1 07 354
J3y the Same ^Author
THE MUSIC OF I.ISZT
TWENTIETH CENTURY
COUNTERPOINT
A Guide for Students by
HUMPHREY SEARLE
NEW YORK
John de Graff Inc.
T'WHN ' JL 'JLE.TH
Copyright 1954 by Vifilliams and Jforgate Ltd*
in Great Britain
Printed in Great Britain
CONTENTS
PAGE
PREFACE Vli
ACKNOWLEDGEMENTS ix
CHAP.
I INTRODUCTION I
II THE DEVELOPMENT OF CHROMATIC COUNTERPOINT 7
III STRAVINSKY AND EXPANDED DIATONICISM 22
IV MILHAUD AND POLYTONALTTY 32
V BART6K. AND THE FREE USE OF DISSONANCE 44
VI mNDEMTTH AND DIATONICISED CHROMATICISM 55
VII SCHOENBERG AND TWELVE-TONE COMPOSITION Jl
VIII SOME INDEPENDENTS Il8
IX CONCLUSION A NEW HYPOTHESIS 132
POSTSCRIPT, 1954 147
BIBLIOGRAPHY 15!
DISCOGRAPHY 153
INDEX 157
PREFACE
THIS book is sub-titled "A Guide for Students"; that is to say,
it is not primarily intended for scholars or musicologists, who
can find fuller information on the subject elsewhere. I
remember, when a student myself^ finding it difficult, if not
impossible, to bridge the gulf between the traditional harmony
and counterpoint taught in most colleges of music and the
music that was actually being written by contemporary
composers especially as one of the justly respected professors
at the college where I was studying was famed for his use of
parallel fifths and polytonal counterpoint in his own works.
This book, then, is an attempt to bridge that gul an attempt
to show how modern composers have come to write as they do,
and perhaps to point out new paths which the student, if
interested, may care to follow up for himself,
This book is, therefore, not a complete " guide to modern
music " it is only intended as a land of signpost on the way;
nor is it a discussion of the Hundred Best Contemporary
Composers. Apart from limitations of space, such a compendium
could easily degenerate into a mere catalogue of names and
works. What I have attempted to do is to single out a number
of composers who represent various different tendencies in
modern music, and to discuss their work in some detail. I have
also tended" to concentrate on those who have gone to the
extremes rather than those who have chosen the middle path;
this means, of course, that a good many well-known and
distinguished composers are not mentioned at all, whereas some
others who are less well known and more rarely performed find
a place here. This is not intended to imply any criticism of the
former; as composers and musicians many of them are certainly
of far greater importance than some of those discussed here.
But I have concentrated on the extremists because I feel it is
important for the student to know the furthest that has been
gone in any particular direction; whether he will wish to go so
far himself is his own affair, but at any rate he should know
vii
viii AUTHOR'S PREFACE
where the limits lie. And I have approached the subject more
from the point of view of technical interest than musical value;
what a student needs to acquire is technique and confidence in
self-expression but nobody can make him into a genius if the
spark is not there already.
In the final chapter, greatly daring, I have attempted to
outline a method of harmonic analysis which may be applicable
to most types of modern music. I am aware that it is an outline
and not a complete system; but I feel that one should beware
of too much rigidity in matters of this kind, and if the ideas
there put forward may be of service to another in the construc-
tion of a more detailed system of analysis, they will not have
been put forward in vain.
In conclusion, I should like to thank Mr. Richard Gorer for
many helpful suggestions during the preparation of this book.
H.S.
London
ACKNOWLEDGEMENTS
Thanks are due to the following for permission to reproduce
copyright material:
PURCEIX: Royal Music Library.
REGER: Messrs. Bote and Bock, Berlin.
STRAUSS: "Thus Spake Zarathustra." Hinrichsen Edition Ltd,
"Ein Heldenleben." F. E. C. Leuckhart, Munich.
MAHLER: By arrangement \vith Universal Edition (London)
Limited.
STRAVINSKY: Messrs. Boosey & Hawkes, and J. & W. Chester
("Les Noces" and "Histoire du Soldat"); United Music
Publishers Ltd.
MILHAUD: By arrangement with Universal Edition (Alfred A.
Kalmus, London).
BART6K: Messrs. Boosey & Hawkes; Quartet No. i, Zeno-
mukiado, Vdllalat, Budapest.
HZNDBMTTH: Messrs. Schott & Co.
SCHOENBERG: Universal Edition, Wilhelm Hansen Musik-
fbrlag (Serenade), Bomart Music Publications*, Editions
L'Arche, Messrs. G. Schirmer Inc.
BERG: By arrangement with Universal Edition (Alfred A.
Kalmus, London).
WEBERN: By arrangement with Universal Edition (Alfred A.
Kalmus, London).
KRJENEK: Messrs. O. Schirmer, Inc. and Messrs. Chappell & Co.
BUSONI: Messrs. Breitkopf & Hartel; British and Continental
Music Agencies.
VAN DIEREN: Oxford University Press.
SZYMANOWSXI: By arrangement with Universal Edition (Alfred
A. Kalmus, London).
JANA&EK: Universal Edition, Hudebni Matice.
IVES: Arrow Music Press, Inc.; Mercury Music Corpn.
VARSE: Messrs. Curwen & Sons Ltd.
VALEN: Norsk Musikforlag (Quartet No. 2): Harold Lyches
Musikfbrlag.
STOGKHAUSEN: By arrangement with Universal Edition
(London) Limited.
*For "A Survivor fiom WaraaV.
CHAPTER I
INTRODUCTION
Is it really possible to give any general rules for modern
contrapuntal writing? To many people modern music seems to
be in a state of complete anarchy; there are so many methods
and systems that it would appear hardly practicable to find any
common factor between them. We get composers who spice up
normal diatonic writing with a skilful use of dissonance, like
Stravinsky, those who go in for polytonality, like Milhaud, those
who use peculiar scales derived from folk music, like Bart6k, and
those, like Schoenberg and Hindemith, who have invented their
own systems of composition and laid down rules which are
chiefly followed by their own disciples. These are the main
tendencies in contemporary music; but there are many others,
and many composers borrow ideas from each or aU of the
methods outlined above. Yet no one would seriously pretend
that there are no rules at all; composers must instinctively feel
what sounds good and what bad. Our purpose then is to try
and discover why modern composers write as they do in
fact to find what method there is (if any) in their variegated
madness.
A student who wishes to become a composer is compelled
(if he goes to a college of music) to spend a great deal of time
writing counterpoint exercises in the styles of Palestrina and
Bach. He may object to this as a waste of time, pointing out
(quite correctly) that all modern composers are continually
breaking the rules which he is so carefully taught to observe.
But in fact he is not wasting his time; by doing these exercises
he is merely re-living the process of musical history. If Palestrina
and Bach had not existed there would have been no Bart6k or
Schoenberg; every composer must learn all the lessons of the past
before he can embark on new developments himself. In fact
there is no break between modern music and that of the past;
every element in every work, written by every composer of
2 TWENTIETH CENTURY COUNTERPOINT
today has developed out of some feature of the music of his
predecessors. It is only by understanding this that one can hope
to dissect or analyse the different tendencies in modern music;
in fact, before embarking on a study of contemporary counter-
point it is absolutely essential for the student to have a thorough
knowledge of the procedure of past generations. It is no good
trying to start reading a detective story in the middle, when one
has no idea who is the detective, who are the potential criminals,
or even who has been murdered.
I am therefore assuming that readers of this book will have a
good knowledge of classical harmony and counterpoint up to,
say, Wagner's day. Where do we go from there? We must first
try to place ourselves in perspective with the musical history of
the last four hundred years. This period may be divided into
three great epochs. The first, beginning in the fifteenth century,
and ending with the death of Bach in 1750, may be called a
polyphonic period, in the sense that in general counterpoint
rather than harmony was the dominant factor. The second,
which covers the period of the Viennese classics and also the
romantic composers, ended about 1910; this was primarily a
harmonic period, with the reverse tendency to its predecessor.
Our modern age is again predominantly contrapuntal; and
there are reasons for this, as there are indeed for the predomi-
nant characteristics of the two previous epochs. TTiese are
bound up with the question of tonality, which is perhaps the
most formidable problem which we have to face in this
enquiry.
The period before Bach saw the gradual dissolution of the
seven medieval church modes, on which music had previously
been based, and their fusion into the major and minor diatonic
scales; hence it was in a sense a transitional epoch. The period
from 1750 to 1910, on the other hand, was a static period,
based on the firm tonality of the major and minor scales, and
it was only towards the end of the period that chromaticism
gradually began to undermine these scales. Our modern period
is again a transitional one, in which the diatonic scale of
sevea notes phis five "accidentals" is gradually being replaced
by a twelve-note scale which has not yet taken a definite
We shall of course be considering this question of tonality in
INTRODUCTION 3
more detail as we proceed; but I should merely like to say
at this point that in general a transitional age seems to be
predominantly contrapuntal, whereas a static age seems to
be predominantly harmonic. Harmony and counterpoint are
of course the obverse and reverse sides of the medal, a-n.d it is
impossible to treat them as separate entities; but it remains true
that in different periods of history one or other of them tends to
become the dominant factor for a certain time. The question
of which will predominate is governed by the degree of solidity
which tonality has acquired during that period. If a tonal
system is securely established, as the diatonic system was during
the major part of the i8th and igth centuries, it is able to build
up a solid structure of chords with which to surround and
accompany its main themes. In fact the idea of a tune and its
accompaniment is only possible within the framework of such
a system, and we can see that this procedure was employed by
every composer from C. P. E, Bach to Wagner. Counterpoint
there can be as well, of course, but it will normally be strictly
governed by the harmonic scheme; i.e. in general -die counter-
point arises out of the harmonies rather than vice versa. (One
has only got to compare the fugues of Mendelssohn, Schumann
or Klengd with those of Bach in order to appreciate this). On
the other hand in a contrapuntal period, such as that from
Palestrina to Bach, and also today, the harmonies will generally
arise out of the movement of independent parts. 1
I ayn. aware that I am generalizing considerably in m^Irmg
this statement one can of course find tunes with accompani-
ments in Purcell, and even Handel and Bach, and there is
plenty of contrapuntal writing in Mozart, Beethoven and
Brahms* but I merely maintain that the outlook of the 'first.
period was mainly contrapuntal, and that of the second mainly
harmonic, and I think that our present period is also a contra-
puntal one. In contrapuntal periods there is a far greater degree
of harmonic experimentation, as the interweaving of a number
of independent parts may often produce surprising results,
like this (by now, I think, fairly well-known) example from
Gesuakb's "Moro lasso", published in 1611:
*Ct "Apollonian Evaluation of aDwnyrian Epoch", Chap. XII of Schoolboys
"Structural Functions of Harmony" (London, 1954).
4 TWENTIETH CENTURY COUNTERPOINT
Ex. i
Here the sequence of chords anticipates the "Kiss" motive in
Die Walkiire, (as Philip Heseltine pointed out in his study of
Gesualdo 1 ); yet each part moves quite simply and naturally,
mostly by step, and there is only one diminished interval, of a
type allowed in every counterpoint treatise. Yet an eighteenth
or early igth century composer would not have dared to write
such a passage, as he would have envisaged it purely from the
harmonic point of view. Similarly the extraordinary "false
relation" clashes in the Elizabethans and Purcell arise from the
logical contrapuntal movement of the parts. Here is a typical
example from PurcelTs "My heart is inditing".
Ex. a
Chorus
String
The fact that such progressions could be written meant that
there was no clearly established harmonic system based on a
definite scale and tonality at that time. (The actual process of
the dissolution of the church modes into the major and minor
scales is far too complex for me to describe here, and in any case
is not part of my subject; but it is sufficient to say that modal
elements are found even in Bach and later composers) . Now we
KUarlo Gesualdo, by Cecil Gray and Philip Heseltine. London 19126.
INTRODUCTION 5
are in exactly the same position today; the diatonic system has
been broken up by the chromaticism of Liszt and Wagner, and
we are left with fragments of it, tossed like flotsam on a sea of
new and strange sounds.
The process by which the diatonic system was undermined
from within is by now fairly familiar to most readers, and there
is no need for me to recapitulate it in detail 1 . IJLJS^Jif&dient to
say that by 1910 composers so different from each other as
Bartok, Busoni, Schoenberg and Stravinsky .were all making a
completely, free M&e, of all the twelve notes of the chromatic
scale, and jSchoenberg had even gone so far as to throw tonality
overboard altogether, at any rate in theory. The whole change
may be summed up by saying, as I mentioned earlier, that
instead of regarding the seven notes of the diatonic scale as
superior to the five accidentals, we can now regard all twelve as
equals. This does not necessarily mean that all modern
composers do regard the twelve notes as equals, nor that there
is no tonality in modern music. In fact all composers use
elements which are directly derived from the diatonic system,
and, as I hope to show, a form of tonality is present in all
music of the present day, even including that of Schoenberg and
his followers; but the fact remains, whether we like it or not,
that we have nowfgot a twelve-note scale instead of a seven-note
one. We can use this twelve-note scale as diatonically or as
chromatically as we wish that is according to our taste but
we cannot escape its implications. In this book I hope to
show the different uses made of it by various modern composers,
and to draw some general conclusions from these.
This brings me again to the question of tonality in modern
music. The diatonic system was firmly based on the major and
minor triads, as we all know; but these are now replaced by far
more complex chord formations. Nevertheless these new chords
developed naturally from the old ones, usually by adding or
altering notes in them, and there are very few (e.g. the chord
built up of a series of perfect fourths) which appear to be entirely
new. The new chords are in fact distant cousins of the old ones;
and though they may look different and do not usually behave
hi the same way as their predecessors I have suggested that
X A concise account will be found in Mosco Garner's A Study of Twentieth-
Century Harmony (London 1942).
B
6 TWENTIETH CENTURY COUNTERPOINT
in any case a good many of them arise as the result of contra-
puntal movement they can still be related to a tonal centre
corresponding to the old keynote. Even Schoenberg called his
system "Composition with twelve notes related only to each
other", meaning that for him there are twelve "tonalities" of
equal importance which require to be balanced equally against
one another.* In fact behind all the complications, variations,
compressions and ellipses of modern music one still finds the
conception of a tonal centre, not of course identical with the old
tonic, and now related to a twelve-note instead of a seven-note
scale. In fact the diatonic system has now been replaced by what
I might call expanded tonality a conception -which I hope to
discuss in more detail in the next few chapters.
To sum up, then, we are living ha a transitional and pre-
dominantly contrapuntal period, in some ways parallel to the
age between Palestrina and Bach; the diatonic system of the
1 8th and igth centuries has ceased to exist in its old form, but
there is no complete break with the past; elements of the old
music have continued to survive in the new, and we have a
different conception of tonality, based on the twelve-note scale.
We shall later consider these points in detail by exarnining the
work of various composers who have brought about this
revolution. But let us first trace briefly the steps which led up
to it.
*Cf. p. n6n.
CHAPTER II
THE DEVELOPMENT OF
CHROMATIC COUNTERPOINT
As we have already seen, the steps which led to the eventual
breakdown of the diatonic system in its old form were already
present in the music of much earlier ages. The Gesualdo
example quoted above shows an advanced use of chromaticism,
and we can find similar examples in Bach and others. Here is a
passage from the Fugue in B minor (Book I of the Well-
Tempered Clavier) :
Ex.3
J&m.
The subject is in the bass, and it will be seen that its twenty
notes contain all the twelve of the chromatic scale. Nevertheless
it is not harmonized chromatically, but is treated as a series of
passing modulations, as indicated above. This is typical of
Bach's harmonic procedure; however chromatic his themes
may be, he never loses sight of the basic principles of tonality.
(Compare also the Chromatic Fantasy and Fugue, which
7
8
TWENTIETH CENTURY COUNTERPOINT
contains some astounding harmonic progressions, and also
Bach's harmonisation of the chorale "Es ist genug'VThe fact
that the twelve-tone composer Alban Berg was able to introduce
the latter in its original harmonisation into his violin cbncerto
without any sense of incongruity shows how "advanced" was
Bach's use of chromatic harmony).
From the example quoted above it is clearly only a step to
this passage from Liszt's Fantasy and Fugue on BACH :
Ex.4
This shows the entry of the third and fourth voices, hi the top
and bottom parts respectively. The theme itself is similar to the
Bach subject quoted in Ex. 3; but here is accompanied by
chromatic counterpoint, and the result is modulation so
constant that it almost amounts to suspension of tonality.
(Liszt himself evidently felt this, for he found it necessary to
follow this passage with a long dominant pedal on D before
introducing a later entry of the subject in G minor). This kind
of chromatic writing, consisting mainly of side-slips and based
to a considerable extent on the chord of the diminished seventh,
can be found in many works of Liszt's middle period, notably
this Fantasy and Fugue, and also the Variations on the basso
DEVELOPMENT OF CHROMATIC COUNTERPOINT Q
ostinato from Bach's Cantata "Weinen, Klagen, Sorgen,
Zagen" itself an entirely chromatic theme. It was in fact
Liszt, more than any other composer of the igth century, who
seized on the chromatic experiments of Bach and developed
them for his own purposes. 1
In this he was followed by several later composers, of whom
the most important was Max Reger (1873-1916). Reger was
pre-eminently a contrapuntal composer, and his style was con-
siderably influenced by that of Bach in fact a good deal of his
work is almost a pastiche of the older master. But he had also
learnt the lessons of the chromaticism of Liszt and Wagner, and
this extract from his Variations and Fugue on an Original
Theme for Organ, Op. 73, is typical of his chromatic method
of writing :
Ex.5
r i r* r
This shows the final entry of the fugue subject (in the pedals).
It is noticeable that the first four bars show a constantly
fluctuating sense of tonality, while the last two gradually
approach a quite conventional cadence. It is this combination
X A considerable use of chromatic harmony, chiefly for purposes of modulation
and "side-slip" can also be found in the works of Spohr.
IO
TWENTIETH CENTURY COUNTERPOINT
of chromatic and diatonic elements which makes Reger's style
illogical and often irritating; there appears to be no particular
purpose in his passing modulations, and the chromaticism often
only seems to be there for its own sake, without any real
structural function.
An even more typical example of Reger's methods may be
seen in one of the variations from the same work :
Ex.6
Here each part moves quite logically, and each chord is
consonant according to the rules of diatonic harmony; but the
total effect is of uncontrolled and unnecessary modulation.
Compare this with the Gesualdo example (Ex. i), which also
produces chromatic modulations through the logical movement
of the individual parts; but there the total effect has a dramatic
and emotional purpose, which is lacking in Reger. Nevertheless
Reger is of importance as one of those who contributed to the
breakdown of tonality; his chromatic treatment of consonances
was followed by other composers who used dissonances in the
same way, as we shall see later on (p. 71).
DEVELOPMENT OF CHROMATIC COUNTERPOINT II
Another composer of the same period who also made an
advanced use of chromaticism was Richard Strauss. Strauss was
primarily a tonal and even a diatonic composer, but as a
contrast to his normal diatonicism he often used discords of a
violent and chromatic nature, chiefly for dramatic effect.
Though he certainly made use of polyphonic writing to a great
extent, his counterpoint is primarily harmonic, and one would
not regard him as a contrapuntalist in the normal sense of the
term; i.e. with him the harmonic background came first,
however many themes might be superimposed on it. A typical
example is this passage from Ein Heldenleben, from the section
where Strauss introduces themes from some of his earlier works.
Ex.7
TL- j; ^-= F =^=
>^.i-i
12
TWENTIETH CENTURY COUNTERPOINT
Though a number of different themes are most ingeniously
combined here (no marks for guessing from which works they
come!), the passage does not go beyond the normal rules of
diatonic counterpoint, except for the occasional sounding of
appoggiaturas simultaneously with their resolutions. With very
few exceptions, Strauss generally kept within the limits of this
kind of contrapuntal writing. A more ambitious attempt,
however, may be seen in the "Von der Wissenschaft" section of
Also sprach Zjarathustra :
Ex.8
This passage begins fiigally, with successive entries in G, G,
D and A; this example shows the final entry. The celli are
divided into four parts, each being doubled an octave below by
double basses. The four-bar fugal theme (in Cello i) consists
DEVELOPMENT OF CHROMATIC COUNTERPOINT 13
of 14 notes, which include all the twelve of the chromatic
scale; nevertheless it is not in the least atonal, being constructed
out of a series of triads, and further is tonally harmonised
throughout; there is in fact a certain parallel with the Reger
example previously quoted (Ex. 6) in that the counterpoint is
predominantly harmonic, and that the chordal scheme does
not seem to fulfil any very logical purpose, except that of
accompanying the main theme; i.e. the subsidiary parts have
very little real life of their own. This is exemplified by the some-
what automatic sequential treatment of the second and third
'cello parts in the first two bars quoted.
It is certainly unfair to dismiss Strauss* contrapuntal writing
on the strength of a couple of examples, and no doubt a very
good case could be made out for him as a contrapuntalist; all I
am trying to suggest is that Strauss, in common with most
composers of his period, still thought primarily in terms of
harmony, and however complicated the surface texture of his
music may become, there is usually a fairly simple under-lying
harmonic scheme. (Cf., for instance, the prelude to Act III of
Der Rosenkavalier 1 , which presents the appearance of a com-
plicated fugato in six or more parts; but there is no real tension
between the different parts, of the type that we find in Bach or
Bartok) . It was not until the early years of this century that the
supremacy of harmony began to be disputed by the
individuality of the different parts that composed it. There were,
however, some late nineteenth century composers who were
striving in this direction, and perhaps the most important of
these was Gustav Mahler (1860-1911).
Mahler's contribution to music is of course too far-reaching
to be summarised in a few words; as a conductor of genius, his
unrivalled knowledge of orchestral effect led him more and
more to explore the possibilities of soloistic treatment of instru-
ments or groups of instruments, and to turn his back on the
Wagnerian web of sound in which practically every instrument
is doubled by another. Mahler, in fact, brought back clarity
into orchestral writing; in spite of the enormous forces he used,
each individual part can be heard without effort. His style
tended to become more polyphonic with the years; whereas
*A typical quotation from this will be found in Eric Blom, The Rose Cavalier
(Musical Pilgrim series, London 1930).
14 TWENTIETH CENTURY COUNTERPOINT
the earlier symphonies are constructed mainly in terms of a
theme surrounded by subsidiary parts, in the later ones each
individual part tends to greater equality with the others. This
passage from the first movement of the 8th Symphony is typical
of his later methods.
This is a real piece of 8-part writing, with several of the voice
parts doubled by instruments. Though the music is entirely
diatonic, the individual parts are driven against each other
with a complete disregard for passing clashes a method in
some ways very parallel to that later used by Stravinsky. But in
the case of Mahler the main harmonies remain comparatively
straightforward.
DEVELOPMENT OF CHROMATIC COUNTERPOINT 15
The example above makes some use of imitation between the
parts; but a later passage from the same movement, a sort of
instrumental stretto y uses all the classical devices of augment-
ation, diminution and inversion, combined with modulation.
Ex. 10
Many other passages in Mahler show the same kind of treatment
(see for instance the quotation from "Das Lied von der Erde" in
Mosco Garner, op. cit. p. 51), and it would be easy to multiply
examples. But I think it is clear from the above that Mahler did
reintroduce into the Romantic tradition of purely harmonic
writing the tendency to value individual parts for their own
sake; i.e. with him the horizontal aspect of' music was as
important, if not more so, than the vertical. In this sense he is
the forerunner of the whole modern contrapuntal school.
A survey of this transitional period would not be complete
i6
TWENTIETH CENTURY COUNTERPOINT
without some discussion of the early works of Schoenberg. His
music from 1908 onwards (the date when he abandoned
tonality), is discussed in Chapter VII, but his earlier composi-
tions, while remaining within a tonal framework, carry still
further the tendencies observed in Mahler. Schoenberg came to
composition by way of chamber music he was an amateur
violinist and 'cellist, but had little knowledge of piano playing
in his younger days and as a result his approach is pre-
dominantly contrapuntal. Though in these early works he
does not go beyond the post-Wagnerian harmonic scheme, his
chords are nearly always arrived at through the movement of
independent parts. The following example of the simultaneous
use of a theme and its inversion, from the string sextet Verkldrte
Nacht (1899), though complex and chromatic, remains funda-
mentally tonal.
An even clearer example of this "Mahlerian" use of counter-
point may be seen in an extract from Pelleas and Melisande (1902) .
DEVELOPMENT OF CHROMATIC COUNTERPOINT I*J
The music represents the meeting of Pelleas and Melisande at
the castle tower; the Melisande theme appears in fourfold
imitation on the flutes and clarinets, and simultaneously
augmented in octaves on two solo violins; against it is played a
secondary theme, associated with Melisande, on ist clarinet
and bass clarinet, and also the Pelleas theme on solo 'cello.
