chord
based on the chord-root Djj! in which case the chords
would be simple. Not so to the ear. In all these
chords do (C) is stable and reports itself as harmonic
root, that is, as 1. The attempt to think do in these
compounds as a small ninth and as unstable, in short,
as anything but 1 and stable, results in a voluntary
intellectual strain which is wholly unsupported and
contradicted by the common reports of feeling and

CHORDS IN THE LIGHT OF THEIR ORIGIN 261

perception. As to number and variety there is no
limit to compound chord-structures of this group, since
they include every imaginable combination of one or
two or three stable tones plus from one to four dis-
tinct unstable tones in forms in which each compound
tone appears but once and in other forms in which
components are doubled and even trebled. More-
over, these compound chords may be conceived on any
tone and in endless relations. In fine, these chords
are distinct structures because each may be a regnant
harmony in which relation the components of each
are regnant tones. The fact that as regnant har-
monies each of these compound chords may be elab-
orated with its bytones may prove suggestive to com-
posers in that it points to a wealth of new melodic,
harmonic and polyphonic possibilities as well as to
many as yet unthought and unpenned ornamental
figures and passages. The study and elaboration of
these compound chords as well as of others about to
be presented may serve as a stimulus to the com-
poser's thought and imagination.

Attention is next directed to what on a previous
page was called a second group of compound chords.
The description of these chords is roughly as follows :
Each of these structures has a triad for its nucleus and
to this triad one tone is added either above or below.
The tone when added above is a supersixth of the
chord-root and the resultant combination is named a
swpersixth-ohord. The tone when added below is a
subsecond of the chord-root and the resultant chord
is named a suhsecond-ohord. To understand these or
any other chords they must be conceived in the con-

262 THE NATURE OF MUSIC

Crete as regnant harmonies the self-reports of which
are perfectly distinct. The distinctive peculiarity of
these compounds is simply this : The added tone does
not disturb the identity and "predominance of the triad.
Conversely, the triad preserves its identity, regnancy
and predominance after the tone is added. For ex-
ample : after superadding A to the C-major tonic-triad
the triad still retains its identity, regnancy and pre-
dominance and we hear the new combination as the
major tonic-triad plus the added tone. True, the
resultant chord is a new and distinct idea and unity,
and the added tone adds something new to the self-
reports of the triad-components, thus creating the
compound chord, nevertheless the truth of our thesis
persists, the triad does not lose its identity and pre-
dominance. The nucleus-triad of a supersixth or sub-
second chord may be major or minor or augmented
or diminished, and every type of these chords may be
found on any tone in any key. This conveys some
idea of their limitless number. Below in parallel ex-
amples are supersixth-chords based on the triads of
the major and minor tonics, dominants and subdomi-
nants in a), h) and c) respectively. These chords
are marked by adding the symbols +6 to the bass-
number, pitch-modifying signs being added when
necessary.

In 6^' ^ ^
Major

l^ Y Y Y^ii Y IV IV+e I
* * *

CHORDS IN THE LIGHT OF THEIR ORIGIN 263

Minor

f

While the added tone in each above supersixth-
chord does not disturb the identity and regnaney of
the nucleus-triad it does affect the two lower tones of
the nucleus-triad in that it transmutes them from
simple to compound harmonics. In fact, the added
tone and these two lower tones of the nucleus-triad
combine in and represent another, a second triad in
each such chord. Hence this definition: A super-
sixth-chord is a complex of two triads one of which pre-
dominates and is the nucleus. How do we know which
of the two triads is the nucleus ? This is reported by
the regnant harmony. We will analyze the first of
these chords marked I 4-6 in a). This chord is a
complex of I (C-major triad) and vi (A-minor triad).
Of these two triads the former is at once nucleus,
tonic, primary and simple, while the latter is at once
submediant, secondary and compound, a compound as
already shown of the harmonies I and IV. Thus
I + 6 is a complex of the triads I — vi and a compound
of the harmonies I — IV. A compound chord how-
ever complex is a distinct idea and unit; it differs
from every other chord of the same and other species
though its structure may be similar; it is felt, heard
and thought as a single idea, which is the direct pro-
duct of its specific combination. This will appear as
we proceed to analyze the other supersixth-chords of
our example. In a) the chord / + 6 is a complex of

264 THE NATURE OF MUSIC

the triads I — VI and a compound of the harmonies
7 — IV, In h) V + 6 (major) is a complex of the
triads V — iii and a compound of the harmonies V — I,
while F + 6 (minor) is a complex of the triads V — TH
and a compound of the harmonies V — I. In c)
IV 4- 6 (major) is a complex of the triads IV — ii and
a compound of the harmonies IV — V against which
IF + 6 (minor) is a complex of the triads iv — n^ and
a compound of the harmonies iv — V. Our analysis
suffices to show the exact structure of these chords and
suggests their natural relations to other chords which
we shall consider in Part II.

Rameau first conceived and presented the super-
sixth-chord which he found on the major subdomi-
nant-triad (as above in c)) and of which he explained
that the added tone did not change the triad. But all
the other supersixth-chords in our example are formed
in the same way, are for the most part in the same
common use, are equally distinct ideas, the harmonic
report of each being equally distinct and definite; in
short, they are actualities not to be overlooked and
commanding general recognition.

The fact that each of the above chords is a complex
of two triads in which one of the two triads is nucleus
and predominates, naturally suggests this question:
Does the other triad in each of these complexes ever
assert itself as nucleus and ^predominant ? Yes, it does.
By what test is this to be verified and known .^ By
the immutable report of regnant harmony. All this
is conclusively demonstrated in the next group of
parallel examples in which the asterisked chords fol-
low each other in the same order as those in the pre-

CHORDS IN THE LIGHT OF THEIR ORIGIN 265

ceding group of examples. One by one in their given
order let the reader compare the corresponding aster-
isk-chords in both groups of examples. He will ob-
serve that each of the corresponding chords in both
groups is a combination of the savie tones, a complex
of the same triads, a compound of the sayne harmonies.
But nevertheless each chord in the group of examples
below is an entirely different, new and distinct struc-
ture and idea. The structure is as follows. Each of
the asterisked chords below is formed by subadding a
second to a triad and is named a subsecond-chord.
The symbols + 2 mark the subsecond-chord.

In
Majoi

a)

b)

-g> £/^

VI

vi+a

a)

In

Minor

-i 2

-aag

IV

J2.

^^

kh^

t

c)

25^-

is:

3

^z^

I I

-i&f2

I

111+3 T

II

II+3
*

V.

i

0)

li=i

VI F7+a '"" "^ f-

^_^;^=g_^

I

JJ9 IJO+2 Vrj

The concrete idea of each of the above subsecond-
chords is explained in the terms of harmonic analysis
as follows: In a) the chord vi + 2 (major) is a
complex of the two triads vi — I, vi predominating,
and a compound of the harmonies I — IV: against this
F/ + 2 (minor) is a complex of the triads VI — /, VI
predominating, and a compound of the harmonies
/ — IV. In b) III + 2 is a complex of the triads
III — V, III predominating, and a compound of the

266

THE NATURE OF MUSIC

harmonies I — ^V, against which TH + 2 (minor) is a
complex of the triads KZ — F, TH predominating, and
a compound of the harmonies / — F. In c) the chord
II + 2 (major) is a complex of the triads ii — IV, ii
predominating, and a compound of the harmonies
V — IV, against which //° + 2 (minor) is a complex of
the triads ll° — iv, ii^ predominating, and a compound
of the harmonies F — iv.

Analysts do not agree on the chord in the opening
measures of Beethoven's Sonata Op. 31 No. 3. This
chord is ii + 2 in its 5 position, the one above in c),
as shown in our next illustration. Most of these
chords appear both in major and minor, their har-
monic reports varying as their relations are changed.
Thus, for example, the chord vi + 2 (above in major)
appears in minor where it becomes / + 2. This is
exemplified below in the opening measures of Bee-
thoven's Sonata Op. 27 No. 2.

Op. 31. No. S.

i^

i^

-m

i^

e

r

f

n+2-

zg: zg: ::gi

Op. 27. No. 2.

CHORDS IN THE LIGHT OF THEIR ORIGIN 267

The thorough-bass mark of the ground-form or
first position of a supersixth-chord is 5, of that of a
subsecond-chord is 2. These chords being combina-
tions of four tones naturally have four positions both
in close and open voicing. Since a combination of
the same four tones is now a supersixth-chord and now
a subsecond-chord, now reports itself in major, now
in minor, since each such chord may appear in one of
four positions either in close or open voicing, how is
it possible to tell which is which? Always by the
report of regnant harmony, which is absolute. The
chords 1 + 6 in major and /-f2 in minor are com-
binations of the same four tones and will serve to illus-
trate all these points. Both are presented below,

a) In Major h) In Minor

5 3 1

Close

Open

268 THE NATURE OF MUSIC

each in four positions in close and open voicing
together with its pecuKar thorough bass numbers.

In a) the regnant harmony of melody and chord
report the major-tonic-triad as nucleus and predomi-
nant, C (do) as chord-root and A (la) as added tone.
In b) the same sources report the minor tonic-triad
as nucleus and predominant, A (la) as chord-root,
G (sol) as added tone. To the eye the chords in a)
and b) appear to present the same structures and
ideas: to the ear, as the above analysis shows, they
present entirely distinct structures and ideas. In a)
we all hear a major triad plus a supersixth ; in b) we
all hear a minor triad plus a subsecond. If music is
what we hear rather than what we see then supersixth-
chords and subsecond-chords are positive realities
and facts of common concrete experience which are
recorded in every music-score and confirmed in every
musical mind. But, it will be asked, are not the
above chords as well as all the other supersixth and
subsecond chords thus far presented simply secondary
seventh-chords ? Yes and no. Yes, in the sense that
they are commonly known and classed as such. Em-
phatically 710, in the sense that their structure is the
same as that of the actual harmonic seventh-chords
V7 in major and V^ in minor. Once more, closely
observe the above two chords 1 + 6 and 7 + 2. Does
either of the two contain a harmonic seventh ? No :
in certain positions both chords present a seventh, but
this seventh is a c/torc^-seventh, that is, an arbitrary
thorough-bass seventh computed from an arbitrary
chord-root; it is not a harmonic seventh, as the fol-
lowing analysis proves. Above in a) the chord 1 + 6

CHORDS IN THE LIGHT OF THEIR ORIGIN

reports the components of its nucleus-triad to be 1, 3, 5
of I and reports its added tone to be 3 of IV, while in
b) the chord / + 2 reports the components of its
nucleus-triad to be i, 3, s of / and reports its added
tone to be 5 of ///. Thus neither of the two chords
contains and reports a harmonic seventh. Hence this
obvious question: Should chords without harmonic
sevenths be known and classed as seventh-chords?
Thorough-bass answers yes; harmony answers no.
That is to say, from the view-point of thorough-bass
the above chords are seventh-chords, from the view-
point of harmony they are not. If we distinguish
between the two view-points, both of which are neces-
sary, there need be no difficulty or confusion. In fact,
the prevalent thorough-bass system and its termi-
nology are indispensable to the theory and practice of
harmony; not only is their utility unquestionable, but
they have become fixed habits. The adoption of a
simple and exact term from the German will, I think,
remove the whole difficulty. To explain: For triad
the German says Dreiklang, for seventh-chord the
German says not only Septimenaccord, but also Vier-
klang. Vierklang is the term in question. According
as we may prefer its Latin or Greek derivation the
English equivalent of Vierklang is quadrad or tetrad.
I suggest the adoption of the term tetrad as the class-
name of all chords of four components. Tetrads may
be subdivided into as many distinct groups as there
are distinct structures. Thus seventh-chords would
form one group, supersixth-chords would form another
group, subsecond-chords still another, and so on.
Such a classification would not only conform both

270

THE NATURE OF MUSIC

with harmony and thorough-bass and render the two
reciprocally explanatory, but it would enable us to
say truly that certain tetrads are seventh-chords,
certain other tetrads are supersixth-chords, and so
forth. This would deliver us from that unnecessary
and harassing evil of trying to force all chords to fit
into one of a few arbitrary and conventional thorough-
bass patterns. The truth is that music resembles
nature in that its species and varieties of distinct struc-
tures are countless and limitless. Everywhere in
nature there is music, everywhere in music there is
nature.

