Searl 20th Century Counterpoint

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.

Copyright 1954 by Vifilliams and Jforgate Ltd* in Great Britain

Printed in Great Britain

CONTENTS PAGE PREFACE

Vli

ACKNOWLEDGEMENTS

ix

CHAP. I II

III

INTRODUCTION

I

THE DEVELOPMENT OF CHROMATIC COUNTERPOINT STRAVINSKY AND EXPANDED DIATONICISM

IV MILHAUD AND POLYTONALTTY

V

BART6K.

AND THE FREE USE OF DISSONANCE

VI mNDEMTTH AND VII VIII

IX

DIATONICISED CHROMATICISM

SCHOENBERG AND TWELVE-TONE COMPOSITION SOME INDEPENDENTS CONCLUSION

A NEW HYPOTHESIS

7

22

32

44 55 Jl

Il8 132

POSTSCRIPT, 1954

147

BIBLIOGRAPHY

15!

DISCOGRAPHY

153

INDEX

157

PREFACE is sub-titled "A Guide for Students"; that is to say, 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

THIS book it is

interested,

may

care to follow

up

for himself,

a complete " guide to modern " a land of signpost on the way; it is music 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 This book

of composers

therefore, not only intended as

is,

who

represent various different tendencies in 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

modern music, and

to discuss their

vii

AUTHOR'S PREFACE

viii

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 construction 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, Zenomukiado, Vdllalat, Budapest. HZNDBMTTH: Messrs. Schott & Co. SCHOENBERG: Universal Edition, Wilhelm Hansen Musikfbrlag (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 (London) Limited. *For "A Survivor fiom WaraaV.

with

Universal Edition

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 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 (if he

TWENTIETH CENTURY COUNTERPOINT

2

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 counterpoint 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 I

who

has been murdered.

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 predominant 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 twelve-note scale which has not yet taken a definite

by a

We shall of course be considering this question of tonality in

INTRODUCTION more

3

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 counterpoint 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 accompaniments 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 contrapuntal 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: detail as

*Ct "Apollonian Evaluation of aDwnyrian Epoch", Chap. "Structural Functions of Harmony" (London, 1954).

XII of Schoolboys

TWENTIETH CENTURY COUNTERPOINT

4 Ex.

i

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

Here the sequence of chords

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 Here is a typical logical contrapuntal movement of the parts. is heart from PurcelTs inditing". "My example Ex. a

Chorus

String

The

such progressions could be written meant that 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 fact that

there

was no

scales

is

clearly established

far too

complex for

me to describe here, and in any case

not part of my subject; but it is sufficient to say that modal elements are found even in Bach and later composers) . Now we

is

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 1 is no need for me to recapitulate it in detail IJLJS^Jif&dient to so different that each other as from by 1910 composers say 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

but the fact remains, whether we like it or not, we have nowfgot a twelve-note scale instead of a seven-note

his followers;

that

one.

We

can use

chromatically as

we cannot

this twelve-note scale as diatonically that is according to our taste

or as

we wish

escape

its

implications.

In

this

book

I

hope

but 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 Century Harmony (London 1942).

B

A

Study of Twentieth-

TWENTIETH CENTURY COUNTERPOINT

6

in any case a good many of them arise as the result of contrapuntal 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 predominantly 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

much earlier ages. The Gesualdo an advanced use of chromaticism, shows above example quoted and we can find similar examples in Bach and others. Here is a passage from the Fugue in B minor (Book I of the Wellpresent in the music of

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

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. it is

(Compare

also the

Chromatic Fantasy and Fugue, which 7

TWENTIETH CENTURY COUNTERPOINT

8

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 before introducing a later entry of the subject in 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

D

G

DEVELOPMENT OF CHROMATIC COUNTERPOINT

Q

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 considerably 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 ostinato

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

A considerable use of chromatic harmony, chiefly for

X

and "side-slip" can

also

be found in the works of Spohr.

purposes of modulation

IO

TWENTIETH CENTURY COUNTERPOINT

of chromatic and diatonic elements which makes Reger's style 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 illogical

structural function.

An even more typical example of Reger's methods seen in one of the variations from the same work

may be

:

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. typical example is this passage from Ein Heldenleben, from the section where Strauss introduces themes from some of his earlier works.

A

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, example shows the final entry. The celli are divided into four parts, each being doubled an octave below by double basses. The four-bar Cello consists fugal theme

D

and A;

this

(in

i)

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 somewhat 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 complicated 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 instruments 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, (Musical Pilgrim series, London 1930).