Ex. 12
l8 TWENTIETH CENTURY COUNTERPOINT
In his following works, the first two string quartets and the
first Chamber Symphony, the chromatic element increases,
and the music is often in a perpetual state of modulation; yet
the tonal framework is still observed, and each part moves
naturally and logically in its own way. Here is an example from
the first string quartet (1905) :
DEVELOPMENT OF CHROMATIC COUNTERPOINT IQ
Ex. 13
A more homophonic, but still fundamentally contrapuntal
passage from the First Chamber Symphony (1906), shows an
advanced use of chromatic harmony, altered and substitute
notes being used freely. The music modulates rapidly without
ever altogether losing its tonal feeling.
Ex. 14
i.vi.
sehr auadrucksvoU
Chromatic harmony could hardly go further than this
without overstepping the bounds of tonality altogether, and
2O TWENTIETH CENTURY COUNTERPOINT
in the finale of his next work, the 2nd/ String Quartet, Schoen-
berg wrote some passages which are almost impossible to explain
from a tonal point of view. A typical passage is quoted here;
for the present it must suffice to say that this represents the
logical conclusion towards which Schoenberg's ever-increasing
use of chromatic elements was leading him.
Ex. 15
Ylni
This chapter has dealt exclusively with composers of the
German school, because it is here that the use of chromaticism
is seen in its most acute form. Some French and Russian
composers, however, notably Debussy, Ravel and Scriabine,
were also working on similar lines, chiefly in the free use of
altered and whole-tone chords. Though partly used for impres-
sionistic effect, these chords tended to remove the feeling of
tonality. As Schoenberg remarks 1 , "Debussy's harmonies,
without constructive meaning, often served the coloristic
purpose of expressing moods and pictures. Moods and pictures,
though extra-musical, thus became constructive elements,
incorporated in the musical functions; they produced a sort of
emotional comprehensibility. In this way tonality was already
dethroned in practice, if not in theory". It is, I think,
unnecessary to illustrate this point by quoting examples,
particularly as neither Debussy, Ravel nor Scriabine were
fundamentally contrapuntal composers; but the student can
find many passages in their works where tonality is either
ambiguous or suspended altogether.
1 Arnold Schoenberg. Style and Idea. (London 1951) p. 104.
DEVELOPMENT OF CHROMATIC COUNTERPOINT 21
We can now proceed to a more detailed study of various
composers who have profoundly influenced contemporary
contrapuntal writing, each in their own way. To begin with, I
shall attempt to discuss five important figures Stravinsky,
Milhaud, Bartok, Hindemith and Schoenberg each repre-
senting a different musical tendency.
CHAPTER III
STRAVINSKY AND
EXPANDED DIATONIGISM
STRAVINSKY, as we have seen, is a firm believer in the diatonic
system, and throughout his life his work has been based on this
system, no matter how many alien elements he has introduced
into it at one time or another. It is usual to think of Stravinsky
as a predominantly contrapuntal composer; but though he
certainly thinks in terms of lines rather than chords on the
whole, his counterpoint is in fact rather rudimentary, being
extensively based on the use of ostinato figures a use which
was no doubt suggested by the idioms of Russian folk music.
It is important to remember, with Stravinsky as with many
modern composers, that a single part may in fact take the form
of chords moving hi parallel, as in the following example from
Petrouchka:
Ex. 16
STRAVINSKY AND EXPANDED DIATONICISM 3
This is, in effect, merely two-part writing, with each part
thickened out in common chords; it is also based on an ostinato
effect. A more complicated example of the same type of thing
may be found in Le Sacre du Printemps:
Ex. 17
Here the thought is fundamentally diatonic, in spite of the
chromatically descending middle part; and again we have an
ostinato. The famous opening section of Le Sacre a again, is
not truly contrapuntal; it really consists of one main theme
with a chromatic accompaniment and a certain number of
decorations, cleverly written so as to suggest contrapuntal
development. The nearest it gets to true counterpoint is in
passages like Ex. 18 [p. 24] again based on an ostinato.
The fact that this is not contrapuntal in the true sense is
shown by the immediate repetition of these two bars, unaltered
except for the elaboration of one part; i.e. here Stravinsky
thinks rhythmically and dramatically, rather than contra-
puntally.
"Les Noces " (1917) deliberately attempts to paint a picture of
Russian peasant life, and therefore there is naturally an almost
continuous use of ostinato. There are however occasional
imitative passages such as Ex. 19 [p. 24].
Here again the counterpoint is extremely simple, and the
ostinato provides a solid background*
24 TWENTIETH CENTURY COUNTERPOINT
Ex. 18
Ex. 19
3.
S
n
r
en
"F" T I
r* T ' i
f
The chorales in "L'Histoire du Soldat" (1918) do provide
some genuine four-part writing; but as they are intended more
or less as parodies, Stravinsky is careful to avoid what would
be the normal diatonic harmonisation of the theme.
STRAVINSKY AND EXPANDED DIATONIGISM
Ex. 20
Largo
Here each part is quite simple and almost entirely diatonic;
but the writing is carefully arranged so that the parts do not
"fit" together in the accepted classical sense. This is the so-
called "wrong note technique" of which Stravinsky is an adept
master. It consists in substituting for what the ear expects
something different which sounds more "interesting" but has
no real logical function.
A more serious attempt at contrapuntal writing may be
found in the second movement of the Symphony of Psalms
(1930), which is in the form of a double fugue though of a
fairly free sort. All the usual contrapuntal devices are found
here, and the movement certainly gives the effect of counter*
point, though it hardly has the architectural solidity of Bach.
For 'example take the beginning of the exposition of the second
subject (in the sopranos): [Ex. 21, p. 26].
The first subject (hi the bass) has previously been exposed by
the orchestra; it is typical of Stravinsky in that it goes round and
round a few notes and never seems to progress anywhere.
Note also the tendency of the orchestral alto and tenor parts
to do the same thing; it is this that gives Stravinsky's counter-
point its curiously static character. It goes through all the formal
motions of being contrapuntal, but the essence of counterpoint,
the interweaving of independent parts which will also create
harmonic tension and progression, is almost entirely absent.
The harmonic style, it will be seen, is fundamentally diatonic,
with a few clashes of passing-notes and some false relations.
The whole movement is well worth studying as a compendium
of Stravinsky's contrapuntal devices.
Two passages from a later work of Stravinsky's, the Mass
(1947) show how little his contrapuntal style has changed with
26 TWENTIETH CENTURY COUNTERPOINT
Ex.21
Soprani
Orch.
the passage of time. The first is a simple imitative passage,
diatonic throughout with an ostinato-like accompaniment.
Ex. 22
Wind
STRAVINSKY AND EXPANDED DIATONIGISM 27
The second passage again introduces the voices imitatively
against a chorale-like figure on the brass.
Ex.23
S.A.
T.B.
28
TWENTIETH CENTURY COUNTERPOINT
As a final example we may take this passage from the Interlude
before the Bacchantes dance in "Orpheus" (1947).
Ex. 24
Moier&to
This again is very typical of Stravinsky's methods, and
evokes a comparison with Ex. 21; there is no actual ostinato,
but the bass descends by step throughout (a feature of the
whole interlude). Against this the upper parts move within
a mainly diatonic framework, but with a certain number of
false-relation clashes arising out of the movement of individual
parts.
This in fact is Stravinsky's main contribution to contrapuntal
writing; his parts move freely against each other within the
STRAVINSKY AND EXPANDED DIATONICISM 29
diatonic scale, without any regard for the older ideas of accented
passing notes or dissonances that have to be resolved. It is
true that concords tend to appear at the more important points
in the phrase, but in the intervening chords Stravinsky has a
predilection for unresolved sevenths and ninths, which he treats
as normal concords. This tendency can be seen as early as
P&rouchka (Ex. 16); our example merely consists of two lines
of chords clashing against each other. In Exs. 20, 21, 23 and 24
we have four or more single lines moving against each other in the
same way, with the added complication of a number of false
relations. These false relations normally arise out of the natural
movement of the parts, and do not constitute any threat to
tonality; they are in fact usually of the type which one finds in
Elizabethan music, arising out of the remnants of the medieval
modes (flattened and sharpened third, sixth or seventh, perfect
and augmented fourth heard simultaneously, etc.). As stated
before, Stravinsky is essentially a diatonic composer, and any
chromatic elements are definitely regarded as foreign to the
main key.
In this appraisal of Stravinsky as a contrapuntalist, I must
make it clear that I am not discussing his place in modern music
as a whole. Clearly his influence on the music of today has been
enormous, and rightly so; but this is due to the dramatic and
rhythmical elements in his music and to his command of
orchestral effect rather than to his contrapuntal technique.
As Constant Lambert rightly said in "Music Ho!" 1 , "his
melodic style has always been marked by extreme short-
windedness and a curious inability to get away from the prin-
cipal note of the tune .... The essence of a classical melody is
continuity of line, contrast and balance of phrases, and the
ability to depart from the nodal point in order that the ultimate
return to it should have significance and finality/' Judged by
this standard, Stravinsky is a singularly poor melodist, and as
Ex. 21 shows, his counterpoint only too often falls into a
pastiche of eighteenth-century passage work spiced up by a
few harmonic clashes. It is by endless, primitive repetition of
1 London, 1934. (at present available in Pelican Books). The whole of Part Two,
"Post- War Pasticheurs", is an excellent account of Stravinsky's aims and methods,
and though Lambert only dealt with Stravinsky's music up to 1930, Stravinsky
has written nothing since which contradicts his judgments.
3O TWENTIETH CENTURY COUNTERPOINT
short phrases that Stravinsky makes his effect, not by the flowing
polyphony of classical composers, and therefore I feel justified
in my claim that Stravinsky is not a contrapuntalist in the true
sense of the word.
Nevertheless he is a composer whose methods can be studied
with advantage. Rhythm is a very important part of counter-
point, and no one can deny that Stravinsky is a master of
rhythmic effect. (Note for instance the placing of the stresses
in Ex. 25 below) . The student, therefore, who feels so inclined
may undertake the following exercises hi this style. (Following
the example of Schoenberg in his Harmonielenre, I feel it is
better not to give the student examples to be "worked", but to
let him start from the beginning composing his own exercises
in the style given).
1. Write some 4-part chorales, of 4 or more phrases, in the
style of Ex. 20. (N.B. The student should write his own
melody, rather than attempt to harmonise an existing
chorale in this style).
2. Is it possible to analyse Ex. 20 according to the rules of
classical harmony?
Alternatively, how few alterations are necessary in order to
harmonise it in the orthodox manner? (e.g. supposing the
second and third notes in the bass part were B[? and A
instead of B and Bb, etc.). The student is recommended to
study the Grand and Petit Choral from L'Hfistoire du Soldat
(published by Chester).
3. Write some pieces of 4-part imitative counterpoint in the
style of the vocal parts of Ex. 22 (i.e. purely diatonic,
without false relations), but at greater length. Write also
some 4-part vocal counterpoint with a 2-part accom-
paniment (not in the form of an ostinato!).
4. Analyse the second movement of the Symphony of Psalms
(published by Boosey and Hawkes).
5. Write some 4-part fugal expositions in the style of the
opening of this movement (i.e. including both diatonic
clashes and false relations).
STRAVINSKY AND EXPANDED DIATONICISM 31
Here are the first three entries :
Ex. 25
nil
i
fo. f1
eU.
CHAPTER IV
MILHAUD AND POLYTONALITY
POLYTONAUTY, or the use of several keys simultaneously, is not
a new device; in fact in all essentials it is as old as music itself.
Edwin Evans once -wrote that "in spirit every canonic conies
at an interval other than the octave and every fugal answer
constituted tentatives towards bitonality" 1 ; and in a sense the
struggle between tonic and dominant or other related keys in
every classical work partakes of a bitonal nature, in that the
rule of the one key is disputed by the other. It was clearly only
a matter of time before the rival disputants were presented
simultaneously, and there are a number of examples from the
early years of this century onwards which show this happening
in a fairly radical manner; e.g. the ending of Strauss' Also
sprach ^arathiistra (B major chords in the upper wood-wind
alternating with C's in the basses); the famous passage from
Stravinsky's Petrouchka:
Ex. 26
and the almost equally well-known one from one of Bart6k's
early Esquisses (1908).
1 Cf. Mosco Garner, op. cil. pp. ^ff, for a fuller account of the historical back-
ground of bitonality and polytonality.
MILHAUD AND POLYTONALITY
33
Ex. 27
But other composers treated this problem more radically.
In the often-quoted Scherzo of Szymanowski's First String
Quartet (191?) the first violin part is written in the key signature
of A major, the second in F#, the viola in Eb and the cello in
C in fact adding up to a diminished seventh. However, if we
take a typical passage from it and write all the parts out in
G major with accidentals, the fourfold tonality does not seem
so apparent, especially if we regard Eb as enharmonic for
D$ major.
TUT T
T
34
TWENTIETH CENTURY COUNTERPOINT
One does not really hear the simultaneous use of four keys;
instead one gets the impression of constant enharmonic modu-
lation what Schoenberg called "schwebende Tonalitat" or
fluctuating tonality. This is because the ear will always try
to relate the sum total of the sounds it hears to a definite tonal
basis; it is only really possible to listen to and distinguish
between two separate tonalities at once.
Nevertheless the use of complex polytonal schemes of this
kind can produce some interesting results, and Milhaud
exploited this idea in many of his earlier works. The finale of
the fourth of his "Cinq Symphonies" (1921) is a good example
of this. Written for ten solo strings, it is entitled "fitude" and
is built on the followingfplan:
Instrument Key 147
Violin i F
Violin 2 C
Violin 3 G
Violin 4 D
Viola i A
Viola 2 A
'Cello i D
'Cello 2 G
D. Bass i C
D. Bass 2 F
Bar
13 16 19 22 25
2nd subject
and subject.
2nd subject
2nd subject
2nd subject
ist subject
ist subject
ist subject
ist subject
ist subject
Bar
44
Instrument Key 28 30 32 34 36 37 38 39 40
Violin i F ist subject
Violin 2 C ist subject
Violin 3 G ist subject
Violin 4 D ist subject
Viola i A ist subject
Viola 2 A 2nd subject
'Cello i D 2nd subject
'Cello 2 G 2nd subject
D. Bass i C 2nd subject
D. Bass 2 F and subject
It is a strict canon in ten parts on two subjects; each subject
is exposed successively in five different keys, the second subject
entering in the same key as the final entry of the first subject
and reversing the order of keys in its exposition. This process
MILHAUD AND POLYTONALITY
35
is carried out twice, once starting from the bottom of the
orchestra, and once from the top with closer entries; then a
coda of two bars rounds off the movement. Though this scheme
may appear a purely mathematical one, musically this move-
ment is a most effective piece. Here are the final three entries
towards the end of the movement (bars 38-40). Note that the
canon here is at two bars' interval in the upper five parts, at
one bar's interval in the lower five.
Ex. 29
(Incidentally a similar scheme was adopted by Bartok in the
first movement of his Music for Strings, Celesta and Percussion
(1936) see p. 48).
36 TWENTIETH CENTURY COUNTERPOINT
In this example again one cannot really hear the five different
keys, except perhaps at the moment of entry of each voice;
the general effect is of diatonic music -with a number of "false
relation" clashes, and the movement (which is well worth
studying in totoj ends quite consonantly in F. The first movement
of the same symphony makes a fairly consistent use of bitonaliry,
the pairs of keys being varied throughout the movement. This
is the opening!
Here it is quite possible to hear both keys at once; and a similar
scheme is carried on throughout the movement. This is a rough
analysis of the key-changes:
Bars 1-14
Top
Middle
Bottom
15-22 23-4 25-7 28-9 3-i 32-5 3^-7 38-43 44-S 49-51 52
, "
A
A
G C
-f*
umi
(Jma
C
<J
Efrmi(Gb
) GJ
* 1C
G
Eb
F#mi
Eb
G
G
G
Bb
D
D B
b G
F#
Gmi
Gma
G
C
t Subject
2nd Subject
ist Subject
and Subject
ist Subject
Both Subjects
Exposition
Middle Section
Reprise
There are of course more variations of detail than it is
possible to indicate in the above table; but it will be seen that
the keys of G and [7 are in general associated with the first
group of themes, and C and F# with the second. The student
is recommended to make a detailed analysis of the movement
for himself (Publishers, Universal Edition). The slow movement
of this symphony is mainly based on a tritonal scheme; the top
and bottom parts begin on block chords of F minor and Eb
MILHAUD AND POLYTONALITY 37
minor respectively, and move outwards chromatically, while
the middle parts hold a chord which wavers between E minor
and the dominant ninth of C.
These methods are typical of Milhaud's processes at that
period, and they are carried even further in other works, such
as the opera "Les Eumenides" (1922). Here Milhaud makes use
of several overlapping ostinatos in the orchestra, against which
the voice part pursues its own independent course, as in this
extract from Orestes' aria hi Act II -.
Ex. 32
O.
je ne le niti-xi pa.s ? En vengeance dt mon pc^e
Here we have four chromatic orchestral parts, three thickcJned
out with double fourths and one with fifths; the voice part
partly coincides with the top line.
38 TWENTIETH CENTURY COUNTERPOINT
The finale of the same opera provides an even more startling
example of polytonal writing. Conceived on a gigantic scale,
it is a kind of perpetually-moving ostinato. This extract is
typical of the texture:
Ex.33
Reading from top to bottom, we have first the triple voice of
the statue of Athena (three parts in B major); then a chorus
in four parts which are respectively in B, A, E b and D b (the fact
that the alto part is really in A is apparent from the two bars
before those quoted here). The first orchestral stave has a two-
bar repeated pattern of chords in Eb; the second also has a
a two-bar pattern, but in Db, while the third has a three-bar
pattern in B. The upper part on the fourth stave has a three-note
MILHAUD AND POLYTONALITY
39
pattern in B of seven crotchets' duration; the lower part
similarly repeats itself every seven crotchets. The fifth stave
contains a D-flattish rhythmical figure which is repeated every
six crotchets, while the bottom part, in A, comes round every
fourteen crotchets. Note the separate accentuation of each part,
which provides a constantly changing rhythmical effect, similar
to the perpetual variation of the contrapuntal complex.
It can be argued that to construct such patterns needs no more
than a knowledge of mathematics, and certainly passages like
this sound forced and ugly when taken out of their context and
played coldly on the piano. Nevertheless when performed by
singers, chorus and orchestra as part of an operatic scene, there
is no denying their immense dramatic effect my strictures on
Stravinsky's use of ostinato in the previous chapter do not
imply that his music is thereby devoid of all interest. Milhaud
was using this kind of style for a particular purpose, in this
case to give the feeling of an immense popular gathering, and
personally I feel he was entirely justified in doing so.
This period of Milhaud's activity certainly shows his style
at its most complex, and in later years he simplified it con-
siderably. Nevertheless he continued to write polytonally for
some time, and in his huge opera Christopher Columbus (1928)
Ex.34
L! A ppa.fi tear
Quetza.lcc*ti
pent du b*.-tra.- AinirA, \\ y * un
40 TWENTIETH CENTURY COUNTERPOINT
there are many passages of considerable complexity. Ex. 34,
p. 39 is an extract from the scene where the ancient gods of
Mexico stir up the sea in order to wreck Columbus' fleet
(Tableau 17).
The whole passage (Vol. I p. 220-239 of the vocal score,
published by Universal Edition) is a 6-part canon which is
exposed and then played backwards in toto (from bar 1370
onwards. This refers only to the orchestral parts, the voices
being independent) . The extract quoted here comes just after
the entry of the sixth part and shortly before the turning point.
It will be seen that the writing here is far more flexible than
in the extracts from Les Eumenides: again the effect is of con-
stantly changing tonality rather than of true polytonality.
This passage is followed by a chorus (pp. 240-251) accom-
panied by the figure in the second orchestral stave of Ex. 34,
but with a varying number of crotchets between the demi-
semiquaver group in each part. Against this the first six bars
of the theme of the canon appear as a two-part double palin-
drome. Here is the central turning-point (bars 1420-1):
u-pe dessus I mords (est tr&v&iUe leur l'e
J J. J> J .
MILHAUD AND POLYTONALITY 41
It will be seen that, of the four parts which have the ostinato
figure, the top part has five crotchets between each demisemi-
quaver group, the second four, the third three and the bottom
part two. The part on the lowest stave is another statement of the
canon theme, which has come in two bars previously. For the
sake of completeness, here is the theme in extenso (here quoted
from the earlier passage, p. 221):
Ex. 36
It is played twice forwards and twice backwards in each of the
top two parts, while the bass, entering ten bars later, plays it
once each forwards and backwards; meanwhile the ostinato
scheme is strictly carried out in the other parts. Here again the
mathematical rigidity of the plan is justified by the enormous
dramatic tension which is built up, and the final resolution on
to a "B-majorish" chord sounds perfectly logical. The whole
passage (pp. 220-251) is well worth studying in detail. Note
that each entry of the canon (in the earlier part of the passage)
is six bars after the previous one, and a major seventh higher;
42 TWENTIETH CENTURY COUNTERPOINT
note also that the ostinato figure (cf. Ex. 35) actually forms part
of the canonic theme, which repeats it five times and then
continues on its own course. It is one of Milhaud's most
ingenious and successful constructions.
In view of the fact that in most of his recent works Milhaud
has more or less given up polytonal writing, the question
remains whether this type of composition is still worthy of
study today. Personally I believe that it is; almost every modern
composer has made some use of the simultaneous combination
of different keys, though naturally the method of approach
varies considerably between them; I have chosen to analyse
Milhaud's methods in some detail, as his approach seems the
most radical and logical, and therefore provides the best basis
of study. Most composers of course do not use polytonality
with such consistency; often they only combine elements
belonging to two different keys for a few bars at a time, and they
do not usually have two parts continuing remorselessly in two
different keys for any length of time without modulating or at
any rate introducing chromatic elements. In fact polytonality,
like the whole-tone scale, has now been absorbed into the
general language of music, and there is no need to practise it
rigidly any more in actual composition, unless a special effect
is needed for some particular purpose. Nevertheless, in order
that the student may have a good grasp of what can be done
within this style, I have included at the end of this chapter some
suggestions for exercises to be worked; later the student will
be able to select for himself such polytonal elements as he needs
and incorporate them into his normal writing.
The other question, a much more fundamental one, still
remains; does polytonality really exist at all, or, is it merely a
"paper tiger"? We have already seen from our examples that
it is very difficult, if not impossible, to hear more than two
keys at once with any kind of continuity, though of course
occasional new entries or elements may impose themselves for
a brief time as alien to the general fabric. But in general, as we
saw, the ear tends to try and resolve the total effect of what it
hears into one main tonality plus a number of incidental notes,
however complex the fabric may be, and therefore Ex. 33, for
instance, cannot be regarded as a four-cornered contest between
four different tonalities, all equally important; one of them is
MILHAUD AND POLYTONALITY 43
bound to predominate, and in this case it is B major, which has
the upper hand both in the vocal and instrumental parts.
Bitonality is the only form of this procedure which can really
represent a see-saw between two different keys, and even this
becomes wearisome after a short time; in fact the ear prefers
to regard the music as constantly modulating in toto rather than
being pulled simultaneously in different directions. (We shall
come back to this in the discussion of twelve-note music, where
the problem occurs in a more acute form). Therefore, poly-
tonality is chiefly useful to the composer in helping him to create
an elaborate and complex texture; but it is in itself too rigid a
concept. When the musical fabric as a whole is so chromatic
and "dissonant" (in the old-fashioned sense) as most polytonal
works are, there is really no reason why one part should stick
firmly to the diatonic scale of one particular key; it would lose
nothing (and in fact would probably gain something) by being
allowed to move freely and chromatically. This is what most
composers have realized in recent years, and that is why poly-
tonality of the orthodox Milhaud type, as exemplified in this
chapter, is hardly ever practised nowadays. Nevertheless it has
had an important influence on the development of con-
temporary music, and therefore I would advise the student to
undertake the following exercises, noting carefully that it is not
enough merely to write one key against another without any
thought for the total musical effect; the total result of all the
parts must also be satisfactory as music.
1. Write bitonal movements on schemes similar to that of the
first movement of Milhaud's Symphonic No. 4 (cf. p. 35).
(N.B. Each key can be represented either by single lines or
by chords).
2. Write polytonal movements on schemes similar to the finale
of the same symphony (cf. p. 34).
3. Write polytonal passages on the lines of Ex. 33 (i.e. including
chorda! parts as well as single lines if desired), but not
necessarily using repetitive ostinatos.