In the next parallel examples the same four tones
combine in forming a subsecond-chord in a) and a
supersixth-chord in 6). The subsecond-chord in c)
and the supersixth-chord in d) are likewise combi-
nations of the same four tones. These chords are
marked by asterisks and their forms are explained by
the accompanying symbols. Minuter analysis is un-
necessary here since each chord is a complex of triads
and compound of harmonies similar to those previ-
ously presented and analyzed.

a)

Major

i^

-i

g — i— 1-^ — i-i 18 g I r^-

r-nr^^

VI

r

IV

^pi¥

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ni

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IV

IV+2 ^"°7

VI

VI+6 J
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V

CHORDS IN THE LIGHT OF THEIR ORIGIN 271

In

Minor

a)

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In the chords marked by asterisks the next collec-
tion of parallel examples presents supersixth-chords
in each of which the added tone is either a chromatic
or an enharmonic. Most of these chords are familiar
and are known in current text-books by other names.
In structure and idea they present and report them-
selves as tetrads of the supersixth-group, of which
there are as many varieties as there are distinct struc-
tures. The possible connections of these chords being
wellnigh boundless only a few examples are given, and
owing to the fact that we have not yet explained the
genesis of these chromatic and enharmonic harmonies
which these chords represent, their further analysis is
deferred.

In

Major

a)

Jg I Jg'

f

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II

# i# , ^ ^_j}J^_lh

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IV

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272

THE NATURE OF MUSIC

mlI^^^

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r— r

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F+6fi F+6X ^^^ F ^^+«'^ ^^+« ^ ^^+« ^^+«« /

I

F+6« Fh6X ""''

The compound tetrad having been introduced and
explained, the subject is here dropped. Of several
other distinct species of compound chords I will point
out but one more with which the present provisional
exposition of this wide and fertile jfield of inquiry may
be brought to a conclusion. The harmonic analysis
of the peculiar and distinct chord-structures now con-
fronting us and marked by asterisks in the next group
of examples is omitted save in one important particu-
lar, namely: the harmonic root of each such chord is
indicated by a capital letter. Thus the harmonic
root of the asterisked chords in a) is G, in 6) is C,
and so on. The key being C major the harmonic
root G in a) is the dominant, C in 6) is the tonic, and
so on. These harmonic roots are reported by the
regnant harmony in each instance.

-e^

f^f^

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4c

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-zt

^

t^-

G

-zr

CHORDS IN THE LIGHT OF THEIR ORIGIN 273
3. 6)1. 2.

t=X

H

-Z5>- "Z^

-# ^

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274

THE NATURE OF MUSIC
2. 3.

fe:

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fe

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f-r

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Each of these chords is a regnant harmony, each
component of each chord is therefore a regnant tone
and reports a harmonic percept. For the present this
ends our harmonic analysis of these structures because
each reports certain harmonic percepts which will not
be explained and ascertained until we reach the chapter
on chromatic and enharmonic harmony. Our present
description of these chords will therefore be superficial
because confined to the abstract interval-terms of
thorough-bass but will nevertheless suffice for their
introduction. The peculiarity common to all these
compound chords and rendering them distinct from
all others is this: Each contains two distinct com-
ponents answering at once to the same letter-name and
to the same interval-denomination as chord-root,
chord-third and so forth. Observe the asterisked
chord in a) 1 and 2 : it contains a G and a G^: G is the
chord-root, Gjj! is the chord-root sharped: apparently
the chord has two roots: harmonically of course this
is not the case : regnant harmony reports that G is the
chord-root and that Gjt is an added tone. The aster-
isked chord in h) 1 and 2 contains Eb and Ejj!, that
in 3 contains E and E^: thus each of these chords
contains two distinct chord-thirds of the root C. The

CHORDS IN THE LIGHT OF THEIR ORIGIN 275

asterisked chord in c) 1 and 2 contains Gi? and Gj^,
that in 3 contains G and Gi?, that in 4 contains A
and Ati: each contains two distinct chord-fifths of a
common chord-root. Likewise each of the asterisked
chords in d) contains two distinct chord-sevenths of
the same root, in ^) two distinct chord-ninths of the
same root. Now it may be objected that all these
structures are nothing but passing chords. Yes, but
they are chords all the same, each is regnant, each is
a combination of harmonic percepts and subject to
harmonic analysis. Next it may be objected that the
above notation of these chords is arbitrary and incor-
rect, that in the asterisked chord in a), for example,
we might substitute At? for G^ and then the chord
would simply be the small ninth-chord of the domi-
nant, marked V^. I reply that Ab in this chord would
be absolutely false and misleading for two patent
reasons. First, because A]7 is a chromatic down-
leader with a downward tend whereas the regnant
harmony reports a chromatic upleader with an uptend :
hence G^. Second, because the step from AU in this
chord to Ajl in the next chord reports a progression
whereas the relative and regnant harmony report this
specific step to be a rising cadence and resolution : hence
again, Gjji. On its logical side no one will gainsay that
the symbols of notation to be accurate should be
selected in conformity with the harmonic idea to be
conveyed, and that this should be insisted on even at
the cost of certain old and time-honored traditions
and conventions, the preservation of which is the func-
tion of history but whose usefulness in practice no
longer exists. Certainly our 20th-century notation of

276

THE NATURE OF MUSIC

the classics should discard the many inaccuracies of
the 17th- and 18th-century notation. At best our
notation has its limitations; still its symbols are
adequate for a more accurate presentation of the har-
monic idea. Editors have done much in this direc-
tion, but editions still contain many harmonic errors.
How are these errors discovered.? By the common
immutable self-reports of regnant harmony. Correct
harmonic notation is a question of conformity with
these common self -reports. I will stop here for but
one illustration and quote the subjoined measure from
the Adagio-theme of Beethoven's E flat piano-con-
certo, the error in which was corrected by von Biilow
in the Cotta-edition, but still occurs in other editions.
At N.B. in a) the melody distinctly and unmistakably
reports itself as the large third of Djjl, that is, as F X :
see correction at N.B. in b). Instead of F X Bee-
thoven wrote Gij, which is a diminished fourth, and Gjj
reappears in every repetition of the melody throughout
the Adagio: see in Peters' edition. It is impossible
to hear this specific tone in this specific relation as a
diminished fourth, nor could Beethoven so have heard
or conceived it. The common self-report as large
third is immutable and therefore the notation Gtf is
misleading and false while that of F X is logical and

a)

M

b)

^

6E^

t=w.

N.B.

N.B.

§S&

P^

^^?

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— I 1 «-

CHORDS IN THE LIGHT OF THEIR ORIGIN 277

true. To the speller and performer of notes such
errors are not troublesome: it is otherwise with the
reader and interpreter of ideas,

52. Melody the Original Reporter of Harmony, There-
fore the Natural Preceptor and Guide in the First
Studies in Chords

The thread of this exposition is here temporarily
dropped in order to inquire into the most simple and
direct way of insuring from the outset the student's
musical understanding and mastery of the chord-
material taken up from lesson to lesson. The ground-
forms of the three primary triads I, V, IV constitute
the material of the usual first lesson. It is customary,
after explaining this material and giving rules for its
treatment, to embody it in a group of exercises each
consisting in a series of fundamental basses. The
student then fills in the chords, in doing which he
carefully ties the bond-tones and avoids the imper-
missible consecutive fifths and octaves. This lesson
is followed by others, each adding more material,
more rules plus exceptions to or modifications of pre-
vious rules, more exercises in the bass, more per-
formances by the student, and so the work proceeds.
It is well known that in performing these tasks most
students do not exercise their natural musical facul-
ties in the slightest degree, they see but do not hear
what they write, their observance of rules, their per-
formances are purely mechanical. Such unprofitable
results point directly to some radical defect in teach-
ing, to some psychological error in our pedagogy.

«78 THE NATURE OF MUSIC

How account for this defect, what is its cause ? The
majority of those composing the rank and file of stu-
dents are only moderately endowed with musical gifts,
yet each student sets out with a deep love of music and
that love is the certain proof that he possesses innate
musical faculties, the activity and healthy growth of
which it is the function of eflBcient pedagogy to stim-
ulate and direct. The defect, its cause, indeed the
source of the whole difficulty lie in the universally
adopted form in which the work is presented to the
student, namely, in the exercises in fundamental
basses, in short, in the fundamental basses. To be
sure, the fundamental tone is the only true viewpoint
of chord-material as such in the light of its structure,
since each structure Tests and is built upon its root or
fundamrental. This being true it would seem that the
only natural and logical form of first exercises for
students is that of a series of fundamentals as is the
prevailing custom. So it would seem, but it is not
true. Our pedagogy has failed adequately to dis-
criminate between two essentially distinct viewpoints
of chord-material; first, that of the chord as a struc-
ture and mere material; second, that of the chord as
applied in the living stream of connected rhythmo-
harmonic feeling and thought. The first of these
viewpoints is that of the fundamental tone. The sec-
ond, as the above heading and all thus far said in
these pages imply, is melody. Melody is the stu-
dent's first consciousness of music, in melody he rec-
ognizes both the object and the proximate cause of his
love of music, to him melody is from the outset some-
thing real, tangible, comprehensible, the one thing he

CHORDS IN THE LIGHT OF THEIR ORIGIN 279

feels, can follow and express because of his innate
sense of the relations of its tones and of the natural
form and sequence of its phrases, the one thing he
knows and delights in, the one thing which to him is
music. From all this the student is cut off by an
exercise in fundamentals at the sight of which his
musical faculties not being stirred are as dead. The
student's intellectual grasp of the rhythmo-harmonic
form and content of a simple melody should be the
first end and aim of a teacher. How this is done has
been shown in preceding chapters. Tell him that
each tone in melody conveys two definite and simul-
taneous reports to his perceptions, a rhythmic report
and a harmonic report. Associate these reports with
correct symbols and the student's feeling and thought
are connected for all time. The resultant intellectual
grasp of these reports is the certain awakener of his
musical faculties and intelligence with which at the
crucial moment his face will not fail to light up. Mel-
ody, the original reporter and raison d'etre of harmony,
the universal voice and form of the inner music-con-
sciousness, is the student's natural key to the what,
how and why of chords. Melody is the direct re-
porter of fundamentals and chords. Fundamentals
and chords are not reporters of melody though they
may suggest them. The common practice of con-
ceiving different melodies to a given bass belongs to
a later stage in study. Thus to begin the study of
chords is to reverse the natural order.