The Rose

Cavalier

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 of the 8th Symphony is typical passage from the first movement

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 stretto uses all the classical devices of augmentdiminution and inversion, combined with modulation.

instrumental ation,

y

Ex. 10

Many other passages in Mahler show the same kind of treatment quotation from "Das Lied von der Erde" in 51), and it would be easy to multiply op. 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. survey of this transitional period would not be complete (see for instance the

Mosco Garner,

A

cit. p.

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 compositions, 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 predominantly 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 counterpoint may be seen in an extract from Pelleas and Melisande (1902) .

DEVELOPMENT OF CHROMATIC COUNTERPOINT

I*J

at represents the meeting of Pelleas and Melisande fourfold in theme the Melisande the castle tower; appears 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

The music

and bass Ex. 12

clarinet,

and

also the Pelleas

theme on

solo 'cello.

TWENTIETH CENTURY COUNTERPOINT

l8

In first

string quartets and the increases, is often in a perpetual state of modulation; yet

his following works, the first

two

Chamber Symphony, the chromatic element

and the music 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 shows an passage from the First Chamber Symphony (1906), 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 sehr auadrucksvoU

i.vi.

Chromatic harmony could hardly go further than this without overstepping the bounds of tonality altogether, and

TWENTIETH CENTURY COUNTERPOINT

2O

in the finale of his next work, the 2nd/ String Quartet, Schoenberg wrote some passages which are almost impossible to explain from a tonal point of view. 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.

A

Ex. 15

Ylni

This chapter has dealt exclusively with composers of the school, because it is here that the use of chromaticism seen in its most acute form. Some French and Russian

German is

composers, however, notably Debussy, Ravel

were

and

Scriabine,

working on similar lines, chiefly in the free use of altered and whole-tone chords. Though partly used for impressionistic effect, these chords tended to remove the feeling of 1 tonality. As Schoenberg remarks , "Debussy's harmonies, without constructive meaning, often served the coloristic also

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 representing 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 a use which extensively based on the use of ostinato figures 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

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 is

decorations, cleverly written so as to suggest contrapuntal development. The nearest it gets to true counterpoint is in again based on an ostinato. passages like Ex. 18 [p. 24]

The

not contrapuntal in the true sense is bars, unaltered i.e. of elaboration here for the one Stravinsky part; except thinks rhythmically and dramatically, rather than contrafact that this

is

shown by the immediate repetition of these two

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*

TWENTIETH CENTURY COUNTERPOINT

24 Ex. 18

Ex. 19

S en

3.

"F" n

The

r

r*

chorales in "L'Histoire

T T

du Soldat"

I

'

i

f

(1918) do provide 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.

some genuine four-part

STRAVINSKY AND EXPANDED DIATONIGISM Ex. 20

Largo

quite simple and almost entirely diatonic; carefully arranged so that the parts do not "fit" together in the accepted classical sense. This is the socalled "wrong note technique" of which Stravinsky is an adept master. It consists in substituting for what the ear expects

Here each part but the writing

is

is

something different which sounds more "interesting" but has

no

real logical function. more serious attempt at contrapuntal writing

A

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):

The

first

[Ex. 21, p. 26].

subject (hi the bass) has previously been exposed by it is typical of Stravinsky in that it goes round and few notes and never seems to progress anywhere.

the orchestra;

round a 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

The second

the voices imitatively passage again introduces figure on the brass.

against a chorale-like Ex.23 S.A.

T.B.

27

TWENTIETH CENTURY COUNTERPOINT

28

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

writing; his parts

move

main contribution

freely against

to contrapuntal 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

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

relations.

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 In

key.

this appraisal make it clear that I

of Stravinsky as a contrapuntalist, I must

am not discussing his place in modern music

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 shortwindedness and a curious inability to get away from the principal 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

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.

TWENTIETH CENTURY COUNTERPOINT

3O

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.

a composer whose methods can be studied is a very important part of counterand no one can deny that Stravinsky is a master of

Nevertheless he

with advantage. point,

is

Rhythm

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

rhythmic

.

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 classical harmony?

Ex. 20 according to the rules of

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 accompaniment (not in the form of an ostinato!).

4.

Analyse the second movement of the (published by Boosey and Hawkes).

5.

Symphony

of Psalms

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 Here are the

first

three entries

:

Ex. 25

i

nil fo.

f1 eU.

31

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, ground of bitonality and polytonality.

for

a

fuller

account of the historical back-

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

A major,

the second in F#, the viola in Eb and the cello in C up to a diminished seventh. However, if we take a typical passage from it and write all the parts out in with accidentals, the fourfold tonality does not seem G

of

in fact adding

major

so apparent, especially if

D$

we

regard

Eb

as

major.