4. Write canonic passages in several parts on chromatic themes
similar to Ex. 36 (but not necessarily including an ostinato
figure) , and following a similar scheme regarding the distance
between entries and their key relationships.
CHAPTER V
BARTOK AND THE
FREE USE OF DISSONANCE
BELA BART6K represents a unique phenomenon, in contempor-
ary musical history. /He has remained throughout an entirely
solitary and individual figure; and though he has influenced
others, and though it is possible to find external influences in
his own works Liszt, Debussy, Hungarian folk music, etc.
he has always stood completely apart from the rest of the
musical world. This is chiefly due to his own dynamic
personality, which has enabled him to digest ideas and recreate
them in an entirely new and personal way.
Onejcouldnot describe Bart6k as primarily either a contra-
puntal or a hafmo rile composer;" Ke ^\v^7A7^^ster"oCbioilL
i^aethods of writing, and^used either^ pxJboth Jn combmation,
according to , J^aee& ^.p^^j^TO^.TT^Ttf.^, A good* deal of his
music makes use of violent percussive or rhythmic effects,
which are not our concern here; but side by side with these
there has always been a strong contrapuntal element. The first
movement of his first string quartet (1907) for instance is a four-
part fugato which has been compared to the first movement
of Beethoven's late G sharp minor quartet; in Ex. 37,
[P- 45] are me third and fourth entries (in cello and viola) .
It will be seen that, for its period, this is much more far-reaching
than anything we have so far come across, except perhaps the
last Schoenberg example in Chapter II (Ex. 15). Though one
could hardly call the writing atonal, it is yet so chromatic that
there is little definite sense of key it could best be described
as "fluctuating tonality", in Schoenberg's phrase. It is in fact
f Bart6k*s unusual handling of tonal relationships that gives his
music a good deal of its individuality, and this is particularly
apparent in his earlier works, where familiar chords and
phrases are given a new twist by Bart6k's unexpected handling
of them. The early piano works, such as the Esquisses, Bagatelles
44
BARTOK. AND FREE USE OF DISSONANCE 45
p motto e$f>ves$
im . pp
Elegies, Dirges, etc., though not always primarily contrapuntal,
exemplify this tendency to a marked degree, and are well worth
studying, as they provide the key to Bartok's later development.
A simpler example of Bartok's chromatic counterpoint may
be seen in this passage from the first Elegy for piano ( 1908) :
Ex.38
Also typical of Bartok at this period are the bars from ^ the
last of the 7 Esquisses (1910); they show a characteristic
"false-relation" (major-minor) harmonic effect. [Ex. 39, p. 46.]
Perhaps the best way of describing Bart6k*s approach at
this time would be to say that he had made tonality morei
fluid: that is to say, that while still upholding the supremacy
46 TWENTIETH CENTURY COUNTERPOINT
Ex.39
8 1*1 I
of a tonal centre, he would combine this with the free use ofall
the twelve notes of the chromatic scale. It is true that in a good
many works of this and later periods he made use of unusual ,
scales derived from Hungarian folk music; but this element is,
I think, not so important as his free use of chromaticism. One
can best sum this up by saying that his music invariably
expresses tonality, but avoids normal diatonic elements. This
can be seen clearly in this extract from a work of his middle
period, the Cantata Prof ana (1934). This passage begins in D
and ends on the dominant of Bfr; but the parts move freely and
chromatically throughout.
BARTOK AND FREE USE OF DISSONANCE
47
In another work of the late middle period, the Sonata for
2 pianos and percussion (1932), we find this four-part fugato,
of which the final entry is quoted here (in Pf. i, R.H.):
Here each entry is a fifth above the previous one, and the
passage is written as a strict four-part canon. The whole section
(Boosey and Hawkes miniature score p. 40 onwards) is well
worth studying in detail. The music cannot be described as
strictly polytonal in the sense that Milhaud's often is; but each
part is constantly moving from one key to another, and there
is certainly the feeling of the opposition to each other of four
parts in different keys. This is chiefly achieved by means of the
clarity and economy of writing. From bar 360 onwards there
are various entries of the main theme (Pf.i R.H.) and its
countersubject (Pf.i L.H.) in inversion, and finally (bar 368)
the theme is split up into its two component parts (a & b),
which are played simultaneously against their own inversions.
In the Fifth String Quartet (1934) (Finale, bar 202 onwards)
48 TWENTIETH CENTURY COUNTERPOINT
occurs a passage which starts as a two-part canon, first at the
fourth and later at the third. On the entry of the two lower
parts, also in canon, the two upper ones move more freely but
still canonically.
Ex. 42
si
This passage, which also is worth studying in detail, becomes
more and more simple as it proceeds, and eventually ends up
in unison a good example of Bartok's use of classical devices
for dramatic effect.
The first movement of the "Music for Strings, Percussion
and Celesta" is a very instructive example of Bart6k's later
contrapuntal methods. It is built up on a series of entries
arranged in the following pattern :
Upperpart:
B
*
D
Lower part:
B
Eb Ab
The notes given above are the first notes of the theme on each
entry. From the central climax (Eb) onwards, the theme
appears in inversion; and after A has again been reached, there
is a short coda in which the original and inversion are heard
together. 'JBut the movement is not just worked out in terms of
BART OK AND FREE USE OF DISSONANCE
49
pure mathematics; there is much variation in the treatment of
the theme, (some entries only state a fragment of it), there are
many subsidiary parts and short connecting episodes, and the
build-up to the central climax is much longer than the descent
from it to the coda. It is in fact a very fine and moving piece of
music, and one of Bart6k's greatest inspirations. This short
extract -will give some idea of the texture.
Ex.43
Vkl.
content
5
TWENTIETH CENTURY COUNTERPOINT
Here again the music is purely chromatic; but in Bartok
we always know that tonality will ultimately be asserted, and
the movement ends with a very definite cadence on to A.
In the slow movement of the Violin Concerto (1937) we
find another of Bart6k's favourite devices a canon at close
distance. In this case it is a four-part canon for pizzicato strings
with a counter-melody for the soloist; curiously enough, the
four string parts enter in the same tonalities as in the
Szymanowski example above (Ex. 28) F#, D #, G and A.
Ex. 44
ttcx.
The whole variation (bars 105-117) is worth studying as an
example of Bartdk's ingenuity in this respect.
An even closer canonic passage may be found in the finale
of the same work; here we have a canon not only at a crotchet's
distance, but with each entry a semitone apart; the purpose
being, of course, to build up a violent dramatic plimax.
Ex.45
OUCH,
A simpler type of three-part canon occurs in the finale of the
Divertimento for strings (1939); here the tonality is modal F
(with flattened seventh), and the three parts simply repeat
each other ha a perpetual round.
BARTOK AND FREE USE OF DISSONANCE
5 1
Ex, 46
Vt*.
All that is intended, of course, is a cheerful, pastoral effect,
gradually building up to a climax.
The last movement of the sixth string quartet (1939) may
well be compared with the first movement of the first quartet
(c Ex. 37); these two examples show the development of
Bart6k's lyrical writing over a period of thirty years. The later
work is of course tenser, more concentrated, and shows the hand
of a master as opposed to that of a young innovator; but the
same lyrical impulse is there, in a sparer frame-work which
eschews all inessentials.
Ex.47
Our final example, from the finale of the Concerto for
Orchestra (1943), provides an interesting contrast with the
fugato from the Sonata for 2 pianos and percussion (Ex. 41)*
Here again there is the same scheme of entries, each a fifth above
the previous one; but the passage is not strictly carried out as
a canon, and the music is far less chromatic and is more
52 TWENTIETH CENTURY COUNTERPOINT ^
definite tonally a tendency observed in many works of
Bartok's last years. These are the third to fifth entries:
Ex.48
The examples given above (apart perhaps from Ex. 44)
do not show Bartok's use of dissonance at its most violent.
There are long passages in many of the middle period works
composed of chords consisting of a number of adjacent semi-
tones sounded percussively together and sometimes endlessly
repeated. But these are not primarily of contrapuntal interest;
their purpose is dramatic, and for this an ostmato effect is
eminently suitable. In contrapuntal writing, however, as we
have seen in the case of Stravinsky, ostinatos are rarely effective,
and Bartok wisely avoids them for the most part. What he does
often do, however, is to combine a number of parts with little
regard for the vertical result, as in Ex. 41, where he deliberately
wishes to create a feeling of tension between the parts; but
though he often appears to allow the individual parts to go
their own way without much thought for their combined
BARTOK AND FREE USE OF DISSONANCE 53
effect, in fact his sensitive ear saw to it that the total musical
result was always satisfactory. We can see this both in his
early works (e.g. Ex. 37) and in his later ones (e.g. Ex, 47);
and in the first movement of the Music for Strings, Percussion
and Celesta (cf. Ex. 43) we find him varying the counter-
subjects with each entry of the main subject in order to obtain
the maximum flexibility and freedom. It is this flexibility of
mind which sets Bart6k apart from the mechanical procedures
of Stravinsky or the mathematical methods of Milhaud, and
gives him a claim to true genius.
This having been said, it is obvious that I cannot recommend
the student to attempt to write exercises in the style of Bartok,
when Bart6k himself used new methods for each piece. True,
Bartok has certain mannerisms which can be imitated (and
only too often are), particularly in his use of rhythmic and
percussive effects. But I have hoped to show that these represent
only one side of Bart6k's genius, and that the other, the more
contrapuntal and often more lyrical side, is of equal importance,
if not greater in the end. I will therefore merely suggest that
the student makes a thorough study of the following passages
from Bart6k's works :
String Quartet No. i First movement (Zenomukiado)
Cantata Profana, bars 1-58, 132 if, (ist movement); 1-25
(3rd movement) (Universal).
Sonata for 2 pianos and percussion, bars 332385 (ist
movement) (Boosey)
String Quartet No. 5, Finale, bars 202-350. (Boosey)
Music for Strings, Percussion and Celesta, First movement
(Boosey)
Violin Concerto. First movement, bars 56-68.
Violin Concerto. Second movement, bars 105-117.
Violin Concerto. Finale, bars 297-319. (Boosey)
Divertimento. Finale, bars 192-247. (Boosey)
String Quartet No. 6 Finale (Boosey)
Mikrokosmos for piano Books 4, 5 & 6. (Boosey)
There are, of course, many other passages which are also
worthy of study; but the above should give a fairly representa-
tive conspectus of Bart6k's contrapuntal methods. "Mikro-
kosmos", a collection of over 150 short piano pieces, is also an
54 TWENTIETH CENTURY COUNTERPOINT
excellent introduction to Bartok's compositional methods;
written towards the end of his life (1926-37), the pieces provide
a kind of modern Gradus ad Parnassum, both for pianists and
composers. Each piece illustrates a particular idea or method
of writing, sometimes of pianistic, sometimes of compositional
interest, and in them Bartok gives a kind of "break-down" of
his technique. His use of modal and other unusual scales may
be studied in them; there are also pieces based on particular
intervals, such as fifths, sixths, sevenths or seconds, and others
demonstrating some particular pianistic effect, e.g. harmonics,
or some unusual rhythm, like the Bulgarian dances which end
the collection. The first three books, though extremely
interesting as examples of Bart6k's methods of writing, are
mainly elementary in character; the last three venture into
more experimental directions. Not all the pieces are primarily
of contrapuntal interest, of course; but the collection provides
as it were the raw stuff from which Bartok's major works spring.
The 44 Duos for 2 violins are also interesting as showing
Bart6k*s contrapuntal methods in their most direct form.
CHAPTKR VI
HINDEMITH AND
DIATONIGISED CHROMATICISM
WITH Hindemith we arrive, for the first time in this survey,
at the case of a composer who has actually worked out and
published a theoretical book on composition, 1 This important
work, which should be digested by all students, is a brave
attempt to give a logical and consistent explanation of all types
of modern compositional procedure, and even if, as we shall
see later, the attempt cannot be said to be entirely successful,
it was certainly worth making. The problem which Hindemith
attempts to solve, as will be clear to all who have followed me
so far, is that of the free use of all the twelve notes of the chro-
matic scale within a tonal framework. We have seen how this
problem arises in the case of Bart6k, and how difficult it is to
give any real theoretical explanation of his procedures; but
Hindemith felt that some explanation of this type of chromatic
writing must be possible, and he set himself to find one. He
started, naturally enough, from the harmonic series, and
attempted to find the order and degree of relationships of each
note in the chromatic scale to a central keynote (hi this case, let
us say C). He takes the first six overtones of the harmonic scale:
Ex.49
320
-e- 2 3 4 5*
(The overtone numbers are given below the notes, the vibration
numbers above). By means of a somewhat mathematical, but
quite logical process of dividing the vibration numbers by the
overtone numbers of the preceding notes in the series, he
arrives at the following table:
i Hindemith. The Craft of Musical Composition. Schott, London, 1942.
55
56 TWENTIETH CENTURY COUNTERPOINT
Ex. 50
(The whole passage (op. cit. pp. 32-43) is worth studying in.
detail as an example of Hindemith's analytical method; see
also his table opposite p. 48). It will be seen that this series
(which Hindemith calk "Series i") contains all the twelve
notes of the chromatic scale; the further a note is to the right
of this series the less strong is its relationship to the keynote G.
It should be made clear at once that this is neither a scale nor a
Schoenbergian note-series (see next chapter); it is simply a
table of the relative order of relationships between a keynote
and the remaining notes in the chromatic scale, and it does
not show the relationship of these notes to each other.
This latter relationship is shown in Hindemith's Series 2,
which is also derived by him in a somewhat complicated way,
in this case from the differential notes. These notes (which
Hindemith, by the way, calls "Combination tones 55 ) I have
throughout used the English "note" rather than the American
or German "tone" in quotations, except in the case of "twelve-
tone composition" 3 which has now become a recognised
formula are produced, as "Grove" says, "when any two
loud and sustained musical sounds are heard at the same time.
The differential note is so called because its number of
vibrations is equal to the difference between those of the
generating sounds". (See article, "Resultant Tones", in
Grove's Dictionary, where the matter is more fully discussed).
A further differential note is also produced between the
original differential note and one of the directly sounded
notes; Hindemith calls these "combination tones of the second
order". (See op. cit. pp. 5?ff). By using these two series of
differential notes he is able to evolve a second table which
shows the relative harmonic value of the various intervals;
he calls this "Series 2".
HINDEMITH AND DIATONICISED CHROMATICISM 57
The intervals in this table become "less pure", as Hindemith
puts it, as we move from left to right. Hindemith shows that
these intervals are invertible (still by using the differential
notes), and is also able to determine the root of each interval
(shown by arrows in the table above) from them. But in the
cases of the minor third and major and minor seconds (and
their inversions) he admits that his decision as to which note is
to be regarded as the root is based more on past compositional
practice than on any theoretical justification derived from the
differential notes. The tritone, he says, has no theoretical
root; but for practical purposes he regards the note in it which
proceeds by the shortest step to the root of the chord on which
it resolves as the "root representative**. It should be noted in
the whole discussion of the table above that Hindemith does
not refer to "consonant" or "dissonant" intervals; he is in fact
following the practice of most modern composers in regarding
this distinction as no longer valid, in view of the collapse of the
diatonic system in its old form.
The above discussion may appear to be primarily of
harmonic, rather than contrapuntal interest; but as harmony
and counterpoint even today remain the two sides of the same
medal, it will be necessary to consider Hindemith's remarks
on harmony a little further before we can discuss his approach
to contrapuntal writing. He first discusses his Series 2 from both
the harmonic and the melodic point of view; "harmonic force",
he says, "is strongest in the intervals at the beginning of the
series, and diminishes towards the end, while melodic force is
distributed in just the opposite order (pp. 88-9) .... The
tritone has no definite significance, either harmonic or
melodic"; it needs a third note added in order to determine its
position, Hindemith next attacks the traditional theory of
harmony, on four grounds :
(i) The old theory that chords are constructed by the super-
imposition of thirds cannot explain many chords, e.g. those
based entirely on fourths,
(ii) Chords cannot now be considered invertible, as this would
often completely alter their character,
(iii) The conception of "altered chords" is out of date now that
harmony is chromatic and no longer related to a diatonic
system.
58 TWENTIETH CENTURY COUNTERPOINT
(iv) The same chord could bear various interpretations in the
old system according to the key it was related to; it is
illogical to continue this practice.
As we shall see, it is by no means certain that Hindemith is
right in all these strictures, particularly as regards point (ii);
but they do give him a working basis on which to build up a
new system of chords which includes all possible formations.
The question then arises of estimating the relative harmonic
value of these chords; and as a chord may contain several
different intervals, Hindemith states that the harmonic value
is determined by the 'best' interval in it, i.e. the one furthest to
the left in Series 2. In the same way the root can be found.
Ex.52
In the first chord the 'best' interval is the perfect fifth A-E, and
its root A is therefore the root of the whole chord. Similarly,
says Hindemith, in the second chord the 'best* interval is the
perfect fifth C-G, and its root G is therefore the root of the
whole chord. Traditional harmony would probably agree with
Hindemith in his analysis of the first chord, regarding it as an
A major chord with major seventh + an A minor chord
(first inversion) with added sixth. (An alternative, though not
so satisfactory explanation, would be to regard it as a 4/3 chord
with F as the root, with added sixth (Db for C#) and minor
third (Ab for G#) as well as major third; but the doubling of
the 7th (E) is against this) . But on the second chord traditional
harmony would undoubtedly disagree with Hindemith, and
I think rightly; it is surely more logical to take the other perfect
fifth A E as tie fundamental interval, and to regard the whole
as an A major-minor chord with flattened seventh and added
sixth. (The student may try these chords for himself, putting
under them in turn the alternative roots suggested, and make
his own decision). This illustrates the danger of adopting a
purely mathematical system of harmonic analysis; Hindemith
attacks the "Procrustean bed" of the traditional inversion
system, but his own system can be equally Procrustean.
HINDEMITH AND DIATONICISED CHROMATICISM 59
I have devoted some space to this discussion of Hindemith's
harmonic theories, as it is essential to understand them before
approaching his method of contrapuntal analysis. He begins
this with his theory of the "two-voice framework, constructed
by the bass voice and the most important of the upper voices'*.
He regards the bass part as the most decisive for the develop-
ment of the harmony; the next most important line may be
entrusted to any one of the upper parts, or may move about
from part to part. If either of the outside parts has a long holding
note or pedal point, then the next part below or above it
becomes the upper or lower member of the framework. Hinde-
mith next tackles the question of chord progressions in some
detail, observing (c Series 2, p. 56) that as the harmonic
tension of chords increases, their harmonic value decreases;
this "up-and-down change of values and tensions" he calls
"harmonic fluctuation". By means of the methods set out above
he is able to determine the relative degree of harmonic value
and harmonic tension of all chords in any given progression.
For this purpose he divides all chords into two groups, those
without and those containing a tritone; each group is again
subdivided into three (see table at the end of Hindemith's
book).
The (condensed) groupings are as follows;
A. Without Tritone
I Without seconds or sevenths
1 . Root & bass note identical
2. Root lies above bass note.
(i.e. major & minor triads & their
inversions)
HI With seconds or sevenths or
both
1 . Root & bass note identical
2. Root lies above bass note
V Indeterminate
(Chords built of major srds or 4ths
only)
II
B. Containing Tritone
Without minor 2nds or major
yths.
Minor yth only; root & bass
note identical
(i.e. "dominant sevenths")
With major ands or minor yths
or both
Root & bass note identical
Root lies above bass note
With more than one tritone
IV With minor ands or major 7ths
or both
1 . Root & bass note identical
2. Root lies above bass note
VI Indetenninate
(Chords built of minor 3rds only)
60 TWENTIETH CENTURY COUNTERPOINT
Hindemith then proceeds to work out the relative value of
root-progressions in some detail, basing his method on his
Series i. From this, by taking the 'best' interval (see Series 2)
in the succession of roots, he is able to determine the tonic of
any progression. Chords containing a tritone, he says, tend to
resolve on to chords which do not contain one; and the root of
the chord of resolution is the tonic in this case. In progressions
where all chords contain a tritone, (and therefore none are
resolved) the tonal centre of the progression is to be regarded
as the dominant of a tonic lying below it. (op. cit. p. 136, Ex. 97).
Hindemith next gives rules for these successions of roots, or
"degree-progressions" as he calls them; he regards as detri-
mental to them "the absence over a long period of the strongest
intervals, the fourth and fifth; the melodic interval of the
tritone; broken chords of any easily recognised species, except
major and minor triads; chromatic progressions, i.e. too many
minor seconds close together; and explicitly melodic treatment,
i.e. the use of passing notes, anticipations etc." The presence of
modulation can also be established from these root-progressions:
(op. cit. p. 151, Ex. 116).
Further, the different tonalities through which a piece moves
themselves form a succession of roots which shows the con-
struction of the piece as a whole; and the tonal centre of this
secondary root-succession is thus the tonic of the whole piece.
We shall see shortly how Hindemith applies this method to the
analysis of both classical and modern works, including even
twelve-tone music.
Hindemith next delivers an attack on atonality and poly-
tonality. "Tonality", he says, "is a natural force, like gravity."
. . . There are but two kinds of music; good music, in which the
tonal relations are handled intelligently and skilfiilly, and bad
music, which disregards them and consequently mixes them
in an aimless fashion". He says, however, that there are two
types of music, "which, although they cannot be called atonal,
yet by the accumulation of harmonic means of expression place
too great a burden on the listening ear for it to be able to follow
them completely." One of these is based on "a multitude of
dominant relations, alterations and enharmonic changes"; the
other makes a continuous use of chords based on seconds and
sevenths, and "produces an opaque kind of harmony which in
HINDEMITH AND DIATONICISED CHROMATICISM 6l
its avoidance of any chord resembling a triad seems to fly in the
face of Nature. Neither of these types can be made reasonable
by the logic of its degree-progression; both are too crowded
with material to be enjoyed." He goes on: "there are today a
considerable number of composers who issue works that they
call atonal. To what extent the atonality of these compositions
rests upon the lack of a convincing degree-progression and to
what extent it is a more or less developed tonality concealed
by an uninterrupted succession of sharp sonorities, the reader
himself can determine by extracting the degree-progressions
of such pieces." Thus Hindemith would appear to say that,
according to his method of analysis, any music in which the
tonal implications are not clear is badly constructed; i.e. he is
not prepared to extend his system in order to cover all the
elements actually manifested in contemporary music though
his system in itself is certainly capable of such extension. This
strikes me as unnecessary prejudice; surely all that one wants
to do is to examine all contemporary phenomena and if possible
find an explanation for them, rather than exclude or dismiss
them if they do not happen to fit well into a preconceived
scheme. It is quite probable, as we shall see in due course, that
twelve-tone music does often exhibit a "developed tonality",
as Hindemith calls it in fact, Hindemith himself finds con-
siderable elements of tonality in Schoenberg's Piano Piece,
Op. 33a (cf. p. 67). I do not therefore feel that Hindemith is
justified in saying "the existence of this style seems to me only
to lend final confirmation to the fact, everywhere to be observed,
of the disappearance of understanding judgment and critical
sense in the field of music." On the other hand, in his discussion
of polytonality, he says quite rightly (as we have seen in
Chapter IV) : "the game of letting two or more tonalities run
along side by side and so achieving new harmonic effects is, to
be sure, very entertaining for the composer, but the listener
cannot follow the separate tonalities, for he relates every
simultaneous combination of sounds to a root and thus we
see the futility of the game Since organic work, growing
out of natural roots, will always stand on a firmer basis than the
arbitrary combination of different elements, polytonality is not
a practical principle of composition."
Hindemith now takes a practical example in order to show
62 TWENTIETH CENTURY COUNTERPOINT
the method of working of his system. Though this concerns a
purely chordal progression, it will be useful to follow it in
detail, as it exemplifies Hindemith's contrapuntal as well as
his harmonic approach. He takes the following progression:
Ex.53
(I have somewhat simplified Huidemith's analytical table from
the original, omitting certain points of purely harmonic
interest). Hindemith says that this progression "sounds
horrible", and sets out to offer criticisms and improvements.
He finds the linear construction poor, except for the top part
but one; he says there is no plan in the two-part framework,
and that "the weak fourth G-C in the fifth chord flatly contra-
dicts the intention to make this the harmonic climax". He
regards the harmonic fluctuation as an "aimless zigzag"; he
arrives at this conclusion from his own method of grouping of
chords, (cf. p. 59). As regards the succession of roots, he says
"the combination of chords from the fourth to the eighth
chord does not allow any harmonic life to unfold, while a
further brake is provided by the repeated Eb of the sixth and
seventh chords." Personally I should be inclined to disagree
with some of his diagnoses of the roots of these chords, and in
Chapter IX (p. isGff.) some alternative suggestions will be
found; these would appear to fit better with the principles of
traditional harmony, which (as I suggest there) can still be ex-
tended to cover more recent developments. The tonality he
regards as G$ (Ab), which appears twice, and is confirmed by the
repeated fifth E|? and the leading note G, as well as the minor
HINDEMITH AND DIATONICISED CHROMATICISM 63
third B; but a case could be made out for the first four chords
being in A, he says.