Below are examples of first exercises embodying the
primary triads. It is a psychological error to suppose
that any beginner however gifted possesses the con-

280

THE NATURE OF MUSIC

ceptive power to grasp the four-voice music-thought
embodied in these given basses. The impossible be-
ing demanded, the student's performance is neces-
sarily mechanical and musically dead since his musical
faculties are not called into requisition. How many
beginners are there who even so much as hear the
given bass itself! Even those who do, what musical
sense can they make of it, what harmonic connection
do they perceive in these series of bass-tones ? None
whatever. Does not the untrained and natural bass-
singer feel and find his tones in relation to something
else which he grasps and remembers as a whole,
namely, to a melody ? When there is no one present
to sing the melody what does this natural bass do,
does he sing the bass-part ? No, he sings the melody.
Thus cut off from melody, from music-thought by
these basses, the student's only intellectual refuge
lies in the prescribed rules for connecting chords
which more often tell him what not to do rather than
what to do. Even though he performs his task cor-
rectly he has gained nothing musically, and the edu-
cational purpose is not attained.

1. 8 2.8

-^:^

-^

75*-

P=t

-(2-

B

I IV I VI IVIIVVI

The same material, in short, the same exercises are
next presented in the form of melody, of music-thought
itself.

i

e

5 1

-U ii I

1 2.1 3 1

^— H ^

-^

I

CHORDS IN THE LIGHT OF THEIR ORIGIN 281

These melodies and their harmonic index plainly set
the student's task before him, and give him the key to
the whole musical rationale of the situation. Melody
being the one simple and real fact in the beginner's
inner consciousness and experience of music, it follows
that the given melody is the one thing that his musical
faculties can seize upon and be stirred by, the one
thing that lies within his intellectual grasp and appre-
ciation, the one thing he appreciates and remembers
as a whole and in relation to which it is easy for him
to add something else since it explains the musical
what, how and why of the addition. The beginner
feels and can follow the inherent relations connecting
the tones of the given melody, he readily learns to hear
the concomitant voices reported by the melody, since
those voices but complete the sense of the melody.
Thus as he adds voice upon voice the student duly
learns to appreciate the concurrences and correla-
tions of all the four voices, in fine, he knows what
he is about and attains the educational purpose of the
exercises. Below is the desired result of his perform-
ance, valuable if worked out from a given melody,
valueless if worked out from a given bass.

2.

-i-s

^

-TTJr

i

-^^-=H-,a

-^-

^^i^

l-r^

:a — ^

i

S

^

i

^

The corresponding material in minor is embodied

282

THE NATURE OF MUSIC

in the following given basses at a), given melodies at
6), and performances at c).
1. 2.

8 # 8 # #

I

^^=1

a I cJ \\

f=^

-Z3*-

/F

F

2.

^^ ^Xj_Jz=z|J4-^^^^^^^^ ^-^ l=^|J I ^ II

It will be observed that the above exercises are the
exact counterparts in minor of those just presented
in major. This comparative study and treatment of
corresponding material in major and minor by means
of such parallel exercises in given melodies is com-
mended for its usefulness to students.

Exercises in the given bass, owing to their arbitrary
prescription of the order and arrangement of material,
completely cut off the student from that independence
of thought and judgment in the use and selection of
chord-material which is so essential to its mastery.
Not so with exercises in given melodies, for these may

CHORDS IN THE LIGHT OF THEIR ORIGIN 283

be presented with and without harmonic prescriptions.
For illustration we will take the first of the above
parallel exercises in major and minor. Present these
melodies without harmonic numbers and ask the
student for their harmonic self-reports. He will
respond with the following: —

Major Minor

1113 1 X X X 3 X

i

I

-<s-

-^

Setting out with a distinct perception of these com-
mon harmonic reports asserted by the melody itself
the student has a great advantage for he is thus
enabled to distinguish between such self-reports of
natural harmony and the personally selected reports
of selected harmony. In short, he learns what is the
difference between self-reported harmony and per-
sonally selected harmony, between reports perceived
and reports conceived, all of which he cannot learn
from a given bass. Now change the harmonic num-
bers of these parallel exercises as follows and ask the
student which harmonies are self-reported and which
are selected.

Major

The student will answer: the second harmony in
both exercises is selected, all the others are self-
reported. Next ask the student to conceive other
harmonizations of the same melodies restricting him-
self of course to the ground forms of the primary

1 5

1 3

1

Minor

1 5

1 3

1

*

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£84

THE NATURE OF MUSIC

triads. He will readily think out the following con-
nections of harmonies : —

a) Major:

1 1

5 3

1

Minor:

1 1

» 3

'

b) Major:

5 1

5 3

1

Minor:

5 1

6 3

1

The student is to work out all these exercises in four
voices both in close and open harmony. Present the
chord-forms 6 and % : require the student to introduce
them in these same exercises placing the thorough-
bass numbers under the notes of the melody. He will
easily produce the following conceptions: —

a) Major:

1 1

1 3

1

1 1

1 3

1

c c

c b

c

Minor:

a a

a g#

a

6

I

6

I

1 5

1 3

1

1 6

1 3

1

C C

c b
I

c

Minor:

a a

a

b) Major:

When the secondary triads are introduced the
student will soon find the right place for the subme-
diant in the same melodies as follows : See asterisks.

Major :

These illustrations suffice to show the practical
value of our harmonic numbers as here applied to
melody, the natural and all-potential harmonic voice
of music. Both when they indicate harmonic self-
reports or percepts and when they indicate selective
harmonic reports or concepts, they directly explain
and interpret the true meaning of harmony to the

1 3

5 3

1

1 3

5 3

1

c c

c b

c

Minor :

a a

a g#

a

^

•Jf

CHORDS IN THE LIGHT OF THEIR ORIGIN 285

student's musical understanding. In fulfilment of an
inherent law, melody evolved the chord. Nature has
bountifully endowed the student with a keen sense of
that inner law and of that concomitant harmony
always reported by and inseparable from melody.
The genesis and development of harmony being due
to melody it lies in the nature of things that the study
of harmony is the study of the harmony of melody, in
a word, of meloharmony.

At the outset the student's inner consciousness and
experience of music assumes but one tangible and
graspable form, melody. Nature's gift to the student
is an inborn appreciation of melody, the power to
follow and remember a melody as a connected whole
and therefore the power to turn it over and over in his
mind as he selects this or that series of chords and
musically reflects upon this or that way of leading the
voices. Given a melody to harmonize, the student
sets out with the one thing he can mentally grasp; he
perfectly comprehends the subject of his work and
therefore also its object. Having a tangible subject he
has a tangible object ; his melody is his preceptor and
guide in his choice of harmonies, explains to him why
now a root or fifth or third is doubled, why a bond-
tone is now tied and now not tied, why an upleader is
sometimes not resolved but led downward and why
the downleader is often treated in a like manner; in
short, he thinks and hears everything in relation to
and from that melody, which is the key to the whole
situation. Harmonic numbers over a given melody
appeal to the student's musical intelligence and rea-
son. Roman numbers under a given bass do not. The

286 THE NATURE OF MUSIC

principles of music are inherent in and assert them-
selves in a melody. This cannot be aflSrmed of a
given bass except when the melody is presented in the
bass. Thus guided through melody to a clear per-
ception of the operation of these rhythmo-harmonic
principles, the student is prepared to appreciate that
rules apply to specific cases and not to all cases.

Teachers will find no difficulty in preparing work-
ing-material for students in the form of given melodies
in which the usual chord-material is progressively
introduced. Besides presenting melodies with and
without harmonic numbers it will be found useful to
require students to conceive a few melodies of their
own which shall embody the material of each lesson.
It is also suggested that the work should introduce
a greater variety of rhythmic forms than is usual.
Exercises in the earlier stages should include the two
forms of dual subrhythm or measure, light — heavy,
heavy — light and the three forms of triple subrhythm
or measure, light — light — heavy, light — heavy — light,
heavy — light — light. In later stages, compound and
even mixed subrhythms should be introduced. In
preceding chapters I explained the original and in-
separable correlations of rhythm (form and relation
in time) and harmony (form and relation in space) of
rhythmic accents and harmonic forms. These corre-
lations obtain in selective harmony as well as in self-
reported harmony, and it follows that the study of
rhythm is as essential as that of harmony. A series
of harmonies occupies a series of rhythm-periods ; the
former cannot be understood apart from the latter.
Its rhythm is the foundation of a music-concept or

CHORDS IN THE LIGHT OF THEIR ORIGIN 287

melody. A familiar melody is recognized when its
rhythm is tapped by the fingers. Melody is intoned
rhythm. Change its rhythm and you produce an-
other, a different melody out of the same series of
tones. It is unscientific and untrue to speak of such
a changed melody as the same melody in another
rhythm. In forming his concept of a melody let the
student begin at the bottom by exaggerating the em-
phasis of its rhythm. Then let him intone the rhythm.
The exaggerated emphasis will then plainly report the
concomitant harmonies in his mind and guide him to
a satisfactory result in his selective harmonization of
the melody.