TUT

T

T

enharmonic

for

TWENTIETH CENTURY COUNTERPOINT

34

One does not really hear the simultaneous use of four keys; instead one gets the impression of constant enharmonic modulation 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 exploited this idea in the fourth of his "Cinq

of

this.

is

built

is

Symphonies" (1921)

Written for ten solo

on the

results,

and Milhaud The finale of

of his earlier works.

many

a good example

entitled "fitude"

strings, it is

and

followingfplan: Bar

Instrument

Violin Violin Violin Violin

Key

i

F

2

C

3

4

Viola Viola

2

'Cello

i

'Cello

2

i

147

Key

25 subject

2nd subject

2nd

subject subject

2nd

ist subject ist subject ist

C

Instrument

22

2nd

G F

19

and subject.

G D A A D

D. Bass i D. Bass 2

16

13

subject

ist subject ist subject

Bar Violin Violin Violin Violin

i

2 3

4

Viola Viola

2

'Cello

i

i

'Cello 2 D. Bass i

D. Bass 2

F

C

G D A A D G C F

28

30

32

34

36

37

38

39

40

44

ist subject ist subject ist subject ist subject

ist subject

2nd

subject

2nd subject 2nd subject 2nd subject and subject

It is a strict canon in ten parts on two subjects; each subject 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

is

MILHAUD AND POLYTONALITY is

35

carried out twice, once starting from the bottom of the

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 movement 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. orchestra,

Ex. 29

Bartok in the (Incidentally a similar scheme was adopted by Percussion and Celesta for Music his of first movement Strings, see p. 48). (1936)

TWENTIETH CENTURY COUNTERPOINT

36 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

15-22 23-4 25-7

28-9

3-i

32-5 3^-7 38-43 44-S 49-51

Top Middle Bottom

Middle Section

Exposition

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

C and F# with the second. The student 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 group of themes, and

is

recommended

to

52

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

of the same opera provides an even more startling on a gigantic scale, of polytonal writing. Conceived example it is a kind of perpetually-moving ostinato. This extract is typical of the texture:

The finale

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 b (the fact is apparent from the two bars that the alto part is really in before those quoted here). The first orchestral stave has a twobar 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

D

A

MILHAUD AND POLYTONALITY pattern in

B

39

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 sound forced and ugly when taken out of their context and played coldly on the piano. Nevertheless when performed by this

singers, chorus is

no denying

and orchestra as part of an operatic scene, there immense dramatic effect my strictures on

their

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 considerably. 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

TWENTIETH CENTURY COUNTERPOINT

40

passages of considerable complexity. Ex. 34, extract from the scene where the ancient gods of stir up the sea in order to wreck Columbus' fleet

there are p.

39

is

Mexico

many

an

(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 constantly changing tonality rather than of true polytonality. This passage is followed by a chorus (pp. 240-251) accompanied by the figure in the second orchestral stave of Ex. 34, but with a varying number of crotchets between the demisemiquaver group in each part. Against this the first six bars of the theme of the canon appear as a two-part double palindrome. Here is the central turning-point (bars 1420-1):

u-pe dessus I

mords (est

J

J.

tr&v&iUe

J>

J

.

leur

l'e

MILHAUD AND POLYTONALITY be seen

41

that, of the four parts figure, the top part has five crotchets It will

which have the ostinato between each demisemithe third three and the bottom

quaver group, the second four, 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

played twice forwards and twice backwards in each of the two top 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; It is

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

any more in actual composition, unless a special effect 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 rigidly is

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 at once with kind of continuity, though of course keys any 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, polytonality 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 polytonality 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 contemporary 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

2.

Write polytonal movements on schemes similar to the finale

3.

Write polytonal passages on the lines of Ex. 33

by

chords).

of the same symphony

4.

(cf.

p. 34).

(i.e. including chorda! parts as well as single lines if desired), but not necessarily using repetitive ostinatos. 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 contrapuntal or a hafmorile composer;" Ke ^\v^7A7^^ster"oCbioilL i^aethods of writing, and^used either^ pxJbothJn combmation, according to J^aee&^.p^^j^TO^.TT^Ttf.^, 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 fourpart fugato which has been compared to the first movement of Beethoven's late G sharp minor quartet; in Ex. 37,

A

,

me third and fourth entries (in cello and viola) 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 [P- 45] are

.

It will

could hardly call the writing atonal, it is yet so chromatic that is little definite sense of key it could best be described

there f

as "fluctuating tonality", in Schoenberg's phrase. It is in fact 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, 44

Bagatelles

BARTOK. AND FREE USE OF DISSONANCE

p

motto e$f>ves$

im

.