After some discussion (pp. 160-3) Hindemith produces an
"improved" version of this progression, as follows:
Ex.54
Personally I cannot see that this is any improvement; admit-
tedly the chords increase in harmonic tension towards the
middle according to HindemitKs chord-table (p. 59) and then
decrease again; but do they do so in actual sound? Here again
Hindemith's root-diagnosis is open to question: surely the roots
of chords 7 and 8 are E and F# respectively. And I cannot see
any objection to the original chord 5 (without tritone) coming
after a series of chords containing tritones; to my mind it
provides a welcome contrast and does actually produce the
harmonic climax which the composer intended. It would appear
that Hindemith, having worked out a methodical scheme for
grouping chords, insists that music can only be good if it
complies with this scheme; i.e. he is working a priori instead of
a posteriori. Surely if any such scheme is to have universal
validity it must take into account all possibilities of expression;
we are in fact back again at the old idea of the Procrustean
bed.
However, it is clear that Hindemith's methods of analysis
contain the elements of something which might well be
developed into a universally applicable scheme, and it is worth
pursuing his exposition of them to its conclusion. After a short
chapter on inessential notes (changing notes, passing notes,
suspensions, anticipations, etc.) in which Hindemith more or
less agrees with the classical method of treatment of these, he
proceeds to discuss melody. In listening to a melody, he says,
the ear always seeks triad formations; hence it is always
64 TWENTIETH CENTURY COUNTERPOINT
possible to establish the "degree-progression" (root-succession)
of any given melody (p. 185, Ex. I56) 1 .
The root-succession of a melody follows the same rules as the
root-successions of chorda! progressions: but is of course, quite
independent of the main root-succession upon which the joint
harmony of the several voices of a piece rests. In a piece made
up of several simultaneous melodic parts, as many root-
successions are possible as there are parts, and these may all
be independent of one another. On the other hand the root-
succession of the melody may fully coincide with that of the
general harmony.
Hindemith then discusses in detail (pp. 187-193) the inter-
relation of the various major and minor seconds within the
compass of a fifth an important passage which I have not
space to give in detail here, but which the student should read
for himself. He calls seconds "the real building units of melody";
they act as the measuring units and content of the briefest
melodic sections, and also as regulators of the larger melodic
connections. "A rising interval creates tension and a falling
interval resolves it", he goes on. But if a rising or falling interval
takes place between two members of the same chord, there is
no feeling of either rising or falling tension. Hindemith then
analyses the falling intervals in detail, remarking that "to know
the effect of the rising ones, we need only change the minus
sign in our result to a plus sign". Next Hindemith discusses
"step-progression" in melody; as opposed to the roots of the
chorda! groups which form the "degree-progression" of a
melody, "more important are those notes which are placed at
important positions in the two-dimensional structure of the
melody: the highest notes, the lowest notes, and notes that
stand out particularly because of their metric position or for
other reasons. The primary law of melodic construction is that
a smooth and convincing melodic outline is achieved only
when these important points form, a progression in seconds.
The line that connects one high point to the next, one low
point to the next, and one rhythmically prominent note to the
ir The page- and example-references in the remainder of this chapter apply
(unless otherwise stated.) to Hindemith's book; unfortunately it has not been
possible to obtain permission to reproduce more than the handful of examples
quoted above.
HINDEMITH AND DIATONICISED CHROMATICISM 65
next, without taking into consideration the less important parts
of the melody lying between these points, is called the step-
progression" (p. 194, Ex. 174).
In simple melodies like the above, "the step-progression consists
of a single succession of upward and downward steps of major
and minor seconds"; but in more complicated melodies there
may be many more step-progressions going on simultaneously.
The notes forming a step-progression are sometimes in direct
succession and sometimes widely separated (p. 195, Ex. 176).
Further points are that sevenths and ninths can take the place
of seconds in step-progressions (cf. the methods of the twelve-
tone technique, discussed in the next chapter) : a melody may
move quickly from one register to another by means of a
broken chord and not by seconds: and "the prominent notes
of a melody may not belong to either a chord or a step-pro-
gression, when the need for intense expression requires that the
attention shall be riveted by the conspicuous strangeness of
such notes" (p. 196, Ex. 179).
Clearly step-progressions may conflict with the root-progressions
of a melody or the former may be completely subservient
to the latter. But in most modern melodies it is the conflict
which is more apparent.
It is clear that Hindemith's schemes of root- or degree-
progression and step-progression do provide a useful basis for
the analysis of melodies of all types. How far they can be applied
in the exact way that Hindemith uses them must be left for
discussion later; but it is at any rate something to have a point
of departure. Hindemith concludes his discussion of melody
by talking firstly of those themes in which the root-progression
is satisfying but the step-progression is faulty (and he quotes a
motive from D' Albert's Tiefland) : "such melodies give no more
than a certain pleasant impression". On the other hand
melodies which "strive for the most definitely linear character,
may have a well worked-out step-progression and a poor root-
progression. Such melodies make the listener restless, since he
can follow the vague harmonic connections only with
difficulty." This latter type of melody of course brings us close
to the central problem of modern composition the recon-
ciliation of its linear and harmonic aspects. We shall be able to
66 TWENTIETH CENTURY COUNTERPOINT
return to this problem in our discussion of twelve-tone music
and afterwards. Hindemith finds the perfect balance between
the two elements, root- and step-progression, in the main
theme of the Andante of Beethoven's Fifth Symphony. He ends
by quoting a melody of which he finds the root-progression
unsatisfactory and the step-progression insufficiently developed:
(p. 199, Ex. 182).
For this he produces an "improved" root-progression, and
inserts further step-progressions (p. 200, Ex. 184).
I think it cannot be denied that this second melody has a better
shape, and that therefore to this extent Hindemith's methods
are justified; but it remains to be seen how far they can be
applied to more chromatic themes.
The final section of Hindemith's book consists of a number
of analyses, carried out according to all the principles
enunciated up to now, of passages from various classical and
modern works. The student is recommended to study the
analyses of the "Dies Irae", Guillaume de Machaut, Bach,
Wagner (the "Tristan" Prelude), and the opening of Stravin-
sky's Piano Sonata. All that I have space to discuss here are
the analyses of passages from Schoenberg's Piano Piece Op.
33a and Hindemith's own "Mathis der Maler". (Concert of
Angels, Allegro, bars 1-16).
We will take the Hindemith example first, as it presents fewer
problems. The composer remarks: "the strongly chordal design
of the degree-progression is based upon the effort to organize
chord-groups as closely as possible around a tonal centre, while
leaving the greatest freedom to the individual parts. The fact
that the notes of the degree-progression in bars 9-13 form a
broken chord of group VI* results in a gentle but very noticeable
cadencing towards the B of bars 13-16. The tonal scheme shows
the same effort. Here, too, a large group of tonal centres is
chordally related, so that great activity of details takes place
against a smooth and gently restful background." Of the three
pedal points in the passage, the first and last are disregarded in
the harmonic analysis; the second (bars 9-12) is reckoned in.
With the aid of the examples given earlier, the student should
find no difficulty in following Hindemith's analysis; he should
note how the degree-progression of the upper part sometimes
*Cf. table on page 59.
HINDEMITH AND DIATONICISED CHROMATICISM 67
varies from and sometimes coincides with the degree-progression
of the passage as a whole.
With the Schoenberg example we reach more debatable
ground. Hindemith gives a purely harmonic analysis; but it is
worth discussing, as the fundamental problem of tonality is
bound up with it. By his own methods Hindemith arrives at a
somewhat complicated system of root-progressions, but I fear
that I must disagree with his analysis to some extent. One
can, I think, adopt Hindemith's rule that chords containing
tritones are normally felt as dominants of tonics a fifth below
(cf. p. 60). Now the root notes of the two chords which
alternate in the bass part of bar 19 are clearly B and C; we
can therefore regard the B as an augmented fourth in F leading
on to the dominant, G; and the bar is therefore in F. Further,
the passage which begins at the end of bar 19 and continues
through bar 20 has a bass part centring round D, the dominant
of G, which is therefore the tonality of the passage. Bars 21-22
begin as if on the dominant of F; but the presence in the bass
part of F, Bfc] (=Cb) and Bb show that the passage is really
based on the dominant of Bb. For the remainder of the passage
my analysis corresponds more closely to Hindemith's in that the
main tonalities are Db (C#) and Gb (F#), but there is also a
clear movement towards the dominant of D at the end of the
quotation. I would therefore prefer to suggest the following
analysis for the whole passage:
Ex.55
68 TWENTIETH CENTURY COUNTERPOINT
HINDEMITH AND DIATONICISED CHROMATICISM 69
It is of course obvious that Schoenberg would have objected
to both Hindemith's and my analysis, in that this piece was
written purely according to the rules of twelve-tone composition
and without any regard for tonality; but it is, I think, still
possible to relate a good deal of twelve-tone music to a tonal
basis, and I believe that that is what the listener's ear actually
does in practice; i.e. instead of "atonality" we have constantly
modulating tonality. I hope to discuss this concept (and also
the method of chordal analysis employed above) in a later
chapter (cf. p. 136 ff.).
Before proceeding to discuss twelve-tone music in detail,
let us sum up what we have learned from Hindemith's theories.
It is clear that he has been at great pains to build up a system
of both harmonic and melodic analysis which will if possible
explain all modern developments and will provide technical,
apart from artistic, standards by which a composer can judge
his own and others' works. Where it appears to go wrong is in
dealing with more advanced chromatic music; here Hinde-
mith's system of root-diagnosis leads him to conclusions which
do not correspond with reality and the fact that he finds
difficulty in analysing music of this kind tends to make him
diminish its artistic value. The fact that such music uses chords
which are low down in Hindemith's table of harmonic values
does not necessarily make it bad music. For the present then
we may in principle accept Hindemith's system of analysis as
valid for music of a more or less diatonic type (such as his own,
or that of Stravinsky and the later Milhaud, for instance), but
we must make some reservations when it comes to discussing
more chromatic music, and will try in due course to see if a
better solution can be found. Nevertheless every musician
must be grateful to Hindemith for having tried to tackle these
problems at all; and he has certainly put forward some valuable
ideas which may well serve as stepping-stones for the future.
I do not propose to suggest any exercises in Hindemith's
style to the student, as Hindemith himself has published a
volume of "Exercises in Two-Part Writing" (Schott, London,
1948), which is to be followed by further exercises in three-part
writing. The exercises so far given are mainly diatonic in
character. In addition, in the German edition of his composition
treatise, Hindemith gives a list (for some reason not included in
7O TWENTIETH CENTURY COUNTERPOINT
the English edition) of various works of his own which particu-
larly exemplify his principles. Of these I quote the following
(all published by Schott & Go.) :
String Quartet No. 3, Op. 22 (1922)
Kleine Kammermusik, Op. 24 2 (1922)
Concert Music for viola & chamber orchestra, Op. 48 (1930)
Concert Music for piano, brass and harps, Op. 49 (1931)
Concert Music for strings and wind, Op. 50 (1931)
Das Unaufhorliche, Oratorio (1931)
Philharmonic Concerto (1932)
String Trio No. 2 (i933)
Symphony, Mathis der Maler (1934)
Mathis der Maler, Opera (1934)
Der Schwanendreher, for viola and small orchestra (1935).
Since then Hindemith has of course published a number of
important works, including three more string quartets; but
perhaps the most useful for our purpose is the "Ludus Tonalis"
for piano (1943). This is sub-titled "Studies in Counterpoint,
Tonal Organisation and Piano Playing" and consists of a
Praeludium, 12 Fugues in all the keys (alternating with n
Intermezzi), and a Postludium, which is the Praeludium
played backwards and upside-down. Incidentally the order of
keys of the Fugues is that of Hindemith's Series i (Ex. 50).
The \vhole collection should be studied as a compendium of
Hindemith's contrapuntal technique.
CHAPTER VII
SGHOENBERG AND
TWELVE-TONE COMPOSITION
WE may now return to Schoenberg at the point where we left
him in Chapter II that is to say in 1908, the year in which he
composed his first "atonal" pieces. So much has been written
both for and against "atonal" and "twelve-tone" music no
other methods of writing seem to have aroused so much
discussion in this century that I think it best to try to clear
the fog of controversy aroused by Schoenberg's more doctrinaire
supporters and opponents by seeing what Schoenberg himself
had to say on the subject. This information is contained in a
lecture, "Composition with Twelve Tones", delivered at the
University of California on March 26, 1941, and published in
Schoenberg's collection of essays, "Style and Idea'*. Study of
this is essential for anyone who wants to understand Schoen-
berg's methods.
Schoenberg begins with a short preamble, in which he says
"Formjn ^^artSa^^and^^pecially in music, aims primarily at
coinprehe^biHtyJ': and that alone isTthe aim of composition
wifH twelve tones, surprising though this may seem in view of
the lack of understanding shown to works written in this style.
He then traces the development of chromatic harmony (cf.
Chapter II); tonality gradually developed into what he calls
"extended tonality", and simultaneously there arose the
"emancipation of the dissonance." The ear had gradually
become acquainted with a great number of dissonances, and
so had lost the fear of their "sense-interrupting effect". One no
longer expected preparations of Wagner's dissonances or
resolutions of Strauss' discords; one was not disturbed by
Debussy's non-fdnctional harmonies, or by the harsh counter-
point of later composers. This state of affairs led to a freer use
of dissonances, comparable to classical composers* treatment
of diminished seventh chords, which could precede and follow
7*
72 TWENTIETH CENTURY COUNTERPOINT
any other harmony, consonant or dissonant, as if there were no
dissonance at all. Schoenberg goes on to say that discords are
distinguished from concords not by beauty but by compre-
hensibility. In his Harmonielehre he suggested that the ear was less
intimately acquainted with dissonant notes than with consonant
ones because the former appeared later in the harmonic series;
but "this phenomenon does not justify such sharply contra-
dictory terms as concord and discord". (Cf. Hindemith's treat-
ment of the same problem, p. 57). Closer acquaintance with
the more remote consonances i.e. the dissonances gradually
eliminated the difficulty of comprehension, and finally admitted
not only the emancipation of dominant and other sevenths,
but also the emancipation of Wagner's, Strauss', Mussorgsky's,
Debussy's, Mahler's, Puccini's and Reger's more remote
. dissonances. 1 This meant in fact that what were formerly
regarded as discords could now be treated as freely as the
traditional concords; and, as we have seen, that is what most
modern composers do in practice.
The other, and more difficult, side of this problem is the
question of tonality. This is what Schoenberg has to say on the
subject: "Very soon it became doubtful whether [a basic note
or root] still remained the centre to which every harmony and
harmonic succession must be referred. Furthermore, it became
doubtful whether a tonic appearing at the beginning, at the end,
or at any other point really had a constructive meaning.
Richard Wagner's harmony had promoted a change in the
logical and constructive power of harmony." He then goes on
to discuss Debussy's impressionistic use of harmony (quoted
in Chapter II, p. 20), ending, as we have seen, by saying: "in
this way, tonality was already dethroned in practice, if not
in theory."
Schoenberg thus takes the opposite point of view to Hinde-
mith's statement (cf. p. 60) that "tonality is a natural force, like
gravity". Which of the two is the more justified will have to be
discussed later; but meanwhile let us follow the further develop-
ment of Schoenberg and his first pupils, Berg and Webern.
Starting from their twin conceptions of the dethronement of
tonality and the free use of the former "discords", they produced
Incidentally Janacek in his treatise on harmony also held that "the history
of harmony is, in fact, the history of the gradual tolerance of dissonances".
SCHOENBERG, TWELVE-TONE COMPOSITION 73
a series of pieces of which "the foremoot oharacteriaticB ;wgre
their extreme expressiveness and their extraordinary brevity."
This phase of development covered the years 1908-1923; that
is to say, up to the discover)- of the twelve-tone" technique.
The principal works of this period were Schoenberg's Piano
Pieces, Op. n and 19, 5 Pieces for Orchestra, Op. 16, the
dramas Erwartung and Die gliickliche Hand, and Pierrot Lawaire;
Berg's String Quartet, Op. 3, Three Pieces for Orchestra,
Op. 6 and the opera Wozzeck;\ Webern's 5 Movements and 6
Bagatelles for string quartet, Op. 5 and 9, two sets of pieces
for orchestra, Op. 6 and 10, Four Pieces for violin and piano,
Op. 7, and several collections of songs, accompanied by various
combinations of instruments. 1
Now it will be seen that nearly all these pieces are compara-
tively short, except where they are settings of literary texts;
and Schoenberg gives the reasons for this. "Formerly harmony
had served not only as a source of beauty, but, more important,
as a means of distinguishing the features of the form", e.g. the
necessity of ending a work with a concord. "Harmonic variation
could be executed intelligently and logically only with due
consideration of the fundamental meaning of the harmonies.
Fulfilment of all these functions comparable to the effect of
punctuation in the construction of sentences, of subdivision
into paragraphs, and of fusion into chapters could scarcely
be assured with chords whose constructive values had not as
yet been explored. Hence, it seemed at first impossible to
compose pieces of complicated organisation or great length."
In fact the music written by Schoenberg and his followers at
this time was primarily experimental; they had rejected the
traditional methods of manipulating the elements of music,
but had not yet found a new and sound method of organising
these elements.
Schoenberg continues: "A little later I discovered how to
construct larger forms by following a^ text or poem. The
differences in size and shape of its parts and the change in
character and mood were mirrored in the shape and size of the
composition, in its dynamics and tempo, figuration and
accentuation, instrumentation and orchestration. Thus the
1 For more detailed discussion of these works, see Ren Leibowitz, Schoenberg
and his School (Hinrichsen, London, 1954).
74 TWENTIETH CENTURY COUNTERPOINT
parts were differentiated as clearly as they had formerly been
by tHe tonal and structural functions of harmony."
Clearly music, if it was going to develop at "all, could not
continue to be merely subservient to a literary text, and
remain unable to create larger forms of its own; but before we
study the further developments which made this expansion
possible, let us consider sonic typical passages from the music
written by Schoenberg and his followers during this transitional
period. These bars are taken from the first of Schoenberg's
Three Piano Pieces, Op. 1 1 his first atonal compositions.
Ex.56
Massig
Here we have a free use of chromaticism and an avoidance
of definite tonal feeling, combined with the normal classical
devices of repetition and imitation. The first three bars do in
fact contain all the twelve notes of the chromatic scale, though
SCHOENBERG, TWELVE-TONE COMPOSITION*
75
there are some repetitions of the same note. Bars 4 6 show
another characteristic of this type of music the perpetual
shifting of the rhythmic accents; this follows the principle of
"perpetual variation" which became more and more important
to Schoenberg and his followers as time went on, leading
eventually to the complete avoidance of sequential figures and
direct repetitions of any type.
A similar preoccupation may be seen in the first of Webern's
Five Movements for String Quartet, Op. 5, written in 1909.
Ex.57
Vlni
Here again we have imitative figures combined with a perpetual
dislocation of the rhythm, while the chromatic nature of the
phrases precludes any tonal feeling.
Ex. 58
^ ^ ^ ^ i
[iJirJJlu/n'Y} f IpjqjiE
Vcl..
=**3
Piano pp
76 TWENTIETH CENTURY COUNTERPOINT
With "Pierrot Lunaire" (1912) contrapuntal problems
begin to dominate the scene. The eighth piece in it, "Nacht",
is a passacaglia, based on a three-note phrase which appears
in every conceivable form throughout it. 1 [Ex. 58, p. 75].
The whole piece is worth studying in detail as an example of
Schoenberg's methods at the time. Similarly the i7th piece,
"Parodie", begins with an imitative passage between the viola
and the speaking part, while the clarinet plays the same figure
in inversion: later the theme is heard in imitation between
speaker and piccolo, while clarinet and viola have a separate
canon by inversion.
Ex.59
tuut Win - k*ut y In form m*
The 1 8th piece "Der Mondfleck", is even more remarkable.
It consists of a double mirror canon, between piccolo and
clarinet on the one hand and violin and cello on the other;
from the middle of the tenth bar all these parts go backwards
note for note. To this is added a three-part fugato on the piano
(which does not, however, reverse) and a free voice "part.
1 Cf. Envin Stein, New Formal Principles, in "Orpheus in New Guises,"
London, 1953; also Leibowitz, Introduction L la musique de 12 sons, p. 46.
(Paris 1949).
SCHOENBERG, TWELVE-TONE COMPOSITION 77
In a slightly later work, Die Jakobsleiter, an oratorio which
Schoenberg left unfinished and unpublished at his death, we
get a premonition of twelve-tone composition. *
1 See Ren6 Leibowitz, Introduction it la musique de 12 sons, pp. 49^, for a fuUer
discussion of this passage.
TWENTIETH CENTURY COUNTERPOINT
From bar 6 onwards we have a held chord of six notes, against
which the other parts play the other six notes of the chromatic
scale, in varying orders.
Act i Scene 4 of Berg's opera Woz&ck, written between
1917 and 1921, is a Passacaglia, based on the following twelve-
note theme.
The scene consists of 21 variations, in which this theme appears
in a great diversity of shapes; but apart from the theme itself,
the general texture of the music is not based on a serial tech-
nique. In addition Berg's increasing preoccupation with formal
problems is sKbwn by the construction ol the opera as a whole.
TheTIrst act consists 6Fa~"set of pieces representing the various
characters in their relations to Wozzeck: these are a Suite, a
Rhapsody, a Military March and Cradle Song, a Passacaglia
SCHOENBERG, TWELVE-TONE COMPOSITION
79
and an Andante affettuoso, quasi Rondo. Similarly the second
act forms a Symphony in five movements a movement in
sonata form. Fantasy and Fugue, Largo, Scherzo and Rondo
con introduzione. The last act consists of six Inventions on a
theme, on a note, on a rhythm, on a chord, on a tonality
(Interlude) and on a regular rhythmical figure.
More definite steps towards twelve-tone composition may be.
found in various works of Schoenberg, Berg and Webern
written about 1923-4; these are Schoenberg's 5 Piano Pieces
Op. 23 and Serenade Op. 24, Berg's Chamber Concerto and
Webern's Canons Op. iG. 1 The first four pieces of Schoenberg's
Op. 23 are based in general on the exclusive use of certain
intervals, and there are some passages which use an actual
serial technique; tile-fifth piece is Schoenberg's first twelve-tone
work. Similarly the first half of the theme of the variations in
the Serenade consists of fourteen notes, of which eleven are
different notes; and the second half consists of the same notes
played in reverse order.
Ex. 62
Theme
Andante
Cl.
The first canon of Webern's Op. 16 also shows the use of a
serial technique which is atonal but is not based on a twelve-
note series. [Ex. 63, p. 80].
As will be seen, this is a strict canon with one part an inversion,
the voices entering at ever closer intervals towards the climax.
a fuller analysis of this tendency see Josef Rufer, Composition with
Twelve Notes, London 1954.
8o TWENTIETH CENTURY COUNTERPOINT
Ex.63
# ^ \^ 9 ~ ' " 1 - B =jSF
Alban Berg's Chamber Concerto (1923-5) also contains
elements which are characteristic of twelve-tone composition.
It is written in a complex form, which I have no space to
analyse here in detail 1 : but we may note, for instance, that the
second variation in the first movement presents the theme in
1 Sec Willi Reich, Alban Berg (Vienna 1937 English translation in preparation) ;
also The Gramophone, Dec. 1950, for a fuller analysis.
SCHOENBERG, TWELVE-TONE COMPOSITION
81
mirror form, the third in inversion and the fourth in retrograde
inversion. Similarly the second half of the slow movement is
the first half in mirror form. In addition the principal themes of
both the first two movements consist of twelve-note series:
Ex.64
<'*
while the third movement introduces no new material but consists
of a combination of the material of the first two movements.