There are other advantages of exercises in given
melody which do not exist in those of the given bass. I
will stop here to point out only one. It is this. Given
melodies may be presented in every voice, not only in
the soprano, but in the bass, tenor and alto as well.
In all these voices the student will comprehend the
melody equally well, and such exercises in each of the
four voices may be presented from the start. It may
be objected that such exercises will infringe upon the
exclusive and erudite domain of simple counterpoint.
Yes, but why not.^ After all, is that domain either
so exclusive or so erudite as tradition would have it
appear ? In all forms of counterpoint does not each
tone in each voice report a root or third or fifth or
seventh or ninth, a consonance or a dissonance ? After
all is said of the basic importance of its rhythm, is not
all counterpoint a question of harmony, of regnant
harmony and byharmony, of regnant tone and by-
tone ? The study of counterpoint as an evolutionary

288 THE NATURE OF MUSIC

chapter in history is one thing; the study of counter-
point as an art to be mastered or a necessary part of
music education is quite another thing. This art of
acquiring independence in the use and selection of
materia musica in the simpler contrapuntal forms
should not be put off until the student has worked his
way through an entire textbook on chords. The con-
ventional cantus firmus is but a melody, and every-
thing that is to be added to the melody lies in it and
grows out of it. The sooner such work is begun the
better. Let A, B, C indicate the order of conceptive
work dealing with a cantus. A : think the rhythm
with exaggerated emphasis. B: intone the rhythm.
C : harmonize the intoned rhythm. Such a concept is
synthetic and complete since B is inseparably asso-
ciated with A, and C with both B and A. Now that
we have discovered in one voice both the origin of
harmony and the fundamental principles of music,
now that we can positively affirm that melody is not
an element but an indissoluble composite of rhythm
and harmony reporting in one voice now a consonance
and now a dissonance and that music had its genesis
in this composite voice of united rhythm and harmony,
now that we are able to view and study the material
of music in the light of its origin and can trace its
development since we can learn from the harmonic
self-reports of homophonic melodies what nature has
done and from selective harmony what art has done
in the evolution of both rhythmic and harmonic mate-
rial : it follows by implication that the entire rhy thmo-
harmonic materia musica both as applied in art and
in textbooks stands forth in a wholly new light. A

CHORDS IN THE LIGHT OF THEIR ORIGIN 289

young child may now gain as perfect an intellectual
grasp of the rhythmo-harmonic form and content of
a melody as that of his teacher. Each step in such
analysis renders clearer and deeper the child's musical
appreciation, since it directly reports and causes the
child to realize the purely miosical content of a melody.
The child sets out with a purely sensory perception
and appreciation of melody: through rhythmo-har-
monic analysis this perception and appreciation are
elevated from that lowest domain of mere sensation
to the higher and alone dignified domain of the
intellect. Thus a little musical savage is at once
metamorphosed into a little intelligent musician.
From A to Z the study of music is the study of the
rhythm and harmony of melody. Thus from the
start our youngest students may not alone really study
but may really study music itself, may begin and con-
tinue with the study of melody, its rhythm and its
harmony. Young students may learn to appreciate
and perform their little pieces by Bach, Mozart and
Beethoven with the same adequate intelligence and
consummate art with which mature artists produce
the more complex works of these masters, in short, so
far as he goes the student may be an intelligent musi-
cian and a true artist. Theory and practice may be
united from the start, their separation is a thing of the
past. The intellectual appreciation and enjoyment
of music may in consequence spread far and wide and
need no longer be regarded as an exclusive possession
of the enlightened few. Than music no art is more
accessible and democratic, therefore less esoteric.

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INDEX

Accent, 31, 42-44, 99, 120; efficient,
24, 25, 27, 54, 55, 95, 102, 105, 108,
109, 112, 113, 117, 125-127, 130-133,
149, 176, 178, 188, 194, 206, 218,
219; measure, 149; relative, 43, 44,
99; rhythmic, 12, 32, 46, 53, 107-109,
286; rhythmo-harmonic, 25, 105;
syllabic, 149; time-, 32.

Acoustic numbers, 227.

Acoustic series, 20, 227.

Acoustic theory, 230.

Acoustics, 17, 227; laws of, 244; physi-
cal, 4, 19,20, 21, 70; psychological,
19.

^Esthetics,10, 21, 22, 75.

Alto, 278.

Ambrosian melodies, 147.

Analysis, acoustical, 9; of feeling, 9;
harmonic, 58, 68, 83, 116, 137, 235,
250, 259, 265, 272, 274, 275; of mu-
sic, 28; rhythmo-harmonic, 289.

Aristides, 148.

Aristotle, 148.

Aristoxenus, 148.

Arnold, Matthew, 175.

Bach, 5, 86, 98, 118, 146, 170, 174, 175,

196-198, 289.

Balance, 13, 31, 32, 42, 152, 162; per-
fect, 33, 41, 44; relative, 44; rhyth-
mic, 31, 32.

Balanced motion, 10, 30, 33, 38, 162.

Balanced sound, 30, 33, 38.

Balanced time-periods, 32.

Bass, fundamental, 277-279; given,
279-285, 287; thorough, 259, 267,
269, 270, 274.

Beat, 130, 163, 168.

Beat-periods, 160, 162.

Beethoven, 5, 132, 146, 150, 170, 174,
175. 212, 213, 266, 276, 289.

BerUoz, 49, 171.

Biads, 245-247, 251-253; compound,

245-256; in minor, 248, 255, 256;

parallel, 255.
Bird -melodies, 116.
Bird-songs, 56, 58, 59, 61, 171, 176.
Bond-tone, 63, 76, 122, 123, 132, 136,

190. 193, 235, 277; original, 122.
Brahms. 49, 171.

Bychord, 141.

Byharmony, 106, 109-113,116,117,126,
127, 141, 187, 205, 287; relative. 111.

Bytone, 106, 107, 109-113, 116-123,
126, 127, 132, 194. 198, 199, 201,
203, 204, 206-210, 255, 256, 261;
diatonic, 118-120; report (harmonic,
self-) of, 118, 119, 219;= (tone-ca-
dence), 121.

Cadence, 29, 54, 56, 69, 103, 122, 129,
142, 177, 180, 206, 208, 211, 214,
216, 223; closing, 123; double, 136,
192; faUing, 92, 97, 136, 187, 190;
five original cadences, 91-96; harmo-
nic, 130, 131, 133; original, of Minor
Mode, 185-198; prototype, 185, 192;
rhythm-, 42-45, 50, 53, 67, 111, 120,
121; rising, 92, 97, 136, 275; single,
136; thread of harmony, 54; tone-,
45-48, 55, 86, 91, 121.

Cadence-chord, 99.

Cadence-harmony, 45-48, 58, 62, 111;
original, 45-47; genesis of, 61-67.

Cadence-moment, 42, 44.

Cadence-relation, 113.

Cadence-repose, 43, 53.

Cadence-tone, 46, 47, 57-59, 61-66,
92, 96-100, 106, 107, 113, 135, 136,

191, 192, 235, 257; (prototype), 191,
194, 208; (original), 46, 92, 98, 106,
135, 136.

308

INDEX

Calls and cries, 56.

Canon, 181.

Cantata, 157.

Canticle, 157.

Cantus-firmus, 288.

Cardinal principle, 15, 21, 24, 28, 162.

Carlyle, 159.

Chant, antiphonal, 181 ; primitive, 165.

China, 16, 17, 212.

Chopin, 169, 171, 212.

Chord, 3, 4, 11, 20, 37, 49-51, 61, 62, 71,
73, 84, 90, 92, 102, 104, 134, 135, 137,
143, 149, 191, 209, 231, 233, 234, 236,
266, 278-280, 284, 285, 288; aug-
mented, 249, 262; cadence-, 99; com-
ponents of, 89, 91, 242, 245, 259;
compound, 90, 141, 237, 240, 243-
245, 248, 255-257, 259-263, 272, 274;
consonant or dissonant, 232, 245;
derived from the original consonance
and dissonance in one voice, 133-141 ;
from the minor forms of consonance
and dissonance in one voice, 231-236 ;
diatonic, 202; diminished seventh-,
234, 239, 240, 260; diminished-di-
minished seventh-, 240 ; diminished-,
small seventh-, 240; dissonant, 144,
232, 245 ; dominant-seventh-, 84, 239;
double, 211, 212; fourth-sixth-, 238;
ground-seventh-, 240; harmonic re-
port of, 138, 139, 141, 234, 245, 259,
266; large ninth-, 240-242; large
third-, 249; major, 227; major-small
seventh-, 239; major subtonic-sev-
enth-, 239 ; major tonic-seventh-, 255 ;
minor, 177,227; minor ninth-, 139,
140, 141, 234, 240-244, 247, 275;
minor subtonic-, seventh-, 239 ; minor
tonic-seventh-, 255 ; ninth-, 240-244 ;
passing, 275; primary, 133, 248; re-
pose-, 99; secondary, 248; secondary
ninth-, 256; secondary seventh-, 253,
255, 268; self-reports of a, 233, 234,
847, 255; seventh-, 84, 139, 140, 234,
238-242 244, 247, 253, 255, 256, 260,
268-270; simple, 90, 141, 144, 243-
245, 248, 249, 251-253, 256; simple

and compound, defined, 243-276;

sixth-, 238; small ninth-, 240-242;

subdominant-seventh-, 254 ; submedi-

ant-seventh-, 254, 256; subsecond-,

261, 262, 265, 267-270; subtonic-

seventh-, 235, 254 ; supersixth-, 261-

264, 267-271 ; supertonic-seventh-,

254; tone-, 86; tonic-, 66.
Chord-analysis, 68, 135.
Chord-basis of harmony, 69.
Chord-building, 140, 244.
Chord-cadence, 99, 136.
Chord -conception of harmony, 86.
Chord-concepts, 91.
Chord-fifth, 234, 238, 240, 241, 248,

275.
Chord of the fifth-sixth, 240.
Chord-forms, 71, 72, 135, 139.
Chord-harmony, 68-74, 147.
Chord-intervals, 89-91, 136, 137, 232,

237, 249.
Chord of the major ninth, 84.
Chord-material, 233, 277, 278, 282,

286.
Chord-ninth, 275.
Chord-position, 240-243, 266.
Chord prototype, 140.
Chord-root, 135, 136, 140, 232, 234,

237-243, 245, 248, 249, 258-261, 268,

274, 275, 278.
Chord of the second, 240.
Chord-seventh, 268, 275.
Chord-sixth, 248.
Chord-structure, 242, 257, 261, 263,

264, 265, 268, 271, 272.
Chord-theories, 89, 230.
Chord-third, 234, 238, 240, 241, 248,

274.
Chord of the third-fourth, 240.
Chord type, 239.
Chromatic, 39, 59, 93, 124, 132, 187,

190, 193, 201-204, 215, 219, 220,

221.
Chromatic scale-system, 95.
Classics, 49.
Composer, 75, 104, 150. 157, 159, 171,

172, 175, 217, 261.

INDEX

309

Concept, 26, 44. 62, 78, 79, 139, 179,
181, 284, 287, 288; harmonic, 76, 91 ;
music, 286.

Concerto, 146; piano-, 276.

Concomitants, 34, 37, 40, 45, 59, 62, 75,
79, 113-115, 117, 124, 131, 140, 148,
149, 193, 194, 202, 206.

Confucius, 16.