45

pp

though not always primarily contrapuntal, tendency to a marked degree, and are well worth exemplify as they provide the key to Bartok's later development. studying, A simpler example of Bartok's chromatic counterpoint may be seen in this passage from the first Elegy for piano ( 1908) Elegies, Dirges, etc., this

:

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.] Bart6k*s approach at Perhaps the best way of describing had made tonality morei he that to this time would be say still while that to is upholding the supremacy fluid: that say,

TWENTIETH CENTURY COUNTERPOINT

46 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 Profana (1934). This passage begins in and ends on the dominant of Bfr; but the parts move freely and

D

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)

TWENTIETH CENTURY COUNTERPOINT

48

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

worth studying in detail, becomes proceeds, and eventually ends up a good example of Bartok's use of classical devices

more and more simple in unison for

dramatic

The

as

is

it

effect.

movement of the "Music

for Strings, Percussion a very instructive example of Bart6k's later contrapuntal methods. It is built up on a series of entries arranged in the following pattern :

and

first

Celesta"

is

Upperpart:

B

*

D B

Lower

part:

Eb

The

Ab

notes given above are the first notes of the theme on each From the central climax (Eb) onwards, the theme has again been reached, there appears in inversion; and after is a short coda in which the original and inversion are heard together. 'JBut the movement is not just worked out in terms of entry.

A

BART OK AND FREE USE OF DISSONANCE

49

much

variation in the treatment of pure mathematics; there a fragment of it), there are state entries the theme, (some only short and connecting episodes, and the many subsidiary parts to the central climax is much longer than the descent is

build-up

is in fact a very fine and moving piece of Bart6k's of one greatest inspirations. This short music, and extract -will give some idea of the texture.

from

it

to the coda. It

Ex.43 content

Vkl.

TWENTIETH CENTURY COUNTERPOINT

5

Here again the music

is

purely chromatic; but in Bartok

and always know that tonality will ultimately be asserted, the movement ends with a very definite cadence on to A. In the slow movement of the Violin Concerto (1937) we

we

a canon at close find another of Bart6k's favourite devices 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.

F#,

28)

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

51

Ex, 46

Vt*.

intended, of course, is a cheerful, pastoral effect, 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 Ex. 37); these two examples show the development of (c 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

All that

is

gradually building

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

tonally a tendency observed in many works Bartok's last years. These are the third to fifth entries:

definite

^

of

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 semitones 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 can see this both in his result was always satisfactory. early works (e.g. Ex. 37) and in his later ones (e.g. Ex, 47);

We

and in the first movement of the Music for Strings, Percussion and Celesta (cf. Ex. 43) we find him varying the countersubjects 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

:

First movement (Zenomukiado) String Quartet No. i 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 representative conspectus of Bart6k's contrapuntal methods. "Mikrokosmos", 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 1 published a theoretical book on composition, 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 chromatic scale within a tonal framework. We have seen how this to problem arises in the case of Bart6k, and how difficult it is his procedures; but of theoretical real explanation any give Hindemith felt that some explanation of this type of chromatic one. He writing must be possible, and he set himself to find and started, naturally enough, from the harmonic series, of each of and the order find to relationships degree attempted 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

4

3

5* the vibration

(The overtone numbers are given below the notes, numbers above). By means of a somewhat mathematical, but the vibration numbers by the quite logical process of dividing 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

TWENTIETH CENTURY COUNTERPOINT

56 Ex. 50

(The whole passage (op. cit. pp. 32-43) is worth studying in. 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 detail as

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 55 Hindemith, by the way, calls "Combination tones ) I have the American the "note" rather than used English throughout or German "tone" in quotations, except in the case of "twelvetone 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). 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;

A

he

calls this "Series 2".

HINDEMITH AND DIATONICISED CHROMATICISM The

intervals in this table

as

we move from

become left

57

pure", as Hindemith Hindemith shows that

"less

to right.

puts 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 it,

The tritone, he says, has no theoretical 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 differential notes.

root;

distributed in just the opposite order (pp. 88-9) .... The has no definite significance, either harmonic or melodic"; it needs a third note added in order to determine its

tritone

Hindemith next attacks the harmony, on four grounds

position,

traditional theory of

:

(i)

(ii)

(iii)

The

old theory that chords are constructed by the superimposition of thirds cannot explain many chords, e.g. those

based entirely on fourths, Chords cannot now be considered invertible, as this would often completely alter their character, The conception of "altered chords" is out of date now that harmony is chromatic and no longer related to a diatonic system.

TWENTIETH CENTURY COUNTERPOINT

58

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.