It will be seen from the foregoing that this transitional period,
Awhile starling with a mainly harmonic revolution against older
methods of writing, became progressively more preoccupied
with contrapuntal problems. Schoenberg thus describes the
developments which led to the evolution of twelve-tone
composition: "Formerly the use of the fundamental harmony
had been theoretically regulated through recognition of the
efiects of root progressions. This practice had grown into a
subconsciously functioning sense of form which gave a real
composer an almost somnambulistic sense of security in
creating, with utmost precision, the most delicate distinctions
of formal elements The desire for a conscious control of
the new (italics mine, H.S.) means and forms will arise in every
artist's mind; and he will wish to know consciously the laws and
rules which govern the forms which he has conceived "as in a
dream" He must find, if not laws or rules, at least ways
to justify the dissonant character of these harmonies and their
successions." It should be pointed out that, as we have seen,
82 TWENTIETH CENTURY COUNTERPOINT
the works ofjSchoenberg and his followers were tending more
andlriore tcTthe equal use of all the twelve notej^oftibie scale,
often arranged in serial form; and therefore, when Schoenberg
discovered twelve-tone composition, " he was rationalising
methods that were already in practical use rather thanlmposing
a purely theoretical discipline from outside. He calls this
procedure "Method of Composing with Twelve Tones which
are related only with one another", and goes on: "This
method consists primarily of the constant and exclusive use of
a set of twelve different notes. This means, of course, that no
note is repeated within the series and that it uses all twelve
notes of the chromatic scale." Schoenberg pointk out that this
is not a "system" but only a method of working; "a method
can, but need not, be one of the consequences of a system."
Twelve-tone composition, then, is founded on a i2-note
series; Schoenberg calls it a "basic set", but it is also often
known as a "tone-row", from the German Tonreihe; for English
readers "note-series" would seem to be the most convenient
term. The series below is the basis of Schoenberg's Wind
Quintet, Op. 26:
Ex. 65
Basic Set (O) Retror*dc Set (R)
Inversion (I) Retro^tde In version (RI)
Such a series should not be regarded as a scale, though it can
act as a "substitute for some of the unifying and formative
advantages of scale and tonality." Like a scale, a series "is the
source of many figurations, parts of melodies and melodies
themselves, ascending and descending passages, and even
broken chords". Further, as will be seen later, "the association
of notes into harmonies and their successions is regulated by
the order of these notes. The series functions in the manner of
a motive". Hence a new series has to be invented for each piece;
and from it every note in the piece is derived, whether by using
SCHOENBERG, TWELVE-TONE COMPOSITION 83
it horizontally as a melody, or vertically as a chord-succession
or by a combination of both methods. No note in the series
should be emphasised at the expense of the others, as this would
create false associations of tonality; for the same reason, only
one series should be used in each piece it would also lessen the
unity to have more than one series, for obvious reasons. The
series may be used in inversion or in its mirror forms, and any
of its four forms may be transposed so as to start on any note
of the chromatic scale. 1 The ultimate principle, for Schoenberg,
is "the absolute and unitary perception of musical space/'
Much ink has been spilt on the question of whether the whole
method is a purely "abstract and mathematical cerebration,"
as some have called it; I feel that it is profitless to discuss this
until we have seen how it works in practice and what results it
can produce. All I will say now is that the method grew out of
actual compositional practice (and not vice versa) ; that it does
satisfy the principle of unity which all serious creative artists
demand; and that a number of works have been produced with
its aid which are generally acknowledged as masterpieces.
The earliest works of Schoenberg in which this method was
used were, as we have seen, the Five Pieces for piano, Op. 23,
and the Serenade, Op. 24; it appears here, however, in a some-
what rudimentary form, and for his first examples of its use
Schoenberg quotes his Wind Quintet, Op. 26, written in 1924.
[Ex. 66, p. 84].
The series (cf. Ex. 65) is here divided into two halves of six
notes each a frequent practice with Schoenberg, as wejshall.
see. The first six notes build the main theme in the upper part,
while the other six provide a chordal accompaniment; then
the position is reversed. It should be noted that pieces written
in this style normally begin with a clear and direct statement
of the series, in its original form and on its ' 'basic" degreejof
*In the musical examples in this chapter the four forms are shown as Original
(O), Inversion (I), Retrograde (R) and Retrograde Inversion (RI). Their
transpositions are indicated by numbers, as follows:
1 = Basic level
2 Semitone higher, major 7th lower
3 = Whole tone , minor 7th
4 = minor 3rd , major 6th
5= major 3rd , minor 6th
= Fourth , fifth
7 = tritone higher or lower
8 = fifth higher, fourth lower
9 =B Minor 6th , major 3rd
10 SB Major 6th , minor 3rd
n= Minor 7th , whole tone
12 Major 7th , semitone
Thus RI 9 =Retrograde Inversion a minor 6th higher than the basic level.
84 TWENTIETH CENTURY COUNTERPOINT
Ex.66 , 2 3 ^ s
the scale; further that the notes in the series may appear jln any
octave (c Hindemith's methods, p. 65) ; but octave doublings
are normally" avoided, though, as we shall see", there _. are
exceptions to this rule.
The next example, taken from the last movement of the same
work, shows, as Schoenberg says, that the same series" of notes
"ca*n produce different themes, different characters."
Ex.67
0.1
*7_ 8 9 M i|
In the top part we have the original series on its basic degree;
the lower parts begin with the inversion on its basic degree
and continue with the inversion transposed a fifth down. On
other occasions the main theme of this Rondo uses the notes
of its retrograde or retrograde inversion, but by maintaining
its original rhythm is still easily recognisable (see Style and
Idea, p. 121).
SCHOENBERG, TWELVE-TONE COMPOSITION 85
A more complicated procedure is shown in the following
example:
Ex/68
Ex.69
,iE^Q~
1
86
TWENTIETH CENTURY COUNTERPOINT
This is based on the retrograde, transposed a tone down, and
repeated three times. The bassoon has three-note phrases, while
the accompaniment uses groups of six notes, so that the series
overlap the phrases, giving adequate variety; yet there is a
definite plan throughout.
A simple example of two-part writing comes from the
Andante of the same work: [Ex. 69, p. 85],
Here the basic series is split up between horn and bassoon in
such a way as to give a definitely contrapuntal effect.
In another example, from the Scherzo of the same work,
we have a further method of using the basic series. The accom-
paniment plays the first three notes of the series; the main theme
enters with the fourth note. The accompaniment then continues
with the notes of the series, but never at the same time as the
theme.
Ex. 70
SCHOENBERG, TWELVE-TONE COMPOSITION 87
Schoenberg's final example from this work shows inversion
and retrograde inversion played against each other.
Ex. 71
8^ 7
The transposition is a major third higher than the basic degree.
The Suite, Op. 25, for piano is based on the following series:
Ex. 72
0.71 (transposed a* diminished 5th.}
0.1-
1.7. (transposed A. diminished 5th.)
88
TWENTIETH CENTURY COUNTERPOINT
This is divided here into three four-note groups, as opposed to
two of six notes (in the previous work) . In the Praeludium we
have the basic series in the right hand combined with its
transposition a diminished fifth away:
Ex.73
In the Gavotte the third group (notes 9-12) appears before the
second (notes 5-8).
Ex.74
Schoenberg justifies this on two grounds: (i) as the Gavotte
is the second movement of the Suite, the series has become
familiar by now; (ii) each group is treated as an independent
unit and does not change within itself and there is a resem-
blance between the first and second groups in that the interval
between the last two notes of each is a diminished fifth. A
similar procedure is followed in the Intermezzo, in which
group s and 3 overlap. The Menuet begins with the fifth note
(Group 2), Group i entering later.
SGHOENBERG, TWELVE-TONE COMPOSITION 89
Ex.75
Schoenberg's final examples are taken from his Variations for
Orchestra, Op. 31, one of the finest works of his maturity. He
prefaces his remarks by saying that in orchestral writing "many
composers can manage with a small number of parts by
doubling them in many instruments or in octaves, by breaking
and doubling the harmony in many ways sometimes thereby
obscuring the presence of a content, sometimes making Its
absence clear." He is against the use of colour purely for its own
sake a preferring * c to be coldly convinced by ihe transparency
of clear-cut ideas." And he recommends the avoidance of octave
doublings, though (as we shall see) he afterwards somewhat
changed his standpoint on this subject. In order to facilitate this,
the first six notes of the basic series, together with their inversion
starting a minor third below, make up the twelve notes .of the
chromatic scale.
Ex.76
J
"
IA
M
3^
' T jj*'^
(tfansp 4, third
of I)
M
9O TWENTIETH CENTURY COUNTERPOINT
The theme (basic series) is announced against chords con-
structed from this transposition of the inversion.
53
It is followed by (a) retrograde inversion at this transposition
(b) retrograde original (c) inversion, transposed as above,
thus completing the four forms. Similarly the accompaniment
to ^ each phrase is derived from a different form of the
series.
In the first variation Schoenberg uses additional trans-
positions of the original and inversion to obtain parallel thirds
and sixths.
SCHOENBERG, TWELVE-TONE COMPOSITION 9!
Ex.78
In variation 5 six independent parts are derived from, one
transposition of the inversion.
Ex.79
92 TWENTIETH CENTURY COUNTERPOINT
In Variation 6 inversion and original are set against each
other in two-part canonic imitation.
Ex. 80
IT.
3S
Oio
&
k+ -* ***
In this bar from the Finale the upper parts consist of the first
six notes of the basic series followed by the remaining six in
retrograde order; the lower parts are derived from the inversion.
Ex. 81
0.1.
Finally Schoenberg even introduces the theme BACH as a
countermelody, taking the notes from the retrograde inversion.
SCHOENBERG, TWELVE-TONE COMPOSITION 93
Ex.82
These examples may give some idea of the contrapuntal and
harmonic variety which is possible by the use of this method;
and before going on to consider some of Schoenberg's later
works, as well as those of his pupils Berg and Webern, we may
quote his concluding words on the subject. "The main advan-
tage of composing with twelve tones is its unifying effect . . . .
Prior to Richard Wagner, operas consisted almost exclusively
of independent pieces, whose mutual relation did not seem to be
a tnusical one. Personally, I refuse to believe that in the great
masterworks pieces are connected only by the superficial
coherence of the dramatic proceedings ... In music there is no
form without logic, there is no logic without unity, I believe
that when Richard Wagner introduced his Leitmotiv for
the same purpose as that for which I introduced my Basic
Series he may have said: 'Let there be unity.*"
Before discussing Schoenberg's later works, let us consider
the rather different handling of tKe twelve-toner method used
by Berg and Webern, which will further exemplify the varied
possiBiEties provided by it. Berg first used the method in his
Lyric Suite for string quartet ; 1925-6^; of its six movements,
two and two half movements axe written according to the
principles of twelve-tone composition, while the remainder
are not. Yet I defy any listener to detect any stylistic difference
between the movements, or even to tell which use the twelve-
tone method and which do not, unless he has previously been
94 TWENTIETH CENTURY COUNTERPOINT
^om^j^J^^p^jstA. the score. (The twelve-tone move-
ments' are ui fact the first, the outer sections of the third, the
middle section of the fifth, and the sixth movement). The
design of the work as a whole again shows Berg's predilection
for symmetrical arrangements; the titles of the movements are
as follows:
i. Allegretto gioviale 2. Andante amoroso
3. Allegro misterioso 4. Adagio appassionato
5. Presto delirando 6. Largo desolato
i.e. the fast movements became successively quicker, and the
slow ones slower. In addition each movement contains some
material from the preceding one, and the circle is closed by the
last movement containing a reminiscence of the first. In the
third movement, which is in the form of a Scherzo and Trio,
the Scherzo is repeated backwards note for note after the Trio,
but in a slightly shortened form. All these devices, however^
are of little importance compared to the dramatic and
emotional significance of the work, which is among Berg's
finest achievements; as the title implies, the form is lyric and
dramatic rather than symphonic, and the Suite has aptly been
called a "concealed opera". It is well worth studying in detail
(score published by Universal Edition); I will not give any
actual quotations, as Berg's individual handling of twelve-tone
composition may perhaps be more clearly seen from his opera
Lulu and his Violin Concerto. (Berg's only other twelve-tone
work, the concert aria Der Wein, though a fine work and well
worthy of study, does not raise any technical problems which
do not also apply to Lulu] .
Like Schoenberg in his opera Moses and Aaron (which
remained unfinished at the composer's death) Berg in Lulu
attacked the problem of creating a whole full-length work from
one single note-series. The dramatic structure of the work is
again built on a symmetrical basis (see Willi Reich, Alban Berg,
for an analysis of this) and just as all the other characters
revolve round the central figure of Lulu, so Berg derives from
his original series:
SCHOENBERG, TWELVE-TONE COMPOSITION 95
Ex. 83
a.-juimber of other scries which represent the various per-
$onalities of the drama. One of Lulu's themes is arrived, at by
taking in turn the upper, middle and lower notes of the four
three-note chords into which the original series can be gro'jpeH
(Ex: 83b):
Ex.84
b)
Similarly by taking ^i\ates-aX stated intervals from the original
series, we get t&is theme of "minor" character, representing
Aiwa:
Ex, 85
^
T"l *'
- J x x x 5 x x x
96 TWENTIETH CENTURY COUNTERPOINT
In the same way the pentatonic music characteristic of the
Countess Geschwitz is derived:
Ex.86
Ce.
"p
r x
and also the theme of Dr. Schoen:
Ex.87
CO (2)
AlUgro trur^ico (J 80 )
b);
SCHOENBERG, TWELVE -TONE COMPOSITION
97
It will be seen that a good many of these themes have a "tonal"
character; and in the last act Berg actually introduces a
perfectly diatonic song composed by Wedekind, the author of
the plays on which the libretto of Lulu is based. This is used as
the theme of a set of variations in an orchestral interlude:
Ex.88
This brings us back again to the question of expressing tonal
feeling within a twelve-tone framework, which, arises in an
even more acute form in Berg's last work, his Violin Concerto.
The basic series of this actually consis-s solely of major and
minor triads plus a whole-tone scale:
Ex.89
Whole- tone sca\e_
Mmo-i
Minor 1
Major
Further, in the last movement, Berg introduces the Bach
chorale "Es ist genug" as the theme of a set of variations; the
opening four notes of this chorale are the same as notes 9-12
of the basic series, and the last four notes of the chorale are
the same as the inversion of notes 8-1 1.
Ex. 90
^
98 TWENTIETH CENTURY COUNTERPOINT
The use of a "tonal" series means that a good many passages
in the work have a "classical" sound; e.g. this one from the
first movement
Ex. 91
The general tonality of the concerto wavers between B flat
and G minor, and it ends with a chord of the added sixth on
B flat; nevertheless the writing is strictly based on twelve-tone
methods, though there is some use of octave doublings.
Tonal composition is thusjclearly possible within a twelye-
tone^framewoA; TjutTis "it" desS-ableE^Schoenberg's remarks,
quoteH ea3FHer7aBbut the necessityto avoid emphasising any
one note at the expense of the others, would appear to be against
it, as well as his statement that by 1908 "tonality was already
dethroned in practice, if not in theory." On the other hand,
his standpoint appears to have undergone a slight modification
in later years, as may be seen from this appendix, dated 1946,
to his essay on "Composition with Twelve Tones". This
was published in the French magazine Polyphonic (4me Cahier,
Le Systeme Dodecaphonique, 1949); as for some reason, it is
not included in "Style and Idea" I reproduce it here in extenso.
"In the course of the last ten years, certain strict rules
concerning octave doublings and the use of certain funda-
mental chords of the older harmony have been relaxed to a
certain extent. In the first place, it became clear that such
isolated happenings were not in a position to transform the
"non-tonal" style into a tonal style. There still remain the
melodies, rhythms, characteristic phrases and other formal
elements which were born together with the style of the
emancipation of the dissonance.
"Also* if the complete avoidance of a tonal centre is found
niiMi.mrfmr i !/* ***>. <<'<> * "" . w - ^"J '
to be ccmira^ctedT^oK occasions and jin a provisional way,
SCHOENBERG, TWELVE-TONE COMPOSITION 99
such a contradiction docs not necessarily destroy the stylistic
merits of a composition.
"I must admit that Alban Berg, who was perhaps the least
orthodox of the three of us Webern, Berg and myself in his
operas mingled pieces or fragments distinctly written in a
given tonality with other pieces or fragments which were
"non-tonal". He explained this by saying that an operatic
composer, for reasons of expression and dramatic characteris-
ation, could not always renounce the contrast provided by the
change from major to minor. Though as a composer he was
right, from the point of view of theory he was wrong; I have
proved in my operas Von Heute aitf Morgen and Moses and Aaron
that every kind of expression and characterisation can be
produced in the style of the free dissonance."
This point of view explains the greater "tonal" feeling which
can be found in many of Schoenberg's later works; but before
considering these we must first discuss the use of the twelve-tone
method made by Schoenberg's other prominent pupil, Anton
Webern. Webem went in exactly the opposite direction J.
Berg; his use of this method reduces it to its simplest and
conciscst terms, and is, if anything, "purer" than that^ofjus.
master Schpenberg. We can see this already iifhis first twelve-
tone wor% the Sacred Songs Op. 17.
In the String Trio, Op. 20, we find this method used on a
larger scale and in a more complex manner: here Webern
IOO
TWENTIETH CENTURY COUNTERPOINT
returns to the classical forms, the first movement being a rondo
and the second in sonata form. But it is the Symphony, Op. ai,
which perhaps gives us the best insight into Webern's methods.
The first movement is a 4-part double canon in contrary motion,
except for the Coda, which is a 2-part canon. Here is the
opening:
It will be seen that the order of entry is basic series; inversion
a major third lower; inversion at original pitch; basic series a
major third higher. Further, as the interval between notes
SCHOENBERG, TWELVE-TONE COMPOSITION IOI
1 1 and 1 2 of the series is the same as that between notes i and
2, Webern takes the last two notes of one series as the first two
of the next and thus forges a perpetual chain of series. In
addition the notes of each series are always leaping from one
instrument to another and also from one octave to another, so
that the canon cannot be heard as a continuous line. This
texture, however, is typical of most of Webern's later works;
and his extraordinarily acute ear enabled him to make the
exact choice of octave and instrumental colour required for
each note, so that the effect in sound is ravishing.
The second movement, in the form of a theme and variations,
shows a slightly less fragmentary method of writing. The theme,
which is the inversion of the series of the first movement is
announced by the clarinet, accompanied by its own retrograde
version on harp and two horns; but as the retrograde consists
of the same intervals as the original, one can say that the theme
is in fact accompanied by itself another example of Webern's
economy of means.
Ex. 94
The variations which follow show the same contrapuntal
control; the first is a 4-part reversible double canon in contrary
motion, the second is also a canon in contrary motion, while
the fifth variation, based on repeated chords, treats the series
from the harmonic point of view. (For a fuller analysis see
102
TWENTIETH CENTURY COUNTERPOINT
Leibowitz, Introduction pp. 232-8 and Schoenberg and his School*
Webern remained faithful to the principles exposed here for
the rest of his compositions; though in his choral works, like
Das Augenlicht and the First and Second Cantatas, Op. 29 and
31, the style is often less rarefied and there is considerable use
of dramatic and emotional effect, there is the same quest for
absolute purity and transparence. Here is the first entry of the
chorus in Das Augenlicht:
Ex- 95
Sopr.
SCHOENBERG, TWELVE-TONE COMPOSITION IO3
The vocal parts form a mirror canon between sopranos and
tenors; and there is another mirror canon in the orchestra
(up to the middle of bar 13). Each of the four parts uses one
of the four different forms of the series.
Lest it be thought that Webern's later works consist of
nothing but academic contrapuntal devices, let me quote this
passage from one of his last works, the Variations for Orchestra,
Op. 30; it is the beginning of the final variation.
Ex. 96
The four-part harmony is made up of three statements of the
basic series and one of the inversion, the latter starting in the
tenor part. Such expressive passages are often to be found in
the works of Webern's final period; and the remarkable
quality of these works is their combination of extraordinary
aural beauty of sound with strict formal control. The key to
Webern's approach may perhaps be found in a letter 1 to
Willi Reich dated 23rd February, 1944 the year before
Webern's tragic and untimely death: "To quote freely from
Holderlin: To live that is to defend a form. . . . Imagine
what an impression it made on me, when this passage occurred
in the notes to Holderlin's Oedipus translation: 'Also, other
works of art lack reliability, as compared with those of the
Greeks. They have, at least up to now, been judged more by
the impression they convey than by the artistic considerations
and otter methods through which their beauty is created. 9 "
Webern was ruled throughout his life by a strong sense of
natural law; he felt that by exploring the nature of these laws
he was also aiming at the creation of beauty; i.e. beauty can
only come through the fulfilment of a natural principle.
Works which ^im solely at beauty without _any regard for
1 Quoted*5i "Tempo", London, March 1946.
IO4 TWENTIETH CENTURY COUNTERPOINT
the_means by which_ this beauty is produced tend to "lack
reliability" one only has to think of, say, Tchaikovsky to see
what he means. As a result Weberh devoted' his life to tEe
e3cpI6fafion of the " cdndTensedr" and ""concentrated "fornrj-nevery
note in his music has its own meaning, and it would be impos-
sible jto omit or alter a single one without damage. He eschewed
works of long^duration his longest atonal work, "tEe Secpn5
Cantata, Op. 31, is in six moyements and lasts for 15 minutes,.
Nevertheless Webern can say more in two minutes than most
other composers in ten; his method of approach is entirely
different to theirs. No wonder then that his music has either
met with complete incomprehension or has been wildly
acclaimed by those who have ears to hear it; by his ultra-
sensR^?Hai^uIaHon oTpe^ct^normal elements of sonority
Webern has created music quite unlike any written before.
It is interesting too that many young composers are now seeking
to adopt his methods rather than the more "normal" ones of
Schoenberg or the expressive technique of Berg; but without
Webern's aural acuteness his technique is not easy to master
successfully, and I feel personally that history will regard
Webern. as an isolated figure of extoordmary^ importance
rather than as the direct ancestor of a new technique of com-
position. (For a fuller discussion of Webern's work, which I Have
only been able to treat here in a very superficial manner, the
student is referred to the two books of Leibowitz previously
mentioned, especially Schoenberg and his School, which contains an
important section on Webern; I have also contributed a short
analysis of Webern's last three works (which are not discussed in
Leibowitz' books) to the Monthly Musical Record for Dec. 1946).
In 1933 Schoenberg left Berlin and settled in the United
States. Thereafter he produced a number of works, of which
the majority use twelve-tone methods, though some are
tonal in character. These latter include a Suite for strings,
written in 1934 for high school performance; a setting of the
traditional Jewish theme Kol Nidrei for reciter, chorus and
orchestra; Variations on a Recitative for organ, based on a
twelve-note theme, but treating it tonally for the .most part;
a Second Chamber Symphony, which in fact merely represents
the completion of a work begun thirty years earlier; and a set
of Variations for military band. Schoenberg explained his
SCHOENBERG, TWELVE-TONE COMPOSITION I(>5
reasons for his occasional returns to a tonal style in a short
essay, On Rsment Toujours, published in "Style and Idea".
He felt that just as the classical composers from Haydn to
Wagner often felt the need to interpolate strict counterpoint
into their own essentially homophonic style, perhaps because
they considered the art of their predecessors superior to their
own, so he himself sometimes felt the longing once again to
try to achieve, in the older style, what he was sure of being able
to produce in his own style. There is thus no question of
Schoenberg definitely "returning to tonality" in these works;
they were written because as he says, "a longing to return to
the older style was always vigorous in me; and from time to
time I had to yield to that urge." But all the other works
written in this period are strictly dodecaphonic, including his
last composition, the Fantasy for violin and piano (1949)
apart from one exceptional work, which deserves special
consideration, the Ode to Napoleon, for speaker, string quartet
(or string orchestra) and piano.
This work is very freely derived from a note-series but its
effect is entirely "atonal", apart from its final E flat major
chord. It is based on a logical and consistent use of certain inter-
vals contained in its opening chord (F G sharp C sharp E) ;
i.e. minor second or major seventh (F-E); major third or minor
sixth (F-C#, E-G#); minor third or major sixth (F-G#,
C#-E); and fifth or fourth (C^GJ). The following extract
shows the use of these two latter intervals:
Ex.97
I* V
I06 TWENTIETH CENTURY COUNTERPOINT
Here we have fifths in the first violin and cello; parallel sixths
leaping a fourth hi the second violin and viola; and both
elements in the piano. The passage also contains all the twelve
notes of the chromatic scale. Elsewhere, in view of the fact that
the opening chord contains the constituent notes of both a
major and a minor triad, Schoenberg makes some use of
superimposed common chords, but not in a "polytonal"
manner. The whole work, which is worth studying in score 1
and is more fully discussed in Rufer, Composition with Twelve
Notes, appears to show a new kind of compositional tech-
nique which may well prove to be of historical importance;
but Schoenberg himself did not attempt to use this method
again in any other work.
Of the strictly twelve-tone works composed during this
period, the most important are the Violin Concerto, the Fourth
String Quartet, the Piano Concerto, the String Trio and the
Fantasy for violin and piano 2 . All these follow the same basic
principles that we have discussed in connection with the
Variations for Orchestra, but there are certain new elements
which are worth noting. The Violin Concerto, one of Schoen-
berg's masterpieces, uses a method which Schoenberg in-
creasingly adopted in his later years the first six notes of
the original series, together with their inversion a fifth lower,
make up the twelve notes of the chromatic scale.