Consonance, 4, 7-9, 18-21, 26, 27, 45,
50, 53-56, 61-64, 66-69, 75, 77, 85,
86, 102, 112, 113, 115, 117, 120, 124,
125, 127, 133, 141, 148, 165, 178, 189,
192, 205, 214, 222, 223, 287, 288;
major, 7, 33-36, 40, 41, 45, 46, 55,
91, 95, 111, 124, 176, 177, 179, 180,
190, 204, 217, 219, 221-223; minor,
59, 91, 177-180, 183-185, 190, 201,
203, 214-218, 221-223, 231 ; origin of
minor, 176-184; prototype, 95, 124,
133, 184, 185, 221, 231.

Consonance thread, 37, 143.

Cotta edition, 276.

Counterpoint, 287.

Dance, 4, 43, 116, 172.

Diatonic, 192, 220, 221; seven, 46, 75,
85, 94, 117, 122, 141, 142, 144.

Diatonic bytone, 118-120, 208, 210,
218.

Diatonic cadence, 98, 99.

Diatonic chord, 202.

Diatonic division of octave, 95.

Diatonic harmony, 124, 125, 201, 203,
205, 216-218.

Diatonic major relation, 123, 134.

Diatonic major triad, 133.

Diatonic melody, 99.

Diatonic minor, 201-203, 235.

Diatonic minor melody, 202, 216.

Diatonic scale, 144.

Diatonic scale-system, 95.

Diatonic stage of tonality, 95.

Dissonance, 4, 7, 8, 18-21, 26, 27, 45,
50, 53, 69, 75, 86, 112, 113, 115, 116,
123-125, 133, 141, 148, 149, 180, 189,
205, 287, 288; acoustical, 9; five-
tone, 95, 221; four-tone, 95, 117,

221 ; genesis of, 103, 120; genesis of
original, in one voice, 61-67; latent
feeUng of, 46, 54, 55 ; major, 124, 180,
190, 209, 214, 222, 223, 231 ; minor,
185, 188, 190, 198, 214, 222, 223, 231 ;
one voice, 7, 62, 68, 91, 102; origin in
one voice of the minor form of, 185-
198; original, 9, 35, 55, 77, 85, 91,
103, 111; prototype, 95, 124, 134,
185, 188, 221, 231 ; regnant, 127, 128.

Dominant, major, 47, 63, 67, 77, 188,
189, 206, 207, 239, 249, 262; major
ninth of, 76, 82; major third of, 76,.
82; minor, 201, 216-218, 262; minor
seventh of, 76 ; prototype, 206 ; pure
fifth of, 76, 82; regnant, 188, 207,
210; regnant minor, 188, 206-218;
rhythmic, 120; small ninth-chord of,
275.

Dominant-fifth, 76.

Dominant-harmony, 58, 60, 61, 65, 75,
77, 83, &4, 90, 93, 108, 183, 187-189,
198, 249.

Dominant-ninth, 76.

Dominant-root, 76, 81, 88, 89.

Dominant-seventh, 76.

Dominant-seventh-chord, 84, 239.

Dominant- third, 76.

Dominant-thread, 47, 82, 84.

Dominant-triad, 84, 235, 249.

Dorian scale, 229.

Downleader, 62, 64, 92, 95, 183, 285;
chromatic, 275; prototype, 95, 192.

Drama, 156, 157.

Dreiklang, 269.

Drum, 165, 166.

Duplicates, 27, 71, 184, 185; 221. 231.

Dynamics, 125.

Ear, 20, 73, 44, 77, 78, 86, 260, 268.

Ecclesiastical melodies, 116.

Ecclesiastical music, 148.

Elements, 2, 6, 41, 44, 50, 67, 74, 79,
130, 150, 176, 180; concurrence of,
129; succession of, 129; union of, 6,
8.

Elements of music, 3, 7, 23, 48, 56.

310

INDEX

Elevenths, 89, 93.
Enharmonic harmonies, 271, 274.
Enharmonic scale-system, 95.
Enharmonic stage of tonality, 95.
Equilibrium, 10-14, 21, 24, 28, 30, 31,

33, 41-43, 48, 51, 112, 113, 151, 153,
164; cardinal principle, 36, 162; =
(harmony), 10-15, 30 ; harmonic, 125 ;
relative, 133; rhythmic, 125; rhyth-
mo-harmonic, 125;= shaping princi-
ple, 10, 11, 24, 41, 51, 120, 130, 195;
stable, 43, 54, 67, 116, 127, 178; un-
stable, 43, 54, 67, 116.

Evolution, 1, 4, 5, 13, 15, 16, 39, 56, 70,
94, 96, 103, 104, 110, 130, 176, 177,
193, 215, 223-225, 233; harmonic,
40-42, 104, 225.

Evolution of perception, 52, 165.

Expansion of subrhythm and rhythm,
160-175.

Eye, 73, 74, 260, 268.

Feeling, 26, 34, 36, 40, 41, 44, 60, 68,

72, 79, 80, 178, 184; (common, com-
mon music-, music-), 2, 5, 6, 8-10,
13, 15, 16, 18-21, 24, 28, 29, 32, 33,
35, 37, 43, 45, 51-53, 62, 66, 69, 76,
78, 86, 88, 91, 104, 108, 139,140, 147,
153, 161, 176, 179, 181, 197, 226, 228;
common report of common, 17-22,
108, 147; rhythm-harmonic, 278;
tone-rhythmic, 10, 11, 12.

Feeling of cadence, 62.

Feeling of dissonance, 46, 54, 55.

Feeling of music per se, 7, 9, 22.

Feeling of rhythm, 33.

Feeling of repose, 62.

Fifth, 25-27, 29, 30, 35, 37, 40, 41, 47,
59, 60, 63, 67, 84, 85, 89, 108, 123,
138, 140, 179, 187, 200, 206, 217,
285, 287; chord-, 234, 238, 240, 241,
248, 275; consecutive, 277; dimin-
ished, 137, 234; harmonic, 135, 234;
large, 223, 224; parallel, 131; pure,

34, 36, 61, 76-78, 81,82, 120, 137;
small, 223.

Folk-melody, 172, 174.

Folk-song, 4, 15, 16, 77, 79, 81, 84,
116, 172.

Form, 5, 7-15, 17, 21, 24, 28, 49, 51,
66, 68, 70, 75, 79, 83, 85, 89, 90, 99,
103, 104, 133, 134, 145, 155, 160-162,
165, 167, 170, 171, 173, 178-180,
206, 216, 217, 219, 220, 221, 224,
232, 234; chord, 71, 72; classic, 160-
175;elemental, 20, 22, 30; harmonic,
4, 8, 9, 10, 23, 25, 30, 33-35, 41, 42, 45,
48, 50, 62, 67, 73, 83, 93, 111, 112,
122, 124, 129, 139, 182, 214, 233,
286 ; prototype of harmonic, 95 ; orig-
inal harmonic, 26, 95; rhythmic, 23,
32, 44, 50, 111, 129, 130, 164, 168,
286; rhythmo-harmonic, 24, 279, 288;
space-, 14; time-, 14; tone-rhythmic,
8; universal, 7, 12, 43.

Form of consonance, 7, 8, 53, 116, 125,
184, 185, 204, 205, 214, 222, 223, 231.

Form of dissonance, 7,8,53,116,125,
214, 222, 223, 227, 231.

Form of regnant minor dominant, 216-
218.

Form in space, 13, 104.

Form in time, 13, 104.

Fourth, 36, 59; augmented, 138; pure,
137, 138.

Fugue, 181.

Fugue-subject, 118.

Fugue-theme, 198.

Fundamental bass, 277-279.

Fundamental forms of harmony, 85.

Fundamental forms of tone, 53.

Fundamental principles, 8, 175, 288.

Gevaert, 146.
Given bass, 285-287.
Goethe, 11, 14.
Greece, 16, 17.
Greek melodies, 146-149.
Greek modes, 145, 146.
Gregorian chants, 148, 149.
Gregorian melodies, 147.

Harmonic, 34-36, 41, 45; compound,
90, 263; concomitant. 59, 62; double.

INDEX

811

211, 248; elementary, 35, 37, 40, 41,
193; simple, 90, 263.

Harmonization, 74, 149, 156, 287.

Harmony, 1-7, 9, 13, 19, 20, 21, 24, 33-
35, 49, 51, 52, 63, 75, 76, 79, 86, 90,
93, 99, 103, 120, 122, 129, 135, 136,
138, 142, 144, 150, 154, 156, 158,
159, 171-173, 177, 178, 185, 189,
190, 197, 199, 206, 210, 213, 215,
217, 218, 221, 226, 242, 243, 248,
256, 269, 279, 283-289; acoustic
theory of, 230; basis of, 33, 68, 69,
102; cadence-, 45-48, 58,62, 111;
chord-, 68-74, 147; chromatic, 201,
202, 205, 219, 220. 271; compound
of, 263, 265, 266, 270; concomitants
of, 131, 140, 148, 149, 202, 211, 224,
284, 285, 287; = (consonance), 91;
contrapuntal, 70; diatonic-, 118, 124,
140, 201-203, 205, 216, 218; = (dis-
sonance), 91; dominant-. 58, 60, 61,
65, 75, 77, 83, 84, 90, 93, 108, 183, 187-
189, 198, 249; double, 211, 212; du-
plicate forms of, 184, 185; = equilib-
rium, 10-15, 30, 150, 151; enhar-
monic, 271, 274; expansion of, 77,
110; evolution of, 103, 176, 224, 233;
five components of, 89-91; genesis
of, 54, 102, 109; homophonic, 70, 102,

105, 205, 229, 230; major, 185; major
tonic-, 54-57-61, 64, 65, 91, 98, 105,

106, 183, 184, 193, 229; minor, 124,
139, 185 ; minor tonic-, 178-180, 184-
187, 198, 214, 221, 230; multi-voice,
75, 147; original (in one voice), 4,
24, 25, 28, 36-40, 47, 49, 50, 61, 64,
66-71, 73-75, 85, 87, 88, 102, 104,
124, 133, 139-141, 147-149, 182, 184,
211, 244; original cadence-, 45-47;
original forms of, 184-185; personal,
71, 283 ; polyphonic, 70 ; potential, 26-
27, 74, 77, 110, 181 ; regnant, 24, 25,
53-55, 58, 60, 65, 67, 83-85, 88, 98,
104-113, 115-118, 125-127, 129-133,
141, 149, 183, 186, 188, 193, 194, 198,
201, 208, 209, 214, 220, 221, 223, 224,
255, 261-264, 267, 268, 272-276, 287;

relative, 54, 55, 111 ; repose-, 45-48,
62, 111 ; selective, 286; subdominant,
58, 60, 61, 108, 198, 248; tiieory of,
51 ; thread of, 35, 37, 38, 41, 54, 63, 79,
80, 81, 84, 96, 107, 109, 124, 133, 134,
137, 139-141, 143, 178, 183, 188, 193,
224; = tone, 23, 28; tone-rhythmic,
10; tonic-, 33, 45, 54, 56-58, 60, 61,
64, 65, 83, 84, 93, 106, 179, 183, 186,
187, 193, 214, 229, 230, 249, 260;
treatise on, 19, 68, 244.