(iv)

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

'best' interval is the perfect fifth A-E, and 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

In the its

first

root

A

chord the

is

whole chord. Traditional harmony would probably agree with Hindemith in his analysis of the first chord, regarding it as an minor chord A major chord with major seventh + an (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

A

.

I think rightly; it

is

surely

more

logical to take the other perfect

A E as tie fundamental interval, and to regard the whole an A major-minor chord with flattened seventh and added

fifth

as

(The student may try these chords for himself, putting under them in turn the alternative roots suggested, and make sixth.

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.

his

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 development 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. Hindemith next tackles the question of chord progressions in some Series 2, p. 56) that as the harmonic detail, observing (c 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; B. Containing Tritone

A. Without Tritone

Without seconds or sevenths 1 Root & bass note identical 2. Root lies above bass note. (i.e. major & minor triads & their

I

Without minor 2nds or major

II

yths.

.

Minor yth

only; root

&

(i.e.

inversions)

"dominant sevenths")

With major ands or minor

HI With

seconds

or

.

2.

Root Root

&

Root & bass note identical Root lies above bass note With more than one tritone

bass note identical

lies

above bass note

V

Indeterminate (Chords built of major srds or 4ths only)

yths

or both

sevenths or

both 1

bass

note identical

IV With minor

ands or major 7ths

or both 1

.

2.

VI

Root Root

&

bass note identical

lies

above bass note

Indetenninate (Chords built of minor 3rds only)

TWENTIETH CENTURY COUNTERPOINT

60

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 detrimental to them "the absence over a long period of the strongest intervals, the fourth and fifth; the melodic interval of the 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,

tritone;

the use of passing notes, anticipations etc." The presence of modulation can also be established from these root-progressions: i.e.

p. 151, Ex. 116). Further, the different tonalities

(op.

cit.

through which a piece moves themselves form a succession of roots which shows the construction of the piece as a whole; and the tonal centre of this secondary root-succession is thus the tonic of the whole piece. 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 polytonality. "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

We

.

.

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

number of composers who

issue works that they 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

considerable

call atonal.

To what

do is to examine all contemporary phenomena and if possible 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 considerable elements of tonality in Schoenberg's Piano Piece, Op. 33a (cf. p. 67). I do not therefore feel that Hindemith is

to

find

me

only justified in saying "the existence of this style seems to to lend final confirmation to the fact, everywhere to be observed, of the disappearance of understanding judgment and critical 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 Since organic work, growing see the futility of the game out of natural roots, will always stand on a firmer basis than the

sense in the field of music."

:

is not a practical principle of composition." Hindemith now takes a practical example in order to show

arbitrary combination of different elements, polytonality

TWENTIETH CENTURY COUNTERPOINT

62

method of working of his

system. Though this concerns a it will be useful to follow it in chordal progression, purely detail, as it exemplifies Hindemith's contrapuntal as well as his harmonic approach. He takes the following progression:

the

Ex.53

have somewhat simplified Huidemith's analytical table from original, omitting certain points of purely harmonic Hindemith says that this progression "sounds interest). horrible", and sets out to offer criticisms and improvements. (I

the

He

finds the linear construction poor, except for the top part is no plan in the two-part framework,

but one; he says there

and that "the weak fourth dicts the intention to

G-C in the fifth chord flatly contrathis the harmonic climax". He

make

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

IX (p. isGff.) some alternative suggestions will be these would appear to fit better with the principles of found; traditional harmony, which (as I suggest there) can still be exChapter

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. discussion (pp. 160-3) Hindemith produces of this progression, as follows: version "improved"

After

some

an

Ex.54

Personally I cannot see that this is any improvement; admittedly 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 the provides a welcome contrast and does actually produce 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 After a short pursuing his exposition of them to its conclusion. chapter on inessential notes (changing notes, passing notes, Hindemith more or suspensions, anticipations, etc.) in which less agrees with the classical method of treatment of these, he to a melody, he says, proceeds to discuss melody. In listening 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 the other hand the rootbe independent of one another.