Ex. 98
*M
m
J A recording is also available (Esquire and French "Classic").
*The scores of his very late choral works [Op. 50] were not available when this
book went to press.
SCHOENBERG, TWELVE-TONE COMPOSITION IO7
The opening of the work exposes these two series in succession:
Ex.99
r
p
^^ i* HVWy*** |^
^"T^ uX^> L^ | I |IM ^ ,^1
fk *
,
The bars which follow consist of the basic series in the violin
accompanied by chords derived from the inversion; then the
violin plays the inversion and the accompaniment is derived
from the basic series.
The end of the whole work introduces another point.
Ex. ioo
In spite of the "polytonal" appearance of this passage, it will
be seen that it is in fact strictly based on the inversion (Ex. 98b),
starting from both ends at once, and with a slight variation
in the order of the notes (Bb before E in the retrograde form).
The opening of the Fourth String Quartet, Op. 37, shows
io8
TWENTIETH CENTURY COUNTERPOINT
us another method of exposing the basic material. The series
is played by the first violin; it falls into four three-note groups
(a, b, c, d), which are simultaneously used as accompanying
chords.
Ex. 101
Note that the relation of the melody to its accompaniment
is logically arranged in the following manner:
Melody a b c d
Accompaniment bed cda dab abc
A similar procedure is carried on for the rest of the theme for
fuller discussion see Leibowitz, Schoenberg and his School:, also
Josef Rufer, Composition with Twelve Notes.
The Piano Concerto introduces a still more interesting
element, in that although it strictly based on twelve-tone
methods, it contain passages which have a definitely "tonal"
effect. An instance is the opening of the final Rondo. [Ex. 102,
p. 109].^
This is in fact derived from two transpositions of the original
series and two of the inversion. The right hand first plays the
first six notes of the inversion (I6 1 ) ; the left hand plays the whole
of the same series. Meanwhile the right hand plays the last
six notes of the original (Oi) in retrograde form. But the first
six notes of 16 are the same as the last six of Oi, in a slightly
different order (similarly the first six of Oi are the same as the
1 This number refers to the degree of transposition of the series; cf. p. 83.
SCHOENBERG, TWELVE-TONE COMPOSITION
Ex. 102
-*o^
last six of 16), so that Schoenberg does not use the remaining
notes of the retrograde of Oi these notes are already in the
left hand part. Instead the right hand begins 04, which is
completed by the left hand, while the left hand begins Ig,
which later crosses to the right hand. Though the whole passage
shows how a "tonal" effect (including the middle pedal on
F#) can be obtained by strictly twelve-tone means, it does not
really imply a "return to the older methods" for -here all the
twelve notes of the scale are strictly and logically used. One can
therefore conclude that while twelve-tone music need not
necessarily avoid a feeling of tonality, its principal aim is the
equilateral exposition of the twelve notes of the chromatic scale.
The same approach applies to the use of octave doublings,
which are also occasionally present in this work; cf.
Schoenberg's remarks on this subject quoted above (p. 98).
If the Piano Concerto and the Prelude to a "Genesis" Suite
( J 945) ina y k e sa ^ to COIltain certain tonal reminiscences, this
is certainly not true of the String Trio (1948), which adopts a
more "radical" style. Here Schoenberg uses the same method
as in many of his later works, of dividing the series into two
halves, each of which, together with the corresponding half
no
TWENTIETH CENTURY COUNTERPOINT
of the inversion transposed a fifth lower, makes up the twelve
notes of the chromatic scale. But he carries this process even
further by making frequent alterations in the order of the notes
within each six-note group; that is to say, that as long as all
twelve notes of the scale are exposed in close sequence (six from
the original series and six from the inversion) their actual order
is not considered so important. (For a detailed analysis see
"Music Review", Vol. XI, No. 3 August 1950).
This method again opens up new possibilities which are clearly
capable of further exploration. In "A Survivor from Warsaw"
(*947) we a g a i n have the use of a series plus its inversion a
fifth below, in this case coupled with the use within the series
of an augmented triad which can act as a "pivot chord"
between three transpositions of the series and three of the
inversion.
Ex. 103
This work (which is fully analysed in Leibowitz, Introduction
p. 322ff) is one of Schoenberg's most moving and dramatic
pieces; apart from the chorale at the end, it is chiefly built up
from small "athematic" fragments, the only motive of im-
portance being the four-note theme with which it opens.
Finally, in the Fantasy for violin and piano (1949), Schoenberg
returns to an almost classical simplicity while exploring every
possible method of variation technique. Its basic series is
mainly founded on major and minor seconds (B[j, A, C#, B,
F, G, Eb, Etl, C, D, Ab, Gb), and there is a considerable use
of sevenths and ninths. It is essentially a work for violin and
piano and not vice versa; the piano part is largely accompani-
mental.
SCHOENBERG, TWELVE-TONE COMPOSITION III
This survey of twelve-tone writing would not be complete
without some discussion of the first handbook to be published
in English on the subject. This is a short treatise called "Studies
in Counterpoint based on the Twelve-Tone Technique" by
Ernst Kfenek (published in 1940 by Schirmer, New York).
Kfenek says in his introduction: "The idea of tonality emanates
from a basically harmonic conception of music. The essentials
of tonality such as the key, the dominant-tonic function, the
tonal cadence are harmonic phenomena. In so far as atonality
depends for its organisation on motif-relationships, it apparently
brings melodic phenomena to the fore. Thus, the new idiom is
based on an essentially polyphonic conception of music, very
much related to the angle from which music was viewed in
the Middle Ages, before tonality (in our sense of the term) had
developed. Therefore it seems sound to approach atonality and
twelve-tone technique by way of counterpoint. Harmonic
facts in atonality have but a secondary significance, at least in
the present stage of atonal development." Explaining that his
book "does not pretend to sum up or codify the practice of
the twelve-note technique as it appears in the works of Schoen-
berg, his disciples Alban Berg and Anton Webern, and several
other composers", but merely "to set forth the elementary
principles of the twelve-tone technique as the author has
applied it in a number of his own works", Kfenek ends by
saying "the knowledge of strict (Palestrina) counterpoint is
recommended as prerequisite, though not indispensable.*'
Two points should be noted from this: (i) that the views
expressed in this book are Kfenek's own, and not necessarily
those of Schoenberg or any other members of his school (ii) that
Kfenek tends to discount the importance of harmony in twelve-
tone writing, though (as we shall see) he does give some rules
regarding harmonic relations. These points should be borne in
mind by any student who wishes to use this book for the purpose
of technical exercises; unfortunately Kfenek's somewhat
mathematical method of analysing twelve-tone writing tends
to give the impression that this style can be approached
a priori, without any previous knowledge of music, whereas
every pupil of Schoenberg, Berg and Webern will know that
these composers insisted on a thorough knowledge of classical
harmony and counterpoint (including both Bach's and Pales-
112 TWENTIETH CENTURY COUNTERPOINT
trina's styles) as an essential prerequisite before embarking on
twelve-tone writing. Even twelve-tone music still has its roots
in the past; and one cannot completely disregard the
importance of harmonic laws which are based on the nature
of music itself. If any note could equally well be played against
any other note, music would cease to have any meaning at all.
If the student will bear these provisos in mind, he may find
Kfenek's book useful as an exposition of twelve-tone methods.
He begins with hints on the construction of a series, recom-
mending the avoidance in it of more than two major or minor
triads formed by consecutive notes, as "incompatible with the
principles of atonality" though, as we have seen. Berg has
made use of such a series, and so have other composers. He
then gives some rules for melodic construction, remarking
quite rightly that "the protracted use of unaltered rhythmic
patterns results in a monotony less admissible in this style than
in any other idiom . . . Symmetric periods are not consistent
with the contrapuntal character of this music." The student
may profitably study this section, and decide for himself whether
or not he agrees with Kfenek's methods of melodic analysis.
The next chapter, Two-Part Writing, of course brings in
the question of harmony, and here Kf enek gives the following
rules:
1. Octaves and parallel unisons are not allowed (cf. Schoen-
berg's remarks on this, p. 89).
2. The following are consonances: Unison, minor and major
third, fifth, minor and major sixth.
3. "Mild" dissonances are major second and minor seventh.
"Sharp" dissonances are minor second and major seventh.
4. The fourth may be either consonant or dissonant, depending
on the context.
5. The tritone is neutral, as it divides the octave into two equal
parts (cf. Hindemith on this, p. 57).
"Culmination-points", he says, should be introduced "by
accelerated motion and increasing sharpness of dissonances.
Where the composition, however, tends to decrease in intensity,
a slowing-down of the motion^ milder dissonances and con-
SCHOENBERG, TWELVE-TONE COMPOSITION 113
sonances will be adequate." Personally I do not feel that it is
still necessary to divide chords into consonances and dissonances
Hindemith's table of harmonic tensions seems a more
satisfactory method of analysis (cf. p. 56) nor does Kfenek
attempt to give any explanation of harmonic progressions.
The student is, momentarily at any rate, left completely in the
air, with only the sentence quoted above to help him. And
why such coyness in the treatment of the perfect fourth?
After a discussion of two-part writing, including imitation,
which the student may find useful, Kfenek introduces the
derivative forms of the series (inversion, retrograde and
retrograde inversion), and shows various methods of handling
them; this again is worthy of study. Next comes a chapter on
three-part writing, which explores the harmonic problem
further. "Atonality", Kfenek says, "has neither rules for a
special treatment of dissonances (as in Palestrina counterpoint)
nor does it formulate a harmonic theory comparable with that
of tonality. The only characteristic of a chord that has to be
taken into consideration is the degree of tension that the chord
shows by virtue of its constituent intervals." He does not
consider it possible to form as definite a harmonic system in this
style as the rules of either strict counterpoint or tonal harmony,
"Music written in the twelve-tone technique as well as music
organized by any other principle rests, in the final analysis,
upon imagination and inspiration." But let us first follow
Krenek a little further in his harmonic analysis.
He divides three-part chords into six groups, consisting of:
1. Three consonances (e.g. perfect or augmented triad),
2. Two consonances and one mild dissonance.
3. One consonance and two mild dissonances.
4. Two consonances and one sharp dissonance.
5. One consonance, one mild and one sharp dissonance.
6. One mild and two sharp dissonances.
(In the above the intervals between all and each of the three
notes are of course reckoned in).
Chords containing perfect fourths or tritones may be
consonances or mild or sharp dissonances, depending on the
third note in the chord apart from the fourth or tritone.
114 TWENTIETH CENTURY COUNTERPOINT
E.g. a second inversion of a triad is consonant; so is a diminished
triad:
Q> Q a b a '* n^ * "*" rtfl"^B S8=
J >-ea J^ " 4- -a- -^ ^^ ^- nS 1 ^ H^
sh. m. cons. m. sh. sh. m. cons. m. sh.
The above classification may be useful as an indication of
relative harmonic tension just as Hindemith's table is; but
Kfenek quite rightly points out that different inversions of
chords in his Group 6:
Ex. 105
may produce different effects of sharpness or mildness. Similarly
the same chord in the same position may make quite different
effects through variations of dynamics and orchestration. One
only has to think of the first chord of Ex. 105 played successively
by violins, clarinets and trumpets (and, if you like, successively
increasing in loudness) to realise this.
The point about dynamics is one that has been with music
since the beginning of time; and though dynamics of course
vary the surface colour of a musical progression, they do not in
fact alter the harmonic structure. The other point, regarding
inversions, is of course more important; Hindemith, as we have
seen (p. 57) tries to disregard them altogether, but, I think,
mistakenly. It is true that in complicated chords it is not
always easy to recognise inversions as such, or even to see what
the root is the chord discussed here (Ex. iO5a) consists of
three equal intervals, and therefore it is impossible to determine
its root without the context. But I still think that it is possible
to adhere to the inversion principle in analysing at any rate
SGHOENBERG, TWELVE-TONE COMPOSITION 115
the vast majority of chords, and I hope later to give a practical
demonstration of this.
Having thus presented us with a method of chordal analysis,
Kfenek leaves us to get on with it, making only the same
remark as before (cf. p. 112) regarding the use of sharper
dissonances towards culmination, points; he does add however
that consonances "should be used with great caution, for the
same reason that excludes the use of the octave interval. It is,
however, admissible to use such consonant chords occasionally
if the context does not obtrude their latent tonal implications"
(cf. Schoenberg's remarks, p. 98). Kfenek now gives some
practical examples of three-part writing, which the student
should study for himself. He then deals with the grouping of
notes of the series so as to form chords, on the lines discussed
above (p. 1 13). He follows this with a note on the repetition of
chords; this, as we have seen, is permissible if the other parts
sound the remaining notes of the series at the same time.
Ex. 106
Next comes the question of the transpositions of the basic
series and its other forms; Kfenek recommends that these
should not be used haphazardly, but rather according to a
certain plan that emerges from definite musical purposes
(cf. the methods of Schoenberg and Webern quoted above,
pp. 89, 100, 1 06). It is obvious that endless variety is possible
from these means; and Kfenek gives further hints in his final
chapter, "Disposition of Larger Forms," though the pattern
quoted for his use of transpositions of the series in his Piano
Variations, Op. 79, would appear on the surface, at any rate,
to be mathematical rather than musicaL An Appendix deals
with symmetrical series (frequently used by Webern), all-
interval series and symmetrical all-interval series.
Il6 TWENTIETH CENTURY COUNTERPOINT
Though Kfenek's book does little more than scratch the
surface of the subject, it does provide some useful hints for
students, and I would certainly recommend its use as a text-
book for those who will approach twelve-tone writing from a
musical rather than a mathematical point of view. For this
reason I do not propose to include any exercises of my own;
but I do repeat that it is useless for a student to handle this
book unless he has a thorough grounding in classical and
romantic harmony. That is to say, he should approach twelve-
tone writing from the point of view that Schoenberg approached
it, from the development of chromatic harmony. (Schoenberg's
Theory of Harmony 1 is the best book for analysing this particular
development; but the student should also examine and analyse
the works of Liszt, Wagner and Strauss from this point of view).
He will see that a great number of chords used in twelve-tone
music are not very different from those used in chromatic
harmony, but they are used with more freedom that is to
say, with less feeling of attachment to a root. Nevertheless the
feeling of attachment still persists to a great extent, and the
listener cannot help hearing it. Instead of twelve-tone music
floating in a completely non-tonal world, it is rather modulating
rapidly from one point to another (one can hardly talk any
more of "key" in the old-fashioned sense), and the student,
with his knowledge of the tonal past, should be able to recognise
the points through which it is floating. I hope to discuss this
in a more detailed manner in a later chapter; meanwhile I
would suggest that the student should analyse for himself as
many twelve-tone works by Schoenberg, Berg and Webern
as possible, particularly those mentioned earlier in this chapter,
1 The subject is also discussed in considerable detail in Schoenberg's "Structural
Functions of Harmony" (London, 1954). In the final chapter Schoenberg makes
some illuminating remarks about tonality and harmonic analysis in twelve-
tone music. The following are significant extracts : "My school does not aim at
the establishment of a tonality, yet does not exclude it entirely. . . . Evaluation
of (quasi-) harmonic progressions in such music is obviously a necessity. . . . But
as such progressions do not derive from roots, harmony is not under discussion. . . .
(These progressions) are vertical projections of the basic set, or parts of it, and
their combination is justified by its logic. . . . There exists no definition of the
concepts of melody and melodic which is better than mere pseudo-aesthetics. . . .
One day the structural evaluation of these sounds will again be based upon their
functional potentialities. But it is improbable that the quality of sharpness or
mildness of the dissonances which in fact is nothing more than a gradation
according to lesser or greater beauty is the appropriate foundation for a
theory. . . . From such gradations one cannot deduce principles of construction."
SCHOENBERG, TWELVE-TONE COMPOSITION
and thereby gain a practical knowledge of the methods of these
great masters. It is only by studying the methods of the present
in relation to those of the past that one can acquire the
"musicality, taste and imagination" which Kfenek demands
of composers. 1
How can one then sum up the achievement of twelve-tone
music? It is clear that the "emancipation of the dissonance"
has conferred complete harmonic freedom on music, and that
it is now possible to make a free and equal use of all the twelve
notes of the chromatic scale; on the other hand the use of a
serial technique has imposed a control which prevents freedom
from becoming chaos. Further, as we have seen, this method
of control did arise out of compositional practice, and was not
imposed a priori; and it does fulfil a genuine compositional
need. On the other hand, the fact that composers have recently
felt the need to relax some of its provisions shows that it may
not remain as a permanent ideal; all revolutions begin with
rigid precepts which are later relaxed. In particular, the doubt
whether it can really be said to have abolished tonality has led
composers to experiment more and more with the introduction
of tonal elements within its framework; and further, it has not
yet produced a harmonic system to replace the one which it has
dethroned. We are back again then at the crucial question of
tonality, with the problem still unsolved; but we have travelled
a good deal further along the road, for we have found a method
of handling the chromatic scale not only systematically but
realistically in fact a method which has not yet realised its
full possibilities, and may even be only in its infancy, for all
we know. Here at least we have fertile soil; for we have a
completely new and self-contained method of writing with
unlimited capabilities, and yet containing a possibility of
ultimate reconciliation with the past. That reconciliation it is
our task to try and find./JBut before making such an attempt
we may profitably examine the contributions made by some
composers who have worked on more or less independent lines,
and have on the whole not been greatly affected by the various
methods so far discussed.
further valuable information on Schoenberg*s methods and aims will be found
in Josef Rufer's Composition with Twelve Notes (London, 1954)? &** k 00 ^
appeared too late to be discussed in this chapter. It contains some suggestions
for exercises to be worked. .
I
CHAPTER VIII
SOME INDEPENDENTS
FERRUCGIO BUSONI (1866-1924) might alraost be regarded as
the prototype of an independent composer. Of mixed Italian
and Austrian parentage, he spent a good deal of his life touring
the world as a concert pianist; a man of restless and enquiring
mind, he absorbed influences from many directions Bach,
Liszt and the Italian operatic tradition being prominent among
these and synthesised them in a number of compositions of
great originality. In his "Sketch of a New Esthetic of Music",
published in 1907, he clearly pointed out the shortcomings of
the traditional diatonic system; what is the point of
transpositions, he asked, when a piece sounds exactly the same
when transposed into another key "when a well-known face
looks out of a window, it matters not whether it gazes down from
the first storey or the third". And how can one divide con-
sonances from dissonances, when we have an octave composed
of twelve equal intervals? He worked out 113 different seven-
note scales within the compass of an octave, and also examined
the possibilities of using thirds and sixths of a tone. (The whole
of this little book, though it does not claim to lay down any
formal principles, is full of stimulating remarks, and is well
worth reading) .
In his compositions Busoni, though using the background of
the diatonic system, made within it a free use of chromatic
elements. His thought was essentially linear, and most of his
works are not "abstract" music, but aim essentially to convey
a mood, picture or idea. Hence his most important work is to
be found in his operas; and these quotations from his last opera,
Doktor Faust, may give some idea of his individual methods.
[Ex. 107 and 108, p. 119].
The first is an agitated dramatic passage; the second comes
from a symphonic interlude (Prologue II). It will be seen that
in the latter, though the thought is certainly linear, the back-
118
SOME INDEPENDENTS
Ex. 107
hJ""n r
173
jsjajE
Ji
t> ~
M ri
H I'
Ex. 1 08
ground is harmonic; but the progressions are of an uncon-
ventional type. The student is also recommended to examine
Busoni's Second Sonatina and Fantasia Contrappuntistica for
piano, which will give a further idea of his tendencies. A full
account of the career of this extraordinary man may be found
in Edward J. Dent's usom 9 (London 1933), and there is also
a long essay on Busoni in Bernard van Dieren's Down Among
the Dead Men (London 1935)-
Van Dieren himself (1887-1936) was an interesting composer
whose tendencies were mainly contrapuntal. Just as Busonfs
Second Sonatina showed him to be going in much the same
direction as Schoenberg's Piano Heces Op. ri (Busoni actually
made a "concert arrangement'* of Schoenberg's Op. n No. 2),
so van Dieren in his early Sketches for piano adopted a more
or less atonal style. Later he somewhat modified this, and his
maturer work, though based almost entirely on chromatic
I2O
TWENTIETH CENTURY COUNTERPOINT
harmony, shows much more tonal attachment. Though each
part moves freely and contrapuntally, and often the texture
is extremely complex, as in the "Chinese Symphony", the
actual harmony produced by the movement of the parts is
normally of the Wagnerian "altered chord" type. This is clear
from this extract from van Dieren's setting of Sonetto VII of
Spenser's Amoretti (1921):
Ex. 109
n
SOME INDEPENDENTS 121
Van Dieren was a most cultured and sensitive musician, and not
a little of the originality of his music rests in the handling of
individual instrumental colours. This may be clearly seen from
the extract above; merely to play it on the piano gives no idea
of the continuous crossing and changing of the parts. This
method is in itself an integral part of modern counterpoint;
though, as we have observed, it is not fundamental to the
harmonic or contrapuntal structure, it can make a considerable
difference to the final effect of a piece. Both Busoni and Schoen-
berg realised this at an early stage, and their methods have had
a profound effect on modern music. A more radical use of
this method of splitting up the parts between individual
instruments may be seen in the extract from Webern's
Symphony quoted above (Ex. 93, p. 100). An early example
of this type of orchestration is of course Schoenberg's First
Chamber Symphony (1906); the student should also examine
Webern's remarkable orchestration of the six-part Ricercar
from Bach's Musical Offering, in which the instrumentation
is continually changing in a kaleidoscopic manner.
Another composer of this period, Karol Szyinanowski
(1883-1937), though not primarily a contrapuntalist, is
interesting in combining the influence of Debussyan impres-
sionism with a modern contrapuntal technique. That is to say,
that though his orchestral writing is brilliant and complex, it
often contains a good deal of decoration and accompaniment
which is not of strictly contrapuntal interest. The passage on
p. 122, the (climax of the slow movement of his Symphonic
Goncertante, Op. 60) illustrates this point. [Ex. no].
Here the piano and wind parts decorate the mam theme and
support the harmonies, while a solid bass pedal holds the
structure together. This kind of writing is typical of many
modern works which appear complex in sound, but in fact
rest on a very simple and firmly tonal basis. It would be easy
to multiply examples, as it is a favourite method of many
modern composers, some of whom write even more compli-
cated-looking arrangements of chords but there is nearly
always a firm underpinning, by means of a sustaining note of
some kind, which makes the whole complex easily assimilable.
(For Szymanowski's use of "polytonality" see Ex, 28, p. 33).
122 TWENTIETH CENTURY COUNTERPOINT
Ex. no
Another Slav composer, Leos Janacek, used an almost
exactly opposite method to Szymanowski; primarily a dramatic
composer, he based his style chiefly on continuous repetition
SOME INDEPENDENTS
of short, simple phrases, coupled with striking and unusual
effects. The texture is usually entirely transparent, and the
voice parts follow the natural rhythm of speech against a con-
tinuous orchestral background; this passage from his last opera,
"The House of the Dead" is typical.
Ex. in
SK.
n \nw I'nmEff
o-ci vy-pl.ie-M. Ho-din-k, u*
Tf
o-ci vy-pi.ie-W. Ho-din-k, tj^VV
/ 5M *rM -je - 5W..(.. Ei* f*,-fi.fi* ii^-*-d<:
Vic.
Occasionally, however, Jandcek did make use of normal
contrapuntal devices, but always in his own unusual way.
The third movement of his First String Quartet ("The Kreutzer
Sonata") begins with what looks like a double canon:
Ex. 112
Con tnbto [J * 5
124 TWENTIETH CENTURY COUNTERPOINT
However, instead of "developing" this in the normal way we
simply have the opening phrase (ist violin and cello) and its
successor (2nd violin and viola) repeated one after the other
several times, still in double canon, but in slightly varied forms.
Just before the end of the opening section all four parts take up
the "successor"; but thereafter completely new material
appears, and it is only at the end of the movement that the
opening phrase returns, this time without the canon, though
its successor remains in canon as before. Yet, though Janacek
is certainly not a normal contrapuntal composer, the freshness
and originality of his approach and his directness of musical
speech make him deserving of much more consideration than
he has so far achieved outside his own country.
Janacek, as we have seen, remained faithful to the tonal,
and even in a certain way to the diatonic system, but the
remaining three composers who will be discussed in this
chapter have all in different ways experimented with atonality.