Harmony of sound, 23, 75, 147.

Hauptmann, M. 19, 244.

Haydn, 174.

History, 4, 40, 65, 66, 68, 111, 165.

Homer, 16.

Homophony, 4-6, 7, 68, 102-105,
194, 195, 202, 223, 226, 232-234,
249.

Instrument, 165, 166.

Interval, 36, 59, 76, 88, 89, 93, 96, 113-
115, 138, 187, 189; chord-, 91, 137;
diminished, 93; evolutionary se-
quence of, 60; harmonic, 91, 136, 137,
232; major, 75, 139; minor, 75,
139.

Interval of concurrence, 137.

Interval-number, 93, 139.

Interval-relation, 80.

Interval of succession, 137.

Key, 48, 61, 87, 96, 239, 262; fifth re-
lated, 123; interharmonic relations of
one, 94.

Key-centre, 220.

Keynote, 27, 60.

Key-relation, 60, 88.

Leading tone, 61.
Liszt, 49, 203.

MacDowell, 49.

Major, cadence -seventh -chord, 1S5;

pure diatonic, 203.
Major chord, 227, 232.
Major consonance, 7, 33-36, 40, 41, 45,

sn

INDEX

46, 55, 91, 95, 111, 124, 176, 177, 179,
180, 190, 204, 219, 221, 223 (origi-
nal), 35, 55.

Major dissonance, 124, 180, 190, 209,
214, 222, 223, 231.

Major dominant, 47, 63, 67, 77, 188,
189, 206, 207, 239, 249, 262.

Major dominant-harmony, 183, 187,
189.

Major dominant-thread, 235.

Major downleader, 192.

Major harmony, 185.

Major mode, 33, 41, 46, 56, 75, 85, 88,

91, 95, 124, 139-141, 176, 178, 181,
182, 186, 187, 191, 210, 214, 215,
236; (prototype), 95, 180, 181, 185,
191, 200, 214.

Major ninth, 76, 77, 82, 137.

Major second, 255.

Major sixth. 36, 138.

Major subdominant, 188.

Major subdominant harmony, 187.

Major subdominant - seventh - chord,

254.
Major subdominant triad, 235.
Major submediant-seventh-chord, 254.
Major subtonic, 253, 256.
Major supertonic triad, 251.
Major tenth, 36.
Major tetrachord, 214.
Major third, 34, 36, 61, 76-78, 81, 82,

120, 137, 138.
Major tonality, 67.
Major tonic, 41, 47, 60, 63, 65, 67, 77,

92, 98, 103, 105-108, 111, 180, 181,
185.

Major tonic-harmony, 54, 57-61, 64,

65, 91, 98, 105, 106, 183, 184, 193,

229.
Major triad, 90, 133, 237, 251, 262,

268.
Major upleader, 187, 192.
Measure, 168, 286; dual, 161, 168;

triple, 161.
Measure-period, 162, 260, 261.
Medicant, 144.
Medicant scale, 146.

Medicant-triad, 248-250.

Meistersinger, 146.

Melody, 1-6, 9, 14, 15, 24, 25, 28, 37,
39, 40, 41, 47-52, 54, 56, 60, 64, 67,
71, 72, 74, 78, 79, 85, 91, 93, 98-100,
121, 124, 130, 132, 140, 147, 148,
154, 155, 172, 177, 178, 180, 186,
187, 192, 193, 197, 198, 200, 202, 203,
205, 206, 208, 209, 211, 214-217,
220-224, 276, 280, 281, 284-289;
analysis of, 65; ancient, 149; a com-
posite, not an element, 23, 24 ; bird-,
116, 183; ecclesiastical, 116; embry-
onic, 106; folk-, 184; Greek-, 116,
149; homophonic, 6, 24, 215, 223,
227, 230, 233, 288; mediaeval, 4;
minor, 221; modern, 182; penta-
tonic stage of, 113; primitive, 64,
104, 109, 176, 182-184, 225; pure
diatonic minor, 216; regnant har-
mony of, 102-175.

Meloharmonic phrase, 187.

Meloharmonic point, 120, 142.

Meloharmonic resolution, 142.

Meloharmony, 24, 104, 120, 142, 197,
285.

Mese, 148.

Metre, 33, 168.

Minor, 123, 139, 195, 209; imitation of
major, 180, 181, 185-187, 200, 205,
214; inverted major, 227; origin and
nature of, 176-184; pendant, 181,
226, 228, 230; pure diatonic, 202,
203, 216; relative, 181.

Minor cadence, 180, 192.

Minor cadence-tone, 186-188.

Minor consonance, 59, 91, 177-180,
183-185, 190. 201, 203, 214-218,
221-223, 231; (origin of), 176-184.

Minor dissonance, 185, 188, 190, 198,
214, 222, 223, 231.

Minor dominant, 187-189, 198, 200,
201-203, 204, 206-218, 220.

Minor dominant-triad, 235.

Minor downleader, 192.

Minor forms of consonance and disso-
nance, 185, 214, 222, 223, 231.

INDEX

313

Minor harmony, 124, 139, 185.

Minor harmonic percept, 214, 236.

Minor melodic scale, 201, 203.

Minor mode, 56, 59, 91, 124, 135, 141,
177-179, 181, 182, 186, 187, 191, 196,
205, 210, 214, 217, 236.

Minor root, 180.

Minor seventh, 38, 76-78, 137.

Minor sixth, 138.

Minor small third, 180, 184, 200.

Minor subdominant, 187, 188, 204, 218,
222.

Minor subdominant harmony, 187, 188,
198, 204, 218, 219, 222.

Minor subdominant triad, 235.

Minor subtonic, 253, 256.

Minor subtonic-seventh-chord, 235.

Minor tenth, 36.

Minor tetrachord, 214.

Minor third, 36, 137, 138.

Minor tonic, 180, 181, 185, 198, 200,
216, 220.

Minor tonic-harmony, 178-180, 184-
187, 198, 214.

Minor triad, 228, 231, 236, 237, 268.

Minor upleader, 187, 192,

Mode, defined, 91-98; major, 33, 41,
46, 56, 75, 85, 88, 91, 95, 124, 139-
141, 176, 178, 181, 182, 186, 187,
191, 210, 214, 215, 236; minor, 5Q,
59, 91, 124, 135, 141, 177-179, 181,
182, 186, 187, 191, 196, 205, 210,
214, 217, 236; prototype major, 95,
180, 181, 185, 191, 200, 214.

Mode-idea, 85, 92, 94.

Mode-relation, 88, 91, 94, 108, 180.

Mode-tones, 87, 93, 94.

Modes, 48; ancient, 147; Greek-, 145,
146.

Modulation, 183, 220.

Moment, musical, 149-160; rhythmic,
32, 38, 44, 51, 151; rhythmo-har-
monic, 23.

Motion, balanced, 10, 30, 33, 38, 162.

Motive, 23, 44, 152, 153, 214.

Mozart, 25, 170, 174, 289.

Music, absolute, 157; analysis of, 28,

66; art-, 15; basis of, 19, 20, 28,
56, 58, 85, 102, 223; books on.
181; chorded, 4, 141, 215, 223, 224,
235; classic form, 173-175; concrete,
233; development of, 9, 66, 105, 111,
166, 171, 175; elemental form of,
22; essence of, 2, 3, 9, 14, 49,
104; evolution of, 1, 15, 49, 107,
220; first regnant harmony of, 55,
61, 83; five original cadences of,
92; form of, 5, 7, 9, 15, 21; genesis
of, 1, 4, 6-8, 10, 14, 15 ; instrumental,
166, 243; message of, 10, 14, 22,
158; messenger of, 10, 14, 22, 149;
modem, 4, 16, 70, 104, 116, 172-174,
203, 212, 215; multi-voice, 25, 85,
116, 161, 223, 224, 226, 233; nature-,
15, 16, 17; one, 15, 16, 17, 28; one-
voice, 4, 24, 25, 39, 45, 70, 85,
102, 116, 147, 148, 194, 223; origin
of, 6-8, 9, 33; pleasure in, 28, 78,
165; polyphonic, 1, 97, 223, 224;
primitive, 56, 66, 86, 104, 110, 116,
165; principle of, 3, 7, 8, 15, 21, 22,
24, 50, 149; rationale of, 17; seven
octaves of, 141; stages of, 1, 6, 70,
103; study of, 1, 6, 21, 28, 289;
voice of, 8, 23, 28, 33, 152, 153, 205,
284.

Music of antiquity, 147.

Music-archgeologist, 202.

Music art, 15, 16, 49, 100, 110, 154.
155, 158, 166, 171, 175, 289.

Music-concept, 286.

Music-consciousness, 6, 278, 285.

Music-culture, 175.

Music-drama, 156, 157.

Music-education, 40, 234.

Music-feeling, 2, 5, 6, 8-10, 13, 15, 16,
18, 20, 21, 28, 32, 52, 53, 66, 69, 78,
147, 153, 161, 181, 197, 226.

Music-history, 3, 40 65, 66, 68, 165.

Music-lesson, 98-100, 277; work for
students, 101, 164, 282-288.

Music perse, 7, 9, 21, 22, 67, 110.

Music-score, 268.

Music-sense, 165.

314

INDEX

Music-structure, 15, 173, 181, 270.
Music-theory, 3, 16, 20, 51, 69, 70, 230,

234.
Music-thought, 23, 24, 161, 171, 280.
Music-works, 13, 159, 170.
Musician, 2, 39, 51, 57, 66, 100, 159,

234, 289.

Ninth, 25-27, 29, 38, 41, 47, 63, 67, 76,
77, 81, 82, 85, 89, 118, 137, 180, 189,
202-210, 223, 287; harmonic, 234;
large, 223; original, 253; prototype,
208;small, 223, 260.

Notation, 60, 65, 229, 275, 276 ; staff, 88.

Nucleus, 141 ; septonal, 142.

Nucleus-triad, 261-264, 268, 269.

Numbers, 89, 90; acoustic, 227; ele-
mentary group-, 167; harmonic, 37,
47, 58, 61, 63, 64, 71, 74, 75, 78, 80,
86-88, 93, 99, 100, 137, 139, 179,
185, 186, 189, 214, 222, 232, 283-
286; interval, 93, 139; percept, 246;
rhythm, 161; scale, 86-88, 94; tho-
rough-bass, 238, 284.