On

melody may fully coincide with that of the harmony. general Hindemith then discusses in detail (pp. 187-193) the interrelation 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 succession of the

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 for himself.

ir

The page- and example-references in the remainder of

this

chapter apply not been

(unless otherwise stated.) to Hindemith's book; unfortunately it has possible to obtain permission to reproduce more than the handful of

quoted above.

examples

HINDEMITH AND DIATONICISED CHROMATICISM 65 next, without taking into consideration the less important parts of the melody lying between these points, is called the stepprogression" (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 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 twelvetone 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-progression, when the need for intense expression requires that the attention shall be riveted by the conspicuous strangeness of succession

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.

clear that Hindemith's schemes of root- or degreeIt progression and step-progression do provide a useful basis for is

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 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 rootprogression. 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 reconciliation of its linear and harmonic aspects. We shall be able to

is

:

TWENTIETH CENTURY COUNTERPOINT

66

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 that therefore to this extent Hindemith's methods are justified; but it remains to be seen how far they can be

shape, and

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 Stravinsky'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). 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

We

*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 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

worth

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 of course obvious that Schoenberg would have objected 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 It is

to

basis,

and

modulating the

is what the listener's ear actually instead of "atonality" we have constantly

I believe that that

does in practice;

i.e.

tonality. I

to discuss this concept (and also analysis employed above) in a later

hope

method of chordal

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

modern developments and will provide technical, 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 Hindemith'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

explain all apart from

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 has published a style to the student, as Hindemith himself

volume of "Exercises in Two-Part Writing" (Schott, London, in three-part 1948), which is to be followed by further exercises diatonic in are far so exercises The mainly given writing. character. In addition, in the German edition of his composition in treatise, Hindemith gives a list (for some reason not included

TWENTIETH CENTURY COUNTERPOINT the English edition) of various works of his own which particuOf these I quote the following larly exemplify his principles. 7O

(all

published by Schott

&

Go.)

:

String Quartet No. 3, Op. 22 (1922) 2 Kleine Kammermusik, Op. 24 (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 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

n

Hindemith's contrapuntal technique.

CHAPTER

VII

SGHOENBERG AND TWELVE-TONE COMPOSITION WE may now return to

Schoenberg at the point where we left 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

him in Chapter II

that

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

of their "sense-interrupting effect". One no of Wagner's dissonances or preparations longer expected resolutions of Strauss' discords; one was not disturbed by Debussy's non-fdnctional harmonies, or by the harsh counteruse point of later composers. This state of affairs led to a freer of dissonances, comparable to classical composers* treatment of diminished seventh chords, which could precede and follow so

had

lost the fear

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 comprehensibility. 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 contradictory terms as concord and discord". (Cf. Hindemith's treatment 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 dissonances. 1 This meant in fact that what

more remote 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,

had a constructive meaning. Richard Wagner's harmony had promoted a change in the logical and constructive power of harmony." He then goes on or at any other point really

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 Hindemith'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 a

73

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 and 19, 5 Pieces for Orchestra, Op. 16, the Pieces, Op. dramas Erwartung and Die gliickliche Hand, and Pierrot Lawaire; series

n

Op. 3, Three Pieces for Orchestra, 6 and the Op. 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 comparatively 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 Berg's String Quartet,

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 his School (Hinrichsen, London, 1954).

and

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. similar preoccupation may be seen in the first of Webern's Five Movements for String Quartet, Op. 5, written in 1909.

A

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

^

^

^

[iJirJJlu/n'Y}

^ i

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]. 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

The whole

canon by

inversion.

Ex.59

tuut

The

Win -

k*uty

In

form

m*

"Der Mondfleck", is even more remarkable. 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 1 8th

piece

It consists of

(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 In a slightly later work, Die

Jakobsleiter,

an

oratorio

Schoenberg left unfinished and unpublished at * get a premonition of twelve-tone composition.

1

See Ren6 Leibowitz, Introduction

discussion of this passage.

it

la

77

which

his death,

we

musique de 12 sons, pp. 49^, for a fuUer

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. Scene 4 of Berg's opera Woz&ck, written between 1917 and 1921, is a Passacaglia, based on the following twelvenote theme.

Act

i

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 technique. 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 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 serial technique; tile-fifth piece is

played in reverse order. Ex.

62

Theme Andante Cl.

canon of Webern's Op. 16 also shows the use of a technique which is atonal but is not based on a twelve-

The serial

note

first

series.

[Ex. 63, p. 80].

is a strict canon with one part an inversion, the voices entering at ever closer intervals towards the climax.

As will be seen, this a

fuller analysis

of

this

Twelve Notes, London 1954.

tendency see Josef Rufer, Composition with

TWENTIETH CENTURY COUNTERPOINT

8o 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 1 analyse here in detail 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) ; The Gramophone, Dec. 1950, for a fuller analysis.

also

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



~

ri

I'

08

ground is harmonic; but the progressions are of an unconventional type. The student is also recommended to examine Busoni's Second Sonatina and Fantasia Contrappuntistica for full his tendencies. piano, which will give a further idea of 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

A

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 extremely complex, as in the "Chinese Symphony", the 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): is

actual

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 impressionism 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 of the slow movement of his Symphonic p. 122, the (climax

Goncertante, Op. 60) illustrates this point. [Ex. no].