None of these however have studied with Schoenberg or any
of his disciples, and they may all well claim to be completely
independent figures. The oldest of the three was Charles Ives,
(1874-1954), of Connecticut. Working without any knowledge
of Schoenberg's experiments, he produced, chiefly between
1895 ^cl 1916, a number of extremely original works in a
highly complex chromatic idiom which borders on atonality.
The following example, from an orchestral suite called "Three
Places in New England" written between 1903 and 1914, gives
a fair idea of his style.
SOME INDEPENDENTS
1*5
Ex. 113
Ow.tel
It \vill be seen that the texture is consistently polyphonic; the
harmonic style is developed from late igth century chromatic
harmony, but used in a far bolder manner. There is no use of
126 TWENTIETH CENTURY COUNTERPOINT
a serial technique; and in general Ives' music corresponds to,
without resembling, the works produced by Schoenberg and
his followers between 1908 and 1923. Another interesting
parallel is that though Ives* music is not fundamentally
pictorial in character, nearly every work of his is based on a
"programme" of some kind, whether it be the description of
a place or person or the evocation of some past or present
happening; this in some way corresponds to the necessity felt
by Schoenberg during the same period to have the shape of his
works controlled by a literary text. 1 As might be expected,
Ives, though regarded with considerable respect in the U.S.A.,
did not found a school or system of composition, and remained
an isolated figure.
An even more extraordinary personality is Edgar Varese
( 1 885) . He was born hi Paris and underwent a normal academic
education (Schola Cantorum with d'Indy and Roussel,
Conservatoire with Widor) and developed an early interest in
old polyphonic music. However, after some years in Berlin and
Prague, he went to the U.S.A. in 1916 and has since made
that country his home. He has become known through a series
of intricately written compositions which have made new
experiments in harmony, rhythm and timbre and it is not
surprising that he has devoted a considerable part of his time
in recent years to the study of acoustics and of new electronic
instruments. He has always been interested in the nature of
sound for its own sake, and has never let himself be bound by
any academic formulae. He has thus created an entirely new
type of music, which is without parallel in our time. The
extract from his Octandre for wind, brass and contrabass is
typical of his methods. [Ex. 114, p. 127],
It will be seen that this is based on (a) the use of extreme
discords (groups of adjacent semitones) constantly and violently
repeated (b) instruments constantly changing in compass and
often playing in unusual parts of their compass (c) phrases
consisting of constant repetition of the same few notes (d) a
subtle use of rhythm. A more complex example may be seen in
his Integrales (1931) for chamber orchestra and percussion.
[Ex. 1 15, p. 128].
1 Ives also made considerable use in some of his works of hymn tunes and folk
songs, often treated in the chromatic style exemplified above.
SOME INDEPENDENTS
127
Ex. 114
C.B.
Here each instrument has constant repetitions of the same
phrase at varying times; the percussion adds further contra-
puntal parts, and the whole is firmly founded on a discordant
pedal for bass and double bass trombone. It must be admitted
that this method of writing is extremely static, and allows
little possibility of development and perhaps for that reason,
most of Varese's pieces are comparatively short. The complex
of sound is, moreover, an extremely violent assault on the ears
it can hardly be called "music" in the normal sense of the
word. On the other hand there is no doubt that as a noise it is
extremely powerful and exciting, and it has a kind of "abstract"
quality at the same time which is something quite new in
music. (Stravinsky's "abstraction" usually means meaningless
padding, whereas with Var&se one's attention is riveted
throughout, and every note is there for a purpose) . "lonisation",
for instance, a work for 41 percussion instruments, is an
extremely remarkable study in purely rhythmic counterpoint,
128
Ex. 115
TWENTIETH CENTURY COUNTERPOINT
and holds the attention by its fascinating use of sonorities.
What Varese's ultimate contribution to music may be is a
question that must remain in abeyance for the present
especially as his more recent works do not seem to be generally
available but there is no doubt that in him we have a pioneer
who has added new elements to the musical language.
The last of these three independent atonalists 1 is Fartein
work of the Czech composer, Alois Haba, lies rather outside the scope of
this book, as he has mainly devoted himself to writing music in f and 1 tones He
has however, also composed some works which show an individual handling of
twelve-tone methods, such as the Fantasia quasi Toccata, Op. 38. He has also
been an exponent of athematic" writing, and had at one time a considerable
influence among the younger Czech composers.
SOME INDEPENDENTS
129
Valen [1887-1952], a Norwegian pupil of Max Reger. For
the last thirty years of his life he composed works based on
a serial technique of his own. Though his series normally
contain all the twelve notes of the chromatic scale, he did not
stick to strict twelve-note series repeated round and round;
each piece is based on a number of different serial themes
which recur sometimes complete, sometimes in fragments,
Ex. 116
130
TWENTIETH CENTURY COUNTERPOINT
and usually without transposition. That is to say, his use of
series was at once freer and more "thematic" than Schoenberg's,
and he did not normally derive his harmonies from his series*
in fact his methods were predominantly linear, and it is only
in certain works, notably those for piano and organ, that he
used chords as such at all. He made an occasional use of
inversions and mirror forms; here is an example of the former
from his Second String Quartet, Op. 13 (published by Norsk
Musikforlag, Oslo). This movement (which is worth studying
as a whole, for it gives a good idea of Valen's contrapuntal
methods) is written in the form of a fugue; after the fourth
entry of the theme, on the cello, the inversion is heard on the
first violin, while the accompanying figures are mainly derived
from fragments of the theme & typical process with Valen.
[Ex. 116, p. 129].
Mirror forms are rarer on the whole, but here is an example
from the Kano Variations, Op. 123; the theme consists of a
twelve-note series followed by its retrograde form.
However, in the variations which follow the theme is varied
and decorated in the usual classical manner, and the accom-
panying harmony is not derived from the series.
Valen thus developed a free atonal style of his own, in
which serial technique provided a constructive element. But
the effect of his music on the whole is rather static, partly
perhaps because the texture is so continuously contrapuntal
without any very strong rhythmic impetus, and partly because
there is a good deal of continuous repetition of themes or
thematic fragments without transposition as if all parts moved
in an unending ostinato. Nevertheless Valen's sensitive handling
of this linear technique did produce some very successful results,
particularly in his orchestral works, where he had the aid of
SOME INDEPENDENTS 13!
instrumental colour. The student is recommended to examine
the scores of "Sonetto di Michelangelo" (Norsk Musikforlag),
"La Isla de las Calmas" and the Violin Concerto 'both pub-
lished by Lyche, Oslo the latter is also available on Norwegian
H.M.V. records). The Violin Concerto in particular makes a
clearer use of its thematic material than many of Valen's
other compositions, and is a very powerful and moving work.
Nearly the whole of the material is derived from the two opening
phrases:
Ex. 118
CHAPTER IX
CONCLUSION A NEW HYPOTHESIS
BEFORE trying to sum up the lessons which may be learnt from
our survey, I must point out again that I have not attempted
to give an account of what all contemporary composers in all
countries are doing in the field of counterpoint. Such a task,
apart from needing a book several times this size, is not my
purpose; all I have attempted to do is to analyse certain
significant tendencies which have had varying effects on almost
all modern composers, and I do not imply that the composers
mentioned in this book are better as composers than those who
are not. The former are discussed here because they exhibit
certain tendencies in an easily appreciable form; many of the
latter also exhibit the same tendencies, but hi most cases they
have inherited these from the original pioneers in the field and
adopted them to suit their own personalities and methods of
expression. The music of Vaughan Williams, for instance,
becomes easy to analyse when we realise that it is mainly based
on the use of (a) modal scales derived from mediaeval and
folk music (b) block chords moving in parallel (cf. the quotation
from Petrouchka, Ex. 16) and (c) polytonality (Flos Campi,
Pastoral Symphony; cf. Chapter IV). But though Vaughan
Williams has invented no specifically new technique, that does
not affect his stature as a composer; Mozart was a greater
composer than C. P. E. Bach, but C. P. E. Bach was a pioneer
of the style in which Mozart wrote. This survey, then, is
solely concerned with the assessment of new techniques as such,
and with the evaluation of general tendencies; and the student
should be able, by comparing the examples given here with the
works of other composers, to see what use the latter have made
of the principles here enunciated, how far they have followed
them and how far deviated from them. I have no wish to
labour this point; I feel there is no need for me to make a
catalogue of composers by schools and influences the student
may (if he feels inclined) undertake this task himself.
132
CONCLUSION A NEW HYPOTHESIS 133
This having been said, we may now see what conclusions,
if any, can be drawn regarding the present and future develop-
ment of music, and whether it is possible to outline a system of
harmonic and contrapuntal rules for it. At first sight this might
seem impossible in view of the chaotic complex of opposing
tendencies which contemporary music appears to present.
As we have seen, this is mainly due to the disintegration of the
old rules of harmony through the breakdown of the diatonic
system; but further factors have entered in through the in-
creased complication of musical texture. This was partly due
to the greater virtuosity in orchestral playing which became
possible during the nineteenth century; just as Paganini
revolutionised the technique of the violin and Liszt that of the
piano, so Berlioz 5 orchestral writing introduced new effects of
sound which could only make their mark if played by the
instruments for which they were intended, and became mean-
ingless if transcribed for another medium. (One has only to
think of the flute and pedal trombone chords in Berlioz'
Requiem to see the point of this). This tendency was carried
successively further by Liszt, Wagner, Strauss and Mahler,
until we reach examples of the complexity of the Szymanowski
and Ives quotations above (Ex. 1 10, p. 122 and Ex. 1 13, p. 125).
It tends increasingly towards the use of sound purely for its own
sake, without any harmonic and contrapuntal control of the
older sort. (Gf. also Debussy's impressionistic effects in La Mer
and the orchestral Images , for instance).
We are thus confronted simultaneously with a breakdown of
harmony and an ever-increasing complication of surface
texture. And an even more serious consequence of the break-
down of harmony is that it undermines the foundations of the
musical structures which were based on the diatonic scale
the sonata form, rondo, fugue etc. All these were based on the
contrast between a main tonality and its nearer or remoter
neighbours; if tonality is removed, how can one continue to
use the form? The Schoenbergian transpositions of the note-
series do not help in this matter, for they axe not really felt as
"modulations", in spite of the efforts of Schoenberg, Webern,
and others to create a new sort of tome-dominant relation
Schoenberg by his use of the original series combined with its
inversion a fifth lower, and Webern by his employment of the
K
134 TWENTIETH CENTURY COUNTERPOINT
tritone as a kind of dominant. Nevertheless, composers have
continued to use the old contrapuntal forms as representing
some method of imposing order on chaos but the canons of
Webern, for instance, are more noticeable to the eye than the
ear, however exquisite their musical result may be. What would
appear to have been the logical solution to the problem, the
Lisztian system of transformation of themes in the symphonic
poem, has fallen into disrepute; perhaps because Liszt was
rated more highly by his contemporaries and successors for his
pictorial imagination than for his symphonic construction
(which admittedly could often be weak), the form he devised
degenerated 1 into the pure impressionism of Debussy and others
and the "Fantasies" of the older generation of English
composers.
This system of "thematic transformation" is of course very akin
to the methods of Schoenberg and his followers and in England
Alan Bush uses a similar system, though not based on twelve-
note series. The difference between Liszt's and Schoenberg's
methods (apart from the question of tonality) is that Liszt's
themes are recognisable as such in their various transformations,
whereas Schoenberg's note-series are not necessarily so. In fact
the tendency of a good deal of modern music is towards
athematism and the avoidance of repetition of any kind; which
can of course be combined with the use of a note-series which
is there as a unifying background, but is not consciously heard
as a theme.
Theme, no theme or transformations of theme? That is one
of the problems of modern music; and another is the question of
movement from one musical region, to another. This is the whole
basis of the diatonic system one has only to think of the
wonderful effect of Schubert's modulations to see that. Busoni
may have been logically right to say that a face seen at one
window does not differ from the same face seen at another;
but he would not be right to say that dress makes no difference
to a woman's appearance and the position with the diatonic
system is more like that. On the other hand chromatic music
which is modulating so constantly that it gives us little or no
sense of position has little or no feeling of movement either;
it can indeed be dramatic, lyrical, expressive and moving,
1 I am speaking here of form, not of music per se.
CONCLUSION A NEW HYPOTHESIS 135
and often is but does it always give a sense of direction? In
dramatic works, such as Berg's Lulu, the alliance of words and
music does help to create a directional feeling; but this cannot
be done by transpositions of the note-series alone.
As we have seen, Schoenberg latterly admitted the pos-
sibility of "tonal references" in twelve-tone music, provided
that they are "not in a position to transform the non-tonal
style into a tonal style." This rather careful point of view would
seem to date back to the early days of atonality, when, in order
to complete the break-up of the diatonic system, tonal references
were deliberately avoided. But now that the diatonic system has
definitely been dethroned in favour of the chromatic system
(by which I mean not atonality, but the free use of all the
notes of the chromatic scale in relation to a tonal centre), is
such caution still necessary? And is it really always necessary
to play every note-series complete and always in the same order?
The fact that twelve transpositions of each of the four forms of
the series are always available means that it is easy 'to introduce
any notes one wants at any given moment by using one or
other of these forms; but one may not want thereafter to use
the whole of the rest of the series thus introduced, and in that
particular order of notes. The experiments made by Schoenberg
in some of his later works (consistent use of certain intervals
loosely based on a series in the Ode to JfcpoLox, variation of
the order of notes within six-note groups in the String Trio)
seem to foreshadow new possibilities which other composers
may exploit further.
I hesitate to add yet another to the numerous systems and
methods employed by present-day composers; but I would like
to suggest a possible method of analysis which may be applicable
to most types of modern music. It is clear that what is needed
is some system of classifying harmonic relations; admittedly
this book is intended primarily as a study of counterpoint, but
to study contemporary music purely from the horizontal
point of view would merely give the impression that no holds
are barred and that any part can do anything it likes against
any other part. It is clearly only possible to see what is in fact
happening by using some method of harmonic analysis, i.e. by
studying the vertical complex produced by the movement of
the various parts.
136 TWENTIETH CENTURY COUNTERPOINT
What we need then is (i) a means of analysing chord-
structures (ii) a method of determining the relative value of
root-progressions. For neither of these do I suggest anything
spectacular; in fact I think it is best to depart from a traditional
viewpoint, and to analyse chords as far as possible according
to the traditions of classical harmony. After all, music still
remains based on the harmonic series, which is a fundamental
law; we are merely making more use of notes higher up in the
series at the expense of those nearer the fundamental. If we
turn back to Hindemith's chordal progression (Ex. 53, p. 62)
we can perhaps see a method of applying this. The first chord
can be analysed in two ways: (i) as a first inversion of A sharp
minor (B flat minor) with two added notes (flattened fifth,
Efcj, and flattened seventh (G#), or (ii), as Hindemith prefers,
root position of C sharp, with both major and minor thirds
(Etj and E#) and added sixth (A#). The latter explanation
certainly puts the chord on a more solid basis, as being a root
position, but historical tradition would probably favour the
former, regarding the so-called "added sixth" as one of the
inversions of a seventh chord (6/5) . Here then, at the very outset,
we are confronted with a chord capable of bearing two different
interpretations, which shows us that our task will not be an
easy one; but there is no need of great alarm, as many such
chords with double meanings can be found throughout classical
and romantic harmony. Then- meaning may be decided by- the
general tonality of the passage, sometimes by the theme they
accompany, or by the root progressions many hi fact are
deliberately treated as "pivot chords", being introduced as
bearing one meaning and left with the meaning changed
(e.g. the use of the so-called French, German and Neapolitan
sixths in igth century modulations). In this case, however, there
is no change of tonal region, A sharp being the relative minor
of C sharp.
We must then consider if the root-progression will help us.
In his Harmonielehre (German ed, p. I4off ) (English ed, p. 6gff )
Schoenberg gives some rules on this subject for diatonic
harmony which may well be expanded to suit chromatic
harmony. The following are "rising" or strong steps: fourth
upwards, third downwards; "falling" or weak steps are fourth
downwards, third upwards. Seconds upwards or downwards
CONCLUSION A NEW HYPOTHESIS
are "super-strong" steps, for they consist in essence of two
strong steps (see loc. cit. for a fuller explanation of the
theoretical basis of this). The step which has the most powerful
effect of all is the rising fourth (or falling fifth) , for it corresponds
most closely to the harmonic series; next after it in power is
the falling third (or rising sixth). The step of the second, though
superstrong by nature, has not in fact such a powerful effect,
simply because it is too strong for everyday use: "Allzu Scharf
macht schartig" (Too sharp makes notches), as the German
proverb goes.
If we adapt these principles to chromatic harmony, we get
the following results:
Ex. 1 19
Strong
: II .P^TTT^ i. u~ =z===^==^- J iK>-4
^ " . . U v II -" bii OC i ir i*J I "' Z^Zfl
-<or
-Q-
Neutr*.l
-*m
(The step of a tritone remains neutral, as we have seen before;
it divides the octave into two equal parts, and therefore
neither rises nor falls). Schoenberg recommends a judicious
mixture of strong and weak progressions; not too many strong
ones in succession (and especially not too many superstrong
ones) , and weak ones to be used sparingly, chiefly in conjunction
with strong progressions (see loc. cit. for further details). All
of this still applies in chromatic music to a considerable extent;
so let us return to the Hindemith progression (Ex. 53) and
see if it helps us.
We are still doubtful if the root of the first chord is A sharp
or C sharp; the root of the second is certainly B, as Hindemith
states (B minor chord with both flattened and sharpened
seventh, A and Bb) so the root-progression does not help us
here, being a super-strong step in either case. Let us then leave
138 TWENTIETH CENTURY COUNTERPOINT
this question for the moment the general tonality of the
passage will probably help us to decide this in due course and
continue with the analysis of the remaining chords.
The root of the third chord is given by Hindemith as G
sharp, on the strength of the fifth G#-D# in the middle of it.
This does not strike me as possible, as the remaining notes all
contradict this interpretation the bass note is Bb (A sharp)
which is the "supertonic" in old-fashioned parlance, and the
others are the augmented fourth (D) and the minor sixth
(E). Two alternatives are preferable E or Bb; the latter has
the advantage of being the bass note, which always tends to
preponderate, and in that case we should have a B flat chord
containing major third, perfect fourth (D#), diminished fifth
(E) and flattened seventh (G#). If we take the root as E, which
would probably be the "classical" method of analysis, we should
have major third, diminished fifth (Bb), and both major and
minor sevenths (D# and D); in favour of this is the movement
of the root a fourth upwards from the previous chord (B E) .
This chord too, then, is doubtful; it is based on two pairs of
major thirds a tritone apart (Bb-D, E-G#), and therefore we
can only decide its root from the remaining note in the chord
(Dfl) and the root-progression in general; let us therefore note
the alternatives (Bb and E) and return to it later.
The root of the fourth chord is given by Hindemith as A,
and this is probably correct; in this case it would contain both
major and minor second, perfect fifth, and minor sixth. The
only alternative is B flat the third inversion of a major seventh
with B flat as its root but the Bfc] and Etj are against this
interpretation. (It should be remembered, however, that if
arranged for orchestra this chord could be scored in such a
way that the Bb would predominate and thus alter its whole
efiect).
The root of the fifth chord is certainly G, as Hindemith
states; in the old days it would have been known as an eleventh.
I feel, however, that Hindemith is wrong in calling the root of
the sixth chord Eb; it is surely an Ab chord with Bb as appog-
giatura for Ab and Etq for Eb. The seventh chord he correcdy
bases on Eb, with augmented fourth, perfect fifth, major
seventh and minor ninth (or minor second, if you prefer) ;
Chord 8 is merely another position of Chord 5 and is of course
CONCLUSION A NEW HYPOTHESIS 139
based on G; and Chord 9 is a triad of A flat minor. Our analysis
thus gives us the following root-progression:
Ex. 120
12345
c\*
1__
-,rX**JL
.> ^ (*'? hit
i ^^
rt LF
O
-!ro
The general tonality is Ab; and therefore it would appear more
logical to regard Chord i as based on C sharp (Dj>), especially
as this makes it a triad in root position. As regards Chord 3,
obviously it is better from the point of view of root-progression
to regard the root as E, which gives us the best type of strong
progression (root moving upwards a fourth) between Chords
2, 3 and 4; if we take Bb as the root we have nothing but
superstrong steps from Chords i to 6. A further factor is that
the major seventh E-D# acts as a better limiting or defining
element than the perfect fourth Bb-D#, which tends to suggest
the tonality of Eb-
I am aware that the above method of analysis is open to
criticism, but I think it better to advance slowly and cautiously,
recognising our difficulties as we go, rather than to impose a
preconceived scheme which may not be in accordance with the
facts of the case. The progression analysed above is of course
not a very "good" one musically, as Hindemith justifiably
remarks, but it will serve as a starting point.
Let us now examine a simple example from twelve-tone
music, the main theme of Schoenberg's Wind Quintet (Ex.
66, p. 84). I would analyse the root-progressions as follows:
Ex. 121
The first chord of bar i is clearly based on E; the movement of
the bass to F# on the fourth beat, together with the D and A
hi the upper parts, clearly indicate D as the next root. The
root on the fourth beat of bar 4 is more debatable; the C has
entered on the third beat as a minor seventh above the root
D, and the appearance of E b and G under it could be construed
I4O TWENTIETH CENTURY COUNTERPOINT
as Implying a classical 6/4 chord; but this is soon negatived
by the entry of the lower parts on A and C#, building up the
neutral chord consisting of two major thirds a tritone apart,
which has two possible roots, A and Eb- It is only in the middle
of bar 5 that C emerges as the root of this chord, confirmed by
the Bb and D in the top part. (Incidentally in the "neutral"
chord above, Eb is clearly preferable to A as the root, both
through the context and as giving a stronger root-progression.)
The passage is not of course long enough for us to be able to
place it in a definite tonality.
The next quotation for the same work (Ex. 67) gives an
even clearer example of tonal implications within a twelve-tone
framework. I would suggest the following analysis of the root-
progressions:
Ex. 122
It will be seen that this gives a succession of descending thirds,
all strong steps, and very much in the classical tradition.
In the following example (Ex. 68) the harmonic basis is also
perfectly clear, as follows:
Bar Root
1-2 Eb
3-4 Db
5-6 B
(7 D)
89 Ab
Again we have a series of superstrong and strong steps, if we
disregard the preparatory D in bar 7. The student may now
attempt the analysis of some of the other Schoenberg examples
given in this chapter, and see what he makes of them. He may
for instance, study the theme of Schoenberg's Variations for
Orchestra (Ex. 77, p. 90) ; here he will find constantly changing
roots, e.g. Bars 34-5, G-C; bars 36-37, E-Bb; bars 39-40, C
amounting to a kind of 6/4 chord; bars 41-42, A~D; bars
43~45> Bb, etc. In fact, instead of regarding this type of writing
CONCLUSION A NEW HYPOTHESIS 14!
as having no tonality at all, it is truer to say that it is constantly
moving from one point to another within the twelve-note scale.
Whether such a passage as a whole can be said to have a general
tonality will of course depend on the root-successions; this
theme has a definite ending rooted on B (bars 56 -7), but one
certainly could not say that the whole theme is "in" B; B is
merely the final point of rest. (Of. also the analysis of a passage
from Schoenberg's Op. 33a, p. 67 above).
We are thus approaching a new conception of tonality in
which root-progressions move freely within the twelve-note
scale, not following the classical laws of preparation and
resolution (in most cases the resolution of what would be a
discord in traditional parlance is simply taken for granted and
omitted) but still governed by the old principles of strong,
superstrong and weak progressions. Note for instance, as a
further example, the series of root-progressions hi the firat half
of Ex. 77 G, G, E, Bb, G, A, D, Bb respectively strong, weak,
neutral (altering the significance of a held chord), superstrong,
and three successive strong progressions. What could be nearer
to classical procedure? We may then lay down then as a
provisional method of analysis for predominantly harmonic
passages (i) find the root note of each chord, which will
normally be the same as in the traditional method of analysis,
and (ii) set out and analyse the root-progressions. From these
it will be possible to discover the general tonality of a passage
or a piece if any; for a composer, whether he uses twelve-
tone methods or not, may engender a general feeling of tonality
by emphasising one particular root note, or he may avoid it
as far as he can by using as many different roots as possible.
I am certain that it is by this means that tonality is suggested
or avoided, and not by the mere use of note-series, which of
themselves neither engender nor suppress tonal feeling.
Let us now see if this method can be applied to predominantly
contrapuntal passages. We will take a simple example first,
the quotation from Bart6k's ist Quartet (Ex. 37, p. 45>- Here
we have music moving chromatically in four parts; the roots
are as follows:
Bar i
Roots F Ab
E (Ab) Bb F
3 4
B G (Bb) I (E) etc,
142 TWENTIETH CENTURY COUNTERPOINT
The roots in brackets in bars 2 and 3 are used only in passing.