Octave, 34, 35, 59, 81, 95, 118, 131, 141,

143, 200; consecutive, 277; parallel,

231 ; pure, 36.
Octonal scale, 144, 146.
Octonal terminal, 144.
Opera, 157.
Orchestra, 166.
Organ, 166.
Original harmony in one voice, 28, 39,

40, 47, 50, 64, 66-69, 73, 75, 85, 88,

104, 124, 133, 140, 148.
Overtones, 20, 227.

Pedagogy, 277, 278.

Pentatonic melody, 109, 186.

Pentatonic period, 183.

Pentatonic scale, 64, 65, 109.

Pentatonic stage of melody, 108-110,
113, 114.

Percept, 26, 41, 44, 82, 284; five origi-
nal harmonic, 77, 84, 85, 95, 122,
224, 227, 235, 249; prototype, 95;

harmonic, 26, 27, 36, 38, 61, 76, 77,

85, 87, 89, 95, 103, 122, 179, 182,
187, 200, 222-225, 234, 235, 275;
harmonic, of minor origin, 222-224;
major harmonic, 179, 222, 229; minor
harmonic, 179, 200, 214, 216, 222,
229, 230.

Percept-numbers, 246.

Perception, 21, 28, 41, 53, 68, 73, 79,
93, 165, 166, 178, 197, 228; common,
19, 20, 22, 29, 37, 43, 45, 64, 66, 69,

86, 89, 91, 108, 179, 181 ; evolution
of, 52, 110; harmonic, 78, 106, 110,
111, 230.

Perception of harmony, 24, 110, 111,
182.

Perception of relation, 76, 139.

Perception of rhythm, 33, 44.

Period, 42, 125, 152, 160, 161, 162,
165, 173, 182; beat-, 160-163; ca-
dence-, 121; dual, 29, 162; elemen-
tary, 170, measure-, 162, 260, 261
repose-, 121; rhythmic, 12, 42, 88
120, 121, 127-130, 217; rhythm-, 12
32, 33, 125, 127, 129, 153,' 193, 250
286; subbeat-, 160, subrhythmic, 163
168; time-, 32, 33, 38; triple-, 29.

Personal election, 25.

Personal element of choice, 5.

Personal equation, 5, 40, 70, 71, 205,
215, 230.

Personal prejudice, 5.

Personal selection, 71, 72, 75, 85, 177,
230.

Peters' edition, 276.

Phrase, 16, 80, 122, 130, 152, 161, 162,
171-173, 187, 278.

Physical acoustics, 20, 21, 70.

Physical tone, 20.

Piano-concerto, 276.

Pianoforte, 95, 96, 166.

Pitch, 20, 30, 33, 34, 36, 53-55, 60, 61,

87, 88, 94, 143, 148, 186; fixed, 60.
Pitch relation, 60, 88, 99, 141, 233.
Plagal ending, 136, 235.
Polyphony, 4, 103, 140, 215, 223, 224,

235.

INDEX

315

Potential harmony, 26, 27, 74, 77, 110,
181; principle of, 26, 27.

Primes, 93.

Principle, 3, 7, 12-14, 16, 17, 19, 21,
22, 40, 47, 65, 66, 140, 151, 166, 182,
197, 198, 200; cardinal-, 15, 21, 28;
fundamental, 8, 175; rhythmo-har-
monic, 286; shaping, 10, 11, 24, 28,
31-33, 36, 41, 48, 50, 51, 120, 130,
149, 161, 162, 171-173, 195; miiversal,
of form and relation, 12-14.

Principle of harmonic genesis, 27, 38,
65, 105, 125, 181.

Principle of music, 3, 7, 8, 15, 21, 22,
24, 50, 149.

Principle of potential harmony, 26, 27.

Principle of tone genesis, 95.

Progression, 13, 48, 96-98, 112, 113,
115,119,142, 152, 187,192,220,275.

Prototype, 95, 124.

Prototype cadence, 185, 192.

Prototype cadence-tone, 191, 194, 208.

Prototype chord, 140.

Prototype consonance, 95, 124, 133,

184, 185, 221, 231.

Prototype dissonance, 95, 124, 134, 185,
188, 221, 231.

Prototype dominant, 206.

Prototype downleader, 95, 192.

Prototype five original percepts, 95.

Prototype of harmonic forms and re-
lations, 95,

Prototype of harmonic percept and
step in minor, 200.

Prototype major harmonic percept,
200.

Prototype major mode, 95, 180, 181,

185, 191, 200, 214.
Prototype ninth, 208.
Prototype repose, 185.
Prototype upleader, 95, 192, 194.

Rameau, 264.
Regnant bytone, 287.
Regnant dissonance, 127, 128.
Regnant dominant, 188, 207, 210.
Regnant harmony, 24, 25, 53, 54, 55,

58, 60, 65, 67, 83-85, 88, 98, 104-
113, 115-118, 125-127, 129-133,
141, 149, 183-188, 193, 194, 198,
201, 208, 209, 214, 220, 221, 223,
224, 261-264, 267, 268, 272, 274-276,
287.

Regnant harmony in one voice, 102-
133.

Regnant major dominant, 188, 206,
207.

Regnant major subdominant, 188.

Regnant major tonic, 108, 185.

Regnant minor consonance, 218.

Regnant minor dominant, 188, 206-218.

Regnant minor subdominant, 188, 218-
222.

Regnant minor tonic, 199-206.

Regnant ninth, 210.

Regnant root, 208.

Regnant subdominant-harmony, 108.

Regnant third, 210.

Regnant tones, 106-112, 116-118, 120-
123, 126, 193, 199, 207, 208, 210,
211, 214, 216, 256, 261, 274, 287.

Regnant tonic-harmony, 102-133.

Relation, 5, 6-9, 15, 17, 20-30, 41, 48,
56, 58, 61, 64, 66, 75-81, 84-86, 89,

92, 95, 99, 107, 110-112, 115, 120,
123, 127-129, 133, 135, 136, 140, 143,
152, 179, 182, 185, 186, 190-193,
198, 200, 203, 205, 207, 211, 212,
214, 233, 234, 248-251, 253, 255,
256, 266, 276, 280, 281, 285, 286;
elemental, 22, 23 ; fifth-, 123, 249 ; har-
monic, 7, 22, 26, 27, 29, 35, 37-39,
50, 60, 62, 65, 67, 76-78, 83, 87, 88,

93, 100, 105, 106, 109, 111, 112, 119,
122, 124, 141, 177, 247; prototype
harmonic, 95; interval, 80; inter-
harmonic, 91, 93, 94; key-, 60, 88;
mode, 88, 91, 94, 108, 180; prototype
mode-, 185; original harmonic, 15, 26,
27, 95, 107, 136; rhythmic, 22, 44, 50,
53,55, 103, 177; rhythmo-harmonic,
14, 23, 24, 98; space-, 14, 22, 23, 30,
38; time-, 14, 22, 30, 38, 79, 104;
tone-, 22, 24, 30, 42, 45, 48, 56, 58, 62,

316

INDEX

67, 78, 89, 94, 98, 104, 180, 214, 224,

278; tonic and dominant, 196.
Relation of cadence and repose, 44-47,

50, 53, 55, 63, 85, 91, 98, 103.
Relation in space (harmony), 79.
Report (common, harmonic, self-), 19,

112, 120, 179, 186, 195, 202, 220, 227,

230 ; common, of common feeling, 17-

22.
Report of biad, 246, 247.
Report of by tone, 118, 119, 219.
Report of chord, 134, 135, 138, 139,

141, 233, 234, 245, 247, 255, 259,

266.
Report of common feeling and percep-
tion, 5, 19, 22, 24, 28, 45, 66, 69, 88,

108, 135, 181, 230.
Report of harmonic numbers, 88, 283,

284.
Report of harmony, 24, 38, 47, 66, 67,

85, 148, 209, 230, 262, 264, 276, 283.
Report of homophony, 5, 6, 215, 230,

232, 288.
Report of melody, 108, 148-149, 176,

179, 181, 182, 215, 216, 223, 224, 279,

283, 284, 288.
Report of mode, 215.
Report of tone, 85, 89, 90, 135, 177.

214, 216, 233, 246, 247.
Report of triad, 232, 233, 248, 262.
Repose, 41, 56, 61, 68, 92, 103, 116,

123, 129, 130, 133, 142, 148, 177,

178, 180, 185, 190, 214, 216, 223;

rhythm-, 42-45, 50, 53, 67, 111, 120,

121 ; tone-, 45-48, 55, 62, 63, 67, 91,

96-100, 121, 190-192, 201.
Repose-harmony, 45-48, 62, 111.
Repose-moment, 42, 44.
Repose-thread (of harmony), 54, 55,

67, 91, 97-99.
Resolution, 48, 54, 55, 62, 64, 93, 96-

98, 112, 113, 115, 135, 142, 152, 192,

220. 235, 275.
Rhapsody, 203.
Rhythm, 1, 6-10, 12-14, 17, 20, 22-

24, 28, 30, 33, 38, 48, 50-52, 54, 56,

63. 65, 74, 79, 83, 89, 98-100, 103,

104, 130, 148-153, 158, 160-163,
171, 176, 180, 229, 286-289; analysis
of, 31-33; = balanced -motion, 10.
30, 33, 38, 162; cadence, 42-45, 50,
53, 67, 111, 120, 121; dual, 29, 32,
43, 99, 173; music-, 30, 32, 42, 50, 51,
158, 165, 167, 171; tone-, 7, 9, 10,
14, 15, 29, 48, 152, 154, 155, 171,
172; triple, 29, 32, 99.

Rhythm-numbers, 161.

Rhythm-period, 12, 32, 33, 125, 127,
129, 153, 193, 250, 286.

Rhythm-repose, 42-44, 45, 50, 53, 67,
111, 120, 121.

Rhythmo-harmonic accent, 25, 105.

Rhythmo-harmonic analysis, 289.

Rhythmo-harmonic content of melody,
279, 288.

Rhythmo-harmonic equilibrium, 125.

Rhythmo-harmonic feeling, 278.

Rhythmo-harmonic form, 24, 279, 288.

Rhythmo-harmonic laws of causation,
224.

Rhythmo-harmonic point, 25, 105.

Rhythmo-harmonic principles, 286.

Rhythmo-harmonic relation, 14, 23, 24,
98.

Rhythmo-harmonic thought, 278.

Rhythmo-harmonic voice of music, 153,
205.

Richter [Ernst F. E.], 249.

Riemann, 181, 226, 230.

Root, 25-27, 29, 30, 34-37, 40, 41, 47,
51, 60, 61, 63, 67, 75-77, 80, 81, 84,
85, 88-90, 93, 108, 113, 118, 123,
142, 179, 180, 185, 189, 217, 223,
227, 232, 234, 285, 287; chord-, 135,
136, 140, 232, 234, 237-243, 245,
248, 249, 258-261, 268, 274, 275, 278;
harmonic, 135, 136, 181, 189, 232,
234, 258, 260, 272.