Here the piano and wind parts decorate the

mam

theme and

holds the support the harmonies, while a solid bass pedal 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 complithere is nearly cated-looking arrangements of chords but a of means sustaining note of always a firm underpinning, by whole the makes which some kind, complex easily assimilable. of use "polytonality" see Ex, 28, p. 33). (For Szymanowski's

TWENTIETH CENTURY COUNTERPOINT

122 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 The texture is usually entirely transparent, and the voice parts follow the natural rhythm of speech against a continuous orchestral background; this passage from his last opera, "The House of the Dead" is typical. effects.

Ex.

in

n \nw

SK.

o-ci 5M

vy-pl.ie-M. vy-pi.ie-W. -

*rM

/

-je

5W..(..

I'nmEff Tf u* tj^VV Ho-din-k,

Ei*

f*,-fi.fi*

ii^-*-d Bb, etc. In fact, instead of regarding this type of writing series

D

CONCLUSION

A

NEW HYPOTHESIS

14!

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 as having

of rest. (Of. also the analysis of a passage p. 67 above). 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,

merely the

final point

from Schoenberg's Op. 33a,

We

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 harmonic provisional method of analysis for predominantly will which each of note root the find chord, (i) passages 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 twelvetone 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 take a simple example first, contrapuntal passages. We will ist Bart6k's the quotation from Quartet (Ex. 37, p. 45>- Here in four parts; the roots music chromatically we have moving are as follows:

Bar Roots

4

3

i

F Ab

E

(Ab) Bb F

B

G (Bb)

I

(E) etc,

TWENTIETH CENTURY COUNTERPOINT

142

The

roots in brackets in bars 2

and 3

are used only in passing.

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 It will

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. 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. 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 bar;

We

*

A

possible

Bar Roots But

I

scheme might be as 2

3

F#

4

56

G Ab B

follows:

7

Bb C

8

admit that such an analysis

Ex. 94

9

10

G D

Bb is

n

12

13

F

D G E

by no means

14

15

satisfactory.

not quite so complex. Bars 1-2 are rooted on B, 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

which

is

acts as

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

very often is; the presence of a fifth or fourth in 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

bass,

though

it

the chord

sharply contradict them, he will approach very close to true can certainly accept a table of the type of atonality. 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 lefthand side of this table, the easier it will be for us to analyse it

We

144

TWENTIETH CENTURY COUNTERPOINT

We

traditional methods. 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;

by

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 twelvenote 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 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 contemporary 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.

is

Most composers do not, I imagine, consciously analyse their when they are writing music; their unconscious ear, trained in the classical past, will help them to produce the

roots

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 rootprogressions.

Can we

also retain the old forms, sonata, fugue, rondo, etc., It can, I think, be done, though

which depend on modulation?

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

which they were given by nineteenth-century composers and treat them organically, as Liszt did in his piano

associations

we may find that new possibilities are I feel it is better to control our material Personally opened up. itself and enlarge the forms rather than to put into the tight framework of the canon and fugue a type of music for which

sonata, for instance,

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

can complex system of harmony in which they partake, and we or the chord root of the to relation in a still hear complex melody 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 that come less use of its fundamental notes and more of those are still implied, fundamentals the but the in series; higher 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

TWENTIETH CENTURY COUNTERPOINT

146

chromatic scale; I also believe that every harmonic and contrapuntal 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 its

and a

historical past. But though also fundamentally an

it is

have helped

music

may have

evolutionary art,

to show that the same forces which processes in the past are still at work today, albeit substantially different form, I shall have achieved my

if I

governed in

and

revolutions,

purpose.

its

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-

some recent works of Stravinsky, like the Septet and the Shakespeare Songs. Meanwhile the younger com-

like texture in

posers have been consolidating the territory by their predecessors; here again there has been

first

no

explored

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

of composition."

A

direct ancestor of

a new technique

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

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 themselves. typical example is taken from the "Kontrapunkte " No. i by the young German composer Karlheinz Stockhausen

is

A

[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 the note-series run through the different instruments. Other composers who are tending in this direction include

how

Pierre Boulez (France), Luigi

(Germany) is

(Italy),

Giselher Klebe

and Jacques Wildberger (Switzerland).