It will be seen that a good many of the progressions are weak
ones, which may account for the slightly indeterminate effect
of this passage, as well as the fact that the music is constantly
moving from one point to another.
A more complex example may be seen in Ex. 80 (from
Schoenberg's Variations for Orchestra). In the first half bar
the successive E, Bb and Gff suggest E as the root of a
"dominant" chord of A; but this is immediately contradicted
by the Gfc] which is clearly the root of the first half of the next
bar; C and D are the roots of the third and fourth quavers
respectively, though on the last semiquaver the bass has
already moved to B.
Ex. 8 1 also presents some complications. We may take the
roots of the first two semiquavers as C# and B, and of the third
and fourth as F; but the second group is not so easy. Though the
main tonal centre is E, the roots of the individual semiquavers
would appear to be E, G, B and G; so that we are back at the
old classical concept of * 'inessential" or "passing" notes, but in
a different form.
Our next examples are taken from Webern (Ex. 93 and 94,
pp. 100-1). Here tonality is so attenuated that it is very difficult
to give any analysis of root-progressions, especially in Ex. 93.
A style which is based to a large extent on the use of adjacent
semi-tones and which also contains so few actual notes marks
the nearest approach to atonality that we have yet met. At the
best one can say that the roots are constantly changing a
possible scheme might be as follows:
Bar 2 3 4 56 7 8 9 10 n 12 13 14 15
Roots F# G Ab B Bb C Bb G D F D G E
But I admit that such an analysis is by no means satisfactory.
Ex. 94 is not quite so complex. Bars 1-2 are rooted on B,
which acts as a kind of "dominant" to the E of bars 3-4.
Bars 5-7 alternate between Bb and E the "neutral" tritone
again ending on E; in bars 8-9 we have successively C, F#
(tritone again) and D, acting as "dominant" of the G which is
the root of bars 10-1 1; so here the root-progression tQQ
a symmetrical shape.
CONCLUSION A NEW HYPOTHESIS 143
As a final example let us take the passage from Valen's
Second Quartet quoted above (Ex. 116). Here there is a use of
a various ostinato-like figures which somewhat confuse the
picture; but one can say that the main root of bar i is
E and bar 2 B; in bars 3-4 we move from A[> (G#) via
G and D to Bfr. Admittedly this sort of music is difficult to
analyse from a tonal point of view, as there is a considerable
use of what one might call "inessential" notes; but if one can
keep the main lines of the harmony clear, it is not difficult to
discover the root-progressions.
I do not think it is necessary to continue to give further
examples, as I hope the method of analysis will be clear by
now, and the student may amuse himself by applying it to
other examples in this book. The chief principle is of course to
discover the main harmonic complex, strip it of its inessentials,
and discover its root. The root may not necessarily be in the
bass, though it very often is; the presence of a fifth or fourth in
the chord may be a help to its discovery, but this cannot be
applied as an automatic rule in the manner of Hindemith,
as we have seen. It is a question mostly of common sense and
experience, but I think it can produce useful results if properly
applied. In very complex combinations, such as the Milhaud
examples above (Ex. 33-35) it may be necessary to find the
predominant chord or note, and derive the root from that
e.g. B in Ex. 33, C# in Ex. 34, E in Ex* 35. 1 fear that I cannot
be more precise than this; the subject is an enormous one, and
has not yet been folly explored by any means.
It should be emphasised that the root notes in themselves do
not always add up to a general tonality; as we have seen, it
is up to the individual composer to decide how much or how
little tonal feeling he wishes to present, and he does this by his
handling of the root progressions. If, as in Webern, his roots are
constantly changing, and are accompanied by other notes which
sharply contradict them, he will approach very close to true
atonality. We can certainly accept a table of the type of
Hindemith*s Series 2 (Ex. 51, p. 56) as showing the relative
degree of tension (or "dissonance" in traditional parlance) in
various intervals, and the more intervals contained in a
chord or harmonic complex which appear towards the left-
hand side of this table, the easier it will be for us to analyse it
144 TWENTIETH CENTURY COUNTERPOINT
by traditional methods. We must however extend our theory
of traditional harmony by admitting the emancipation of
the dissonance and removing the traditional distinction between
concords and discords; intervals in a chord which are further
to the right of our table may be less consonant or less essential,
but they are not dissonant or inessential. Nor does this imply
that the major triad is the "best'* chord musically; it is certainly
the nearest to the harmonic series, but we may not want to
stick to the harmonic series. It is purely an aesthetic matter
whether we use more concordant or less concordant material;
all one asks is that each piece of music shall be consistent with
itself. One cannot lay down any formulae for artistic values;
one can merely analyse technical processes and try to see how
they work.
Similarly, though we cannot speak any longer of dominants,
subdominants, mediants, etc., we do have a number of roots
in each piece which may revolve round a main tonal centre
or may move freely from one point to another; or one can of
course combine both methods, i.e. having a main tonal centre
which is only stressed at crucial points, with the roots moving
freely in between these. These roots now move within a twelve-
note instead of a seven-note scale, but the relations of the roots
to each other still remain the same, as we saw in our discussion
of strong and weak progressions; and the strongest progression
is still that corresponding to the old dominant-tonic step
(V-I). It does not matter if both the "dominant" and "tonic"
chords contain innumerable altered or additional notes the
underlying movement is still there. So that in a sense there is
no real division between the different methods used by con-
temporary composers; some of them have a "main root" which
they exalt by repetition or other means of emphasis into
becoming a "tonal centre", while others do not.
Most composers do not, I imagine, consciously analyse their
roots when they are writing music; their unconscious ear,
trained in the classical past, will help them to produce the
results they want. Nevertheless the study of root-analysis will
show us how to produce effects which many people complain
are missing from the music of today; one can emphasise one
root as a tonal centre, perhaps leaving it for short stretches
and then returning to it; then a decided move to and dwelling
CONCLUSION A NEW HYPOTHESIS 145
on another root will give an effect comparable to modulation
from one diatonic key to another no matter how chromatic
the complex above each root may be. Admittedly the more
chromatic the complex is, the more it will contradict the root;
but this method of procedure is at any rate possible, and we
at any rate know the relative value of the different root-
progressions.
Can we also retain the old forms, sonata, fugue, rondo, etc.,
which depend on modulation? It can, I think, be done, though
modulations of this kind will not perhaps have the incisiveness
or effect of the classical modulations, simply because they are
likely to be carried out with more complex means; but in
theory they are certainly possible. But I think also that the
freer forms engendered by the Lisztian transformation of themes
may have a good deal to offer us; if we can forget the pictorial
associations which they were given by nineteenth-century
composers and treat them organically, as Liszt did in his piano
sonata, for instance, we may find that new possibilities are
opened up. Personally I feel it is better to control our material
itself and enlarge the forms rather than to put into the tight
framework of the canon and fugue a type of music for which
they were never designed.
Our last point concerns melody; if we have found some
glimmerings of a method of evaluating the vertical basis of
contemporary music, what about the horizontal? Here again
we have tradition to guide us; the traditional values of the
different intervals are not necessarily upset by the more
complex system of harmony in which they partake, and we can
still hear a melody in relation to the root of the chord or complex
in which it participates. The relations between a melody and
its accompanying harmony may have become more abstruse,
but it is a question of degree, not of a fundamental revolution.
And this brings me to my conclusion; the fundamental basis
of music is still the same. The harmonic series is still there,
however much we get away from it, and it remains a strong,
unseen power in the background. We are perhaps making
less use of its fundamental notes and more of those that come
higher in the series; but the fundamentals are still implied,
and all that we are doing is to work at a remove from them.
I believe therefore in the free use of all the twelve notes of the
146 TWENTIETH CENTURY COUNTERPOINT
chromatic scale; I also believe that every harmonic and contra-
puntal complex contains a root note which can be discovered.
The root note may lie still for a long time or it may change
rapidly; and the more any one root note is emphasised the
more "tonal" will the music sound and vice versa. "Tonality"
and "atonality" are thus questions of degree, not of fundamental
difference; the consistent and equal use of all the twelve notes
of the scale can still produce a feeling of tonality if required.
Music cannot get away from its roots, and it is through the
variation in the movement of its roots that it produces its varied
effects. If in this survey I have concentrated on the more
extreme and chromatic handling of the roots, it is because
this is the most difficult to analyse and reconcile with the
traditional and historical past. But though music may have
its revolutions, it is also fundamentally an evolutionary art,
and if I have helped to show that the same forces which
governed its processes in the past are still at work today, albeit
in a substantially different form, I shall have achieved my
purpose.
POSTSCRIPT, 1954
THIS book has been some time in the press; and corr.scsitio:: has
naturally not stood still during this period. Schoenberg has died;
and the remaining three leading figures of the old guard of
revolutionaries Stravinsky, Milhaud and Hindemith have
not shown any signs of launching out in new directions, apart
from some use of a serial technique (of a kind) and a Webern-
like texture in some recent works of Stravinsky, like the Septet
and the Shakespeare Songs. Meanwhile the younger com-
posers have been consolidating the territory first explored
by their predecessors; here again there has been no specifically
new development apart from one which affects a number of
the younger twelve-tone composers, and which appears to
contradict my statement in Chapter VII that Webern is
unlikely to become "the direct ancestor of a new technique
of composition." A group of young composers, all at present
in their twenties, and belonging to several different countries,
are experimenting with a style which clearly steins from
Webern's later technique; they are, however, attempting to
carry this further by a much more complex use of rhythm and
sonority, in some cases based on mathematical principles; that
is to say, they appear to be aiming to impose the same type of
formal control on the rhythm, tone-colour and pitch of the
music as the twelve-tone method imposes on the notes them-
selves. A typical example is taken from the "Kontrapunkte
No. i " by the young German composer Karlheinz Stockhausen
[Ex. 123, p. 148]. (The ties over the bar-lines indicate that the
notes are held on). It will be seen that this is pre-eminently
contrapuntal, and the student may be interested in seeing
how the note-series run through the different instruments.
Other composers who are tending in this direction include
Pierre Boulez (France), Luigi Nono (Italy), Giselher Klebe
(Germany) and Jacques Wildberger (Switzerland). It is
obviously too early to make generalisations about a movement
which is as yet only in its infancy, but certain points can be
47
POSTSCRIPT, 1954
VI*.
(N.B. All notes sound as written.)
noted regarding this style. Tonality is clearly avoided as
rigorously as possible, rhythm is dislocated to the utmost
(Stockhausen's "Kontrapunkte" contains several passages of
even greater rhythmical complexity than the one quoted here),
POSTSCRIPT, 1954 149
there is no question of the use of themes longer than small
motifs of the type seen above, and isolated notes provide the
main basis of the music; in addition there is a tendency to use
the extreme registers of the instruments as much as possible
(cf. Varese's methods) and also to pass rapidly from one
extreme to the other the trumpet part seen here is a good
example of this. The difficulty of this sort of music is to avoid
lack of continuity; it is hard to see any overall form or design
in many of the works in this style, though each individual
passage is logically constructed within itself. That is to say,
the music gives a predominantly static effect, and one cannot
feel that it is normally aiming towards a goal or conclusion.
However, there is no doubt that it presents some new elements
from the technical point of view, and its future development
will be interesting to watch.
Finally, I should mention the appearance of an important
analysis of Schoenberg's methods by his pupil and assistant
Josef Rufer, Composition with Twelve Notes (Rockliff, London
1954). This may be regarded as the authorised exposition of
"classical" twelve-tone technique, and it also discusses the
innovations made by Schoenberg in his last works. Unfor-
tunately its publication came too late for it to be discussed in
the main body of this book, but its contents may be briefly
summarised here. After chapters devoted to general theoretical
discussion and to an account of the break-up of the major-
minor tonality, Rufer deals with the concept of the Grundgestalt
(literally, basic shape) : this is the musical phrase which is the
basis of each work and is its "first creative thought", in Schoen-
berg's words from it everything else in the work is derived,
including the series itself. This concept applies equally to
classical music, and Rufer shows how all the elements in Beetho-
ven's Sonata Op. 10, No. i are derived from the Gnmdgestati
in its first four bars. Rufer then deals in detail with Schoenberg's
"transitional" works, Op. 23 and 24, before giving a full
account of the principles of twelve-tone composition itself:
in this chapter he discusses whether it is legitimate to base a
work on more than one series, and whether twelve-tone music
should tend towards athematism, as has been suggested by some
writers. He next describes the special uses of melody, harmony
and rhythm in twelve-tone music, and gives a detailed exposi-
POSTSCRIPT, 1954
tion of Schoenberg's methods of inventing thematic material
from a twelve-tone series: the final chapter deals with problems
of form, including an analysis of Schoenberg's Fantasy for
violin and piano. Op. 47. The whole book is a most valuable
account of Schoenberg's own approach to the subject, in both
theory and practice: an appendix is contributed by a number
of contemporary composers, describing their individual methods
of twelve-tone composition.
SELECT BIBLIOGRAPHY
Books and articles on contemporary music are legion I
have only chosen those which are likely to be of most use to
the student. As far as possible, all are written in English,
though in certain cases, where no other equally valid sources
are available, I have mentioned books in French or German.
They are arranged in the order of subjects discussed in this booL
General
ABRAHAM, GERALD. This Modern Stuff. London 1939.
GARNER, Mosco. A Study ofzoth Century Harmony. London 1942.
DYSON, SIR GEORGE. The New Music. London 1924.
GRAY, CECIL. A Survey of Contemporary Music, London 1924.
LAMBERT, CONSTANT. Music Ho/ London 1934.
MELLERS, W. H. Studies in Contemporary Music. London 1947.
MYERS, ROLLO H. Music in the Modern World. London 1939.
PISTON, WALTER. Counterpoint.
SLONIMSKY, NICHOLAS. Music since igoo. New York 1949.
Stravinsky
STRAVINSKY, IGOR. Chronicles of my life. London 1936.
Poetics ofMusic 9 London 1947,
WHITE, ERIC WALTER. Stravinsky. London 1947.
Milhaud
BECK, G* L'Oeuvre de Darius Milhaud. Paris 1949.
COLLAER, PAUL. Darius Milhaud. Brussels 1948.
MILHAUD, DARIUS, Notes sans musique. Paris 1949.
Bartok
HARASZTI, EMIL. Bela Bart6k. Paris 1939 (in English).
MOREUX, SERGE. Bela Bart6L London 1953.
STEVENS, HALSEY. The Life and Music of Bela BarttL London
1953-
152 SELECT BIBLIOGRAPHY
Hindemith
HINDEMTTH, PAUL. The Craft of Musical Composition.
Vol. I, Theory. London 1945.
Vol. II, Exercises in Two-Part Writing. London 1948.
Twelve-Tone Music.
KRENEK, ERNST. Studies in Counterpoint. New York 1940.
LEIBOWTTZ, RENE. Introduction d la musique de 12 sons. Paris 1949
Qu'est-ce que la musique de 12 sons? Li&ge 1948.
Schoenberg and his School. London 1 954.
NEWLIN, DIKA. Bruckner , Mahler, Schoenberg. London 1947.
REICH, WILU. Alban Berg. Vienna 1937.*
ROGNONI, LUIGI. Espressionismo e Dodecafonia. Turin 1954.
RUFER, JOSEF. Composition with Twelve Notes. London 1954.
SCHOENBERG, ARNOLD. Harmonielehre. Vienna 1921*
Theory of Harmony.* New York 1948.
Style and Idea. London 1951.
Structural Functions of Harmony. London 1954.
STEIN, ERWIN. Orpheus in New Guises. London 1953.
WELLESZ, EGON. Arnold Schoenberg. London 1924.
Independents
BUSONI, FERRUCCIO. A New Esthetic of Music. New York 191 1.
Von der Einheit der Musik. Berlin.*
DENT, EDWARD J. Ferruccio Busoni. London 1933.
VAN DIEREN, BERNARD. Down Among the Dead Men. London 1935.
AP!VOR, DENIS. Bernard van Dieren. Music Survey. Vol. Ill, No. 4.
JACHIMECKI, Z. Karol Szymanowski. London (School of Slavonic
Studies).
MULLER, DANIEL. Leos jfandcek. Paris 1930.
BELLAMANN, HENRY. Charles Ives. Musical Quarterly, Jan. 1933.
Go WELL, HENRY. Charles Ives. Modern Music, Nov. 1932.
HELM, EVERETT. Charles Ives. Musical Times, July 1954.
COWELL, HENRY. The Music of Edgar Varise. Modern Music,
Jan. 1928.
KLAREN, J. H. Edgar Varese. Boston.
1 Tbis, unfortunately, is only a translation of extracts from the Harmonielehre;
most of the important theoretical discussions are omitted.
^English translation in preparation.
DISGOGRAPHY
A GOOD many records of contemporary music are now available,
especially in the United States since the advent of the long-
playing record. These are useful adjuncts to the study of the
works discussed in this book, but the student is recommended
to follow them with the score where possible. The following
list does not pretend to completeness, and should be supple-
mented by enquiries at gramophone shops etc. regarding up-
to-date recordings 1 . (N.3B. LP = long playing, 33 r.p.nu All
other records mentioned are 78 r.p.m.)
Stravinsky
Most of Stravinsky's major works have been recorded, and are
readily available, both on 78 and 33 r.p.m.
Milhaud
La Creation du Monde (Columbia)
Miniature operas (Columbia)
Extracts from the Oresteia (including Les Eumenides) (Fr.
Columbia)
Nos. i, 2, 3 and 5 of Cinq Symphonies (Concert Hall, U.S.)
Suite, Protee (Victor)
Bart6k
A good deal of Bartok has been recorded, including all 6
quartets (U.S. LP; some also available on 78 r.p.m.). Music
for Strings, Percussion and Celesta, Violin Concerto, Piano
Concerto No. 3, Concerto for Orchestra, Sonata for 2 pianos and
percussion, and a series made for U.S. LP. in collaboration
with the composer's son, including The Wonderful Mandarin,
Two Portraits, Dance Suite and Viola Concerto.
*The Record Gwdc, by Edward Sackville West and Desmond Shawe-Taylor
(London 1951), together with all its regular supplements, provides an up-to-date
guide to records available in Great Britain. Exhaustive information about all
types of records will be found in Clough & Cuming's The World's Encyclopaedia,
of Recorded Music (London 1952), which is also kept up to date by regular supple-
ments.
153
154 DISCOGRAPHY
Hindemith
Here too, a certain amount has been recorded, of which the
most important is the Mathis der Maler Symphony (Telefunken-
Decca), and some of the chamber works.
Schoenberg
Verklarte Nacht (HMV and Capitol LP)
Pelleas and Melisande (Capitol LP)
Gurrelieder (HMV)
Chamber Symphony No. i (French Classic)
Pierrot Lunaire (U.S.)
Piano Pieces, Op. n and 19 (Danish HMV)
Quartets Nos. 1-4 (U.S. LP)
Ode to Napoleon (Esquire-Classic)
Complete Piano Works (Esquire LP)
Serenade (U.S. LP)
Suite Op. 29 (Classic)
Prelude to Genesis Suite (Artist, U.S.)
A Survivor from Warsaw, Kol Nidrei, 2nd Chamber
Symphony (U.S. LP)
Berg
Songs, Op. 2 (Esquire-Classic)
Three Fragments from Wozzeck (Columbia)
Chamber Concerto (Esquire-Classic)
Lyric Suite (Polydor-Decca)
Violin Concerto (Columbia LP)
Seven Early Songs (U.S.)
Piano Sonata (U.S.)
String Quartet Op. 3 (U.S.)
Woz&ek complete opera (U.S. LP)
Lulu complete opera (U.S. LP).
Der Wein (Capitol LP)
Webern
Selection of Chamber Works (including 5 Movements for
string quartet, Op. 5 U.S. LP)
String Trio (Decca)
Symphony (Classic)
Cello pieces Op. 11 and Saxophone Quartet (U.S. LP)
DISGOORAPHY 155
Busoni
Die Ndchtlichen (Polydor)
Sonatina 5 (Friends of Recorded Music, U.S.)
Fantasia in memory of his father (Columbia) and several
other piano works recorded by Egon Petri.
Van Dieren
Nothing, unfortunately, seems to have been recorded.
Stymanowski
ist Violin Concerto (Parfophone) otherwise seems to
be represented only by some unimportant pieces
The Fountain of Arethusa and Theme and Variations in
B flat (both Columbia): also Mazurkas, Op. 50
(HMV) and fitudes, Op.33 (U.S. Columbia)
Jandcek
Concertino for Piano and 6 Instruments (Supraphon)
String Quartet (Kreutzer Sonata) (Supraphon)
Overtures, Mafcropoulos and Katya Kabanova (Supraphon)
Music from "The Cunning Vixen" (Supraphon)
Taras Bulba (Supraphon)
Laski Dances (Supraphon)
Capriccio for Piano (left hand) and Chamber Orch.
(Supraphon)
Various smaller choral works (Supraphon)
Sinfonietta (HMV)
Diary of a Young Man who Disappeared (Supraphon)
Glagolithic Festival Mass (Supraphon)
Ives
Concord Sonata (U.S. Columbia)
2nd Quartet (Nixa, Period)
No. 3 of Three Places hi New England (Artist, U.S.)
Violin Sonatas 2 and 4 (Alco and NMQR, U.S.)
Holidays, Suite (NMQR)
Songs (NMQR and Concert Hall, U.S.)
Varise
Octandre, Integrates, lonisation, Density. 217 (U.S. LP)
156 DISCOGRAPHY
Valen
Violin Concerto (Norwegian HMV)
Le Cimetiere Marin (Norwegian HMV)
Symphony No. 3 (Norwegian HMV)
Hdba
Various works in J and tones (Supraphon and Esta)
INDEX
d' Albert, Eug&ie, 65 d'Indy, 126
Ives, Charles, 124-6, 133
Bach, G. P. E., 3, 132
Bach, J. S., 1-4, 6-9, 13, 25, 66, Jandcek, 7272, 122-4
III, Il8, 121
Bart6k, i, 5, 13, 21, 32, 35, 44- Klebe, Gisclher, 147
54, 55, I4 1 ' 2 Klengel, 3
Beethoven, 3, 66 Kfenek, 111-117
Berlioz, 133
Berg, Alban, 8, 72-3, 78-81, 93- Lambert, Constant, 29
8, 99, 104, in, 112, 116, Leibowitz, Ren<, 73*, 77*, 102,
104, no
Blorn, Eric, 13/1
Boulez, Pierre, 147
Brahms, 3
Busoni, 5, 118-9, IJ
Bush, Alan, 134
Liszt, 5, 8-9, 44, 116, i 18, 133-4*
145
Garner, Mosco, 5/2, 15, 32^
Debussy, 20, 44, 71-2, 121,
133-4
Dent, Edward J., 119
Dieren, Bernard van, 119-121
Gesualdo, 3-4, 7, 10
Gray, Cecil, 4*1
Haba, Alois, 128/1
Handel, 3
Haydn, 105
Heseltine, Philip, 4
Hindenuth, i, 21, 55-70, 72, &
Hdlderlin, 103
Machaut, Guillaume de, 66
Mahler, 13-15, 16, 72, 133
Mendelssohn, 3
Milhaud, i, 21, 34-43, 47, 53,
69, 143, 147
Mozart, 3, 132
Mussorgsky, 72
Nono, Luigi, 147
Paganini, 133
Palestrina, i, 3, 6, in, 113
Puccini, 72
Purcell, 3-4
Ravel, 20
Reger, 9-10, 72, 130
Reich, Willi, 94, 103
Roussel, 126
Rufer, Josef, 7971, 106, 108,
149-150
158
INDEX
Schoenberg, i, 3/1, 5-6, 16-21, Szymanowski, 33-4, 50, 121-2,
30, 34, 44, 61, 66-9,
98-9, 104-111, 115-6,
119, 121, 124, 126, 130
Schubert, 134
Schumann, 3
Scriabine, 20
Spohr, gn
Stein, Erwin, 76*2
Stockhausen, Karlheinz, 147-9
Strauss, Richard, 11-13, 3 2
71-2, 1 1 6, 133
Stravinsky, i, 5, 14, 21, 22-31,
32, 52, 53> 66, 69, 127, 132, Widor, 126
133
Valen, 129-131, 143
Varese, 126-8, 149
Vaughan Williams, 132
Wagner, i, 3, 5, 9, 66, 71, 72,
93* !05> n6, 120, 133
Webern, 72, 73, 75, 79-80, 93,
99-104, in, 115, u6, 121,
i33-4 r 42 5 14
Wedekind, 97
147
Wildberger, Jacques, 147
Great XZiritam by CJ. Tinling *F Co-