Round-song, 181.

Scale, 141, 142, 192, 205, 217, 230;
ascending, 97, 228; descending, 97,
229; diatonic, 144, 192; Dorian-, 229;
enharmonic, 215; great, 64; major.

INDEX

317

26, 86, 143, 203; mediant, 146; melo-
dic minor, 201, 203; octonal, 144,
146; original, of the tonic, 145; pen-
dant minor, 228; pentatonic, 64, 65,
109; primitive, 64; septonal, 146;
small, 64; supertonic-, 146; tonic-,
146; Zarlino-Riemann, 228, 229.

Scale-numbers, 86-88, 94.

Scale terminals, 143, 144.

Schopenhauer, 14.

Schumann, 49. 169, 171.

Selection, 75, 140, 149, 183; natural,
17, 70, 71, 85; personal, 70-72, 85,
176,177,230.

Sense, harmonic, 69, 121, 147, 148, 182;
music-, 165.

Septimenaccord, 269.

Septonate, The, 24, 98, 104.

Sequence, 6, 9, 25, 40, 51, 52, 60, 64,
65, 102, 105, 181, 278.

Seventh, 25-27, 29, 30, 41, 47, 61, 63,
65, 67, 76-78, 81, 82, 85, 87, 89, 134,
135, 137, 223, 268, 269, 287; dimin-
ished, 234; harmonic, 234, 268, 269;
minor, 76-78. 137; small, 222, 223;
thorough-bass, 268.

Shaping principle, 10, 11, 24, 28, 31-
33, 36, 41, 48, 50, 51, 120, 130, 149,
161, 162, 171-173, 195.

Silence, 1, 7.

Sixth, 36, 59, 138, 139.

Sonata, 116, 155, 173, 174, 212, 266.

Songs, 4, 15, 43, 53, 56, 157, 165; bird,
56. 58, 59, 61, 171, 176.

Soprano, 287.

Sound, 1, 7, 8, 21, 33, 34, 38, 43, 51,
55, 165, 166.

Space, 12-14, 22, 23, 30, 38, 79, 104,
122, 150, 153.

Spencer [Herbert], 68.

Step, 36, 59, 60, 64, 81, 87, 92, 93, 96,
98, 112. 119. 125, 137, 138, 142, 144,
145, 200, 209, 214, 228, 275.

Strauss [Richard], 171.

Stringed instrument, 166.

Student, 39, 59, 73, 87, 93, 96, 99, 100,
101, 139, 163, 164. 277, 279, 280,

282-289; work for, 101, 164, 261,

284, 286-288.
Study of music, 1, 6, 21, 28, 289.
Stumpf, C, 21.
Subbeat-period, 160.
Subdominant, 144. 187. 188, 204, 253;

regnant minor, 218-220.
Subdominant-harmony, 58, 60, 61, 108,

198.
Subdominant seventh chord, 254.
Subdominant triad, 235, 251, 262, 264.
Subfix-tone, 257,
Subharmony, 85, 88.
Submediant, 144, 253, 263.
Submediant seventh-chord, 254, 256.
Submediant triad, 249-250, 256, 263.
Subrhythm, 161-163, 167-170, 288;

compound, dual, mixed, triple, 286.
Subsecond. 261, 268.
Subsecond-chord, 261, 262, 265, 267-

270.
Subtonic, 144.
Subtonic-chords, 253, 256.
Subtonic seventh-chord, 235, 254.
Subtonic-triad, 251-253.
Superfix-tone. 257.
Supersixth. 261, 268.
Supersixth chord, 261-264, 267-270,

271.
Supertonic, 144, 253.
Supertonic seventh-chord, 254.
Supertonic-triad. 251-253. 256.
Syllables, 43, 61, 86-88, 94, 99, 100,

144, 145, 186, 189, 229.
Symbols, 30, 33, 61, 73, 86-89, 94, 135,

145, 159, 161, 164, 180, 275, 276,
279.

Symphony, 116, 155, 173, 174, 212, 266.
Syncopation, 169.

Technique, 93, 100.

Temperament, 95, 96.

Tempo, 86.

Tenor, 287.

Tenths, 36.

Tetrachord, 142-146, 200, 202, 208, 214.

Tetrad, 269-272; compound, 272.

318

INDEX

Theme, 214.

Theory, 3, 16, 17, 20, 22, 51, 52, 69, 70,
89, 181, 200, 226-228, 233, 234, 244,
269, 289; acoustic, 230; Zarlino-
Riemann-, 181, 226, 230.

Theory of pendant minor, 226, 227.

Third, 25-27, 29, 30, 34-37, 40, 41, 47,
59-61, 63, 65, 67, 76, 81, 82, 85, 89,
93, 108, 120, 137-139, 178, 179, 184,
187, 189, 200, 206, 210, 211, 223, 224,
285, 287; double, 211, 212; harmonic,
135, 137, 234; major, 34, 36, 61, 76-
78, 81, 82, 120, 137, 138; minor, 36,
137, 138; superadded, 257.

Thirteenth, 82, 89.

Thorough-bass, 259, 267, 269, 270, 274.

Thread, cadence, of harmony, 54;
consonance, 37, 143; dissonant, 143;
dominant, 47, 82, 84; harmonic, 35,
36, 37, 38, 41, 54, 63, 79, 80, 81, 84,
96, 107, 109, 124, 133, 134, 137, 139-
141, 143, 178, 183, 188, 193,224;
repose-, 54; tonic-, 47, 59.

Time, clock, 174; mathematical, 174 ;
rhythmic, 174 ; rhythmic period of, 38,
42.

Time-accent, 32.

Time-period, 32, 33, 38.

Time-relation, 14, 22, 30, 38, 79, 104.

Tonality, 1. 39, 41, 56, 60, 61, 65, 67,
77, 94-96, 103, 215, 224.

Tone, 5-10, 13, 17, 25, 28, 29, 35-37,
44, 46, 50, 53, 55, 74, 87, 88, 94-97,
109, 112, 114, 117-119, 124, 127,
133, 136-138, 140-142, 144, 148,
153, 156, 165, 176, 182, 189, 190,
192, 198, 201, 205, 206, 208, 210, 212,
215, 228, 232, 233, 235, 239, 243, 247;
accented and unaccented, 43; added,
262-264, 268, 274; analysis of, 33-
35; =balanced sound, 30, 38; bond-,
63, 76, 122, 1 23, 285 ; cadence-, 46, 47,
67-59, 61-66, 92, 96-100, 106, 107,
113, 135, 136, 191, 192, 235, 257;
(prototype), 191, 194, 208 ; chord-, 86 ;
component, 85, 103, 106, 234 ; elemen-
tary, 34, 79; = equilibrium, 30, 125;

harmonic thread of a, 35-36 ; hfirmo-
nic, 38, 86; harmonic complex of, 34,
35, 37, 40, 41 ; harmonic pedigree, 224-
231; = harmony, 30, 33; infix, 257;
initial, 247; isolated, 34, 37, 40, 41,
45, 55, 59, 60, 108, 177; leading, 61 ;
melodic-, 86; mode-, 87, 93, 94; origi-
nal, 26, 27. 75, 76, 85, 107, 233;
original cadence-, 46, 92, 98, 106, 135,
136; original repose-, 46; physical,
20; pitching a, 54; regnant, 106-112,
116-118, 120, 121, 123, 126, 193,
199, 207, 208, 210, 211, 214, 216,
256, 261, 274, 287; repose-, 46, 62,
63, 67, 86, 96-100, 257; seventh, 82;
seven original, 26, 27, 75-86, 103,
107, 225, 226; single, 68, 79, 135, 139;
stable, 257-260; subfix-, 257; super-
fix-, 257; terminal, 82; thirteenth-,
82; three stages of, 193, 194; un-
stable, 257-260.

Tone-cadence, 45-48, 55, 86, 91, 121.

Tone-feeling, 28.

Tone-genesis, 33, 51, 54, 95.

Tone-material, 214, 220, 221, 257.

Tone-moment, 23, 153.

Tone-region, 141-149.

Tone-relation, 22, 24, 30, 42, 45, 48, 56,
58, 62, 67, 78, 89, 94, 98, 104, 180,

214, 224, 278.

Tone-repose, 45-47, 55, 62, 63, 67, 91,

96-100, 190, 192, 201, 221.
Tone-rhythm, 7, 9, 10-14, 15, 29, 48,

152, 154, 155, 171, 172.
Tone-system, 1, 27, 39, 65, 95, 147, 205,

215, 224, 233.

Tonic, 84, 90, 93, 229, 253, 272; ma-
jor, harmony, 33, 41, 45, 47, 54-61,
63-65, 67, 77, 83, 84, 90-93, 98,
103, 105-108,111,180,181,183-187,
193,221,229, 260; minor, harmony,
179, 180, 181, 184-187, 199-206, 214,
221, 230; rhythmic, 120.

Tonic-centre, 143.

Tonic-chord, 66.

Tonic components, 83.

Tonic-root. 76.

INDEX

319

Tonic-scale, 146.

Tonic-septonate, 144, 145.

Tonic-triad, 66, 84, 262, 268.

Triad, 133, 134, 136, 139, 140, 255-
241, 244, 248, 249, 264; augmented,
249, 262 ; basic, 240 ; diminished, 237,
262; gromid-, 238; major, 90, 133,
237, 251, 262, 268; major dominant-,
84, 235, 249; major subdominant-,
235, 264; major tonic-, 262, 268;
mediant-, 248-250; minor, 237,249,
251, 262, 268; minor dominant-,
235, 262; minor mediant-, 248,249,
minor subdominant-, 235, 262 ; minor
tonic-, 262, 268; nucleus, 169, 262,
263, 268, 269; primary, 250, 251,
253; secondary, 249-251, 284; sub-
dominant-, 235, 251, 262, 264; sub-
mediant-, 249, 250, 256, 263 ; sub-tonic,
251-253; supertonic, 251-253, 256;
tonic-, 66, 84, 262.

Triad positions, 238-241,

Tritonus, 144.

Undertones, 227, 228.

Upleader, 64, 92, 183, 208, 209, 239,
285; chromatic, 275; major, 187,
192; minor, 187, 192; prototype, 95,
192, 194.

Vierklang, 269.

Voicing, close and open, 267.

Von Biilow, 276.

Wagner, 5, 49, 74, 140, 150, 171.

Weber, G.. 50, 74.

WeU-tempered Clavichord, 170, 198.

Wind instruments, 166.

Work for students, 101, 164, 282-

288.
World, energy, 11, 12.
World equilibrium, 12.
World harmony, 12, 14.
World principle, 11.
World rhythm, 12.

Zarlino, 181, 226, 230.

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