obviously too early to

which

Nono

its

is

generalisations about a movement infancy, but certain points can be

make

as yet only in

It

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 and also to pass rapidly from one (cf. Varese's methods) 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. of an important Finally, I should mention the appearance his pupil and assistant analysis of Schoenberg's methods by London Josef Rufer, Composition with Twelve Notes (Rockliff, of authorised as the be This exposition regarded may 1954). "classical" twelve-tone technique, and it also discusses the innovations made by Schoenberg in his last works. Unforbe discussed in tunately its publication came too late for it to 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 majorminor tonality, Rufer deals with the concept of the Grundgestalt this is the musical phrase which is the (literally, basic shape) basis of each work and is its "first creative thought", in Schoenelse in the work is derived, berg's words from it everything This itself. concept applies equally to including the series Beethoclassical music, and Rufer shows how all the elements in 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 :

full "transitional" works, Op. 23 and 24, before giving a account of the principles of twelve-tone composition itself: to base a in this chapter he discusses whether it is legitimate music twelve-tone whether and one than more series, work on

some should tend towards athematism, as has been suggested by of uses the harmony melody, special writers. He next describes and rhythm in twelve-tone music, and gives a detailed exposi-

POSTSCRIPT, 1954 methods of inventing thematic material the final chapter deals with problems of form, including an analysis of Schoenberg's Fantasy for a most valuable violin and piano. Op. 47. The whole book is the to own subject, in both of approach account Schoenberg's is contributed by a number an and appendix practice: theory of contemporary composers, describing their individual methods tion of Schoenberg's

from a twelve-tone

series:

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 life. London 1936. London 1947, ofMusic WHITE, ERIC WALTER. Stravinsky. London 1947.

STRAVINSKY, IGOR. Poetics

Chronicles of my 9

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). Bela Bart6L London 1953. The Life and Music of Bela BarttL London HALSEY. STEVENS,

MOREUX, SERGE. 1953-

SELECT BIBLIOGRAPHY

152 Hindemith

HINDEMTTH, PAUL. The Craft of Musical Vol. I, Theory. London 1945.

Composition.

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. Von der Einheit der Musik. Berlin.*

New York

191

DENT, EDWARD J. Ferruccio Busoni. London 1933. VAN DIEREN, BERNARD. Down Among the Dead Men. London

1.

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. GoWELL, 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 longplaying 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 supplemented by enquiries at gramophone shops etc. regarding upto-date recordings1 (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, readily available, both on 78 and 33 r.p.m.

and are

Milhaud

La

Creation du Monde (Columbia) Miniature operas (Columbia)

Extracts from the Oresteia (including Les Eumenides) (Fr.

Nos.

Columbia) 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 supplements. 153

DISCOGRAPHY

154 Hindemith

Here too, a certain amount has been recorded, of which the most important is the Mathis der Maler Symphony (TelefunkenDecca), and some of the chamber works. Schoenberg

Verklarte Nacht Pelleas

(HMV and Capitol LP) and Melisande (Capitol LP)

Gurrelieder

(HMV)

Chamber Symphony No.

i

(French Classic)

Pierrot Lunaire (U.S.)

n

Piano Pieces, Op. and 19 (Danish Quartets Nos. 1-4 (U.S. LP)

Ode to Napoleon

HMV)

(Esquire-Classic)

Complete Piano Works (Esquire LP) Serenade (U.S. LP) Suite Op. 29 (Classic) Prelude to Genesis Suite (Artist, U.S.) Survivor from Warsaw, Kol Nidrei,

A

Symphony

2nd Chamber

(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

string quartet,

Op. 5

(including 5

Movements

for

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 otherwise seems to ist Violin Concerto (Parfophone) 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

Glagolithic Festival

(Supraphon)

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

Songs

(NMQR)

(NMQR and

Concert Hall, U.S.)

Varise

Octandre, Integrates, lonisation, Density. 217 (U.S. LP)

DISCOGRAPHY

156 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,

d'Indy, 126 Ives, Charles, 124-6, 133

Eug&ie, 65

Bach, G. P. E., 3, 132 Bach, J. S., 1-4, 6-9, 13, 25, 66, III, Il8, 121 Bart6k, i, 5, 13, 21, 32, 35, 44' 54, 55, I4 1 2

Beethoven, 3, 66 Berlioz, 133 Berg, Alban, 8, 72-3, 78-81, 938,

99,

in,

104,

112, 116,

Jandcek,

7272,

122-4

Klebe, Gisclher, 147 Klengel, 3 Kfenek, 111-117

Lambert, Constant, 29 Leibowitz, Ren n6, 120, 133 Webern, 72, 73, 75, 79-80, 93, 99-104, in, 115, u6, 121,

Stravinsky, i, 5, 14, 21, 22-31, 32, 52, 53> 66, 69, 127, 132,

Wedekind, 97 Widor, 126

147

Wagner,

i33-4

r

42 14 5

Wildberger, Jacques, 147

Great XZiritam by

CJ.

Tinling

*F

Co-