Bartok - Bela Bartok an Analysis of His Music 1971

Fin, publUbcd iD 1971 by SWlDIorc Prcu Ltd wuIcr their auodaud imprint: KabA" Avcri1l

Copyri,bt to £m6 Lctadvai 1971

Rcvilcdrcpdnt 1979 Mw.lc:al cumplca ate quoted by k1nd pcrmiIaloD of &oc.cy "

Hawka Lld and AlCtcd A. KalmUl Lui (Univena1 EditioD). The publiahen would Iikc to &hank AteI O'1a Cor bit "'&ance in tbe prcparatioa of the mtWc c:xamplca.

ISBN 0 900707 (K 6 Printed and

bound In CIUI Brhain UDWOOO .UIlH uwrn.D Trowbridlc

by

Contents

IDtroduetion Tonal

..

Principles

The Ad 5)'1lem

Form Principlcl Golden Seclion Fibonacci Series The Vae of Chorda and Interva4 Chromatic S)'Item

Diatonic Syatem

'7 '7

..

'7

App.endUt I

..

Appendlx n

'03

Appendlx III

110

Introduction

The publication of this .tudy of the music ofB6a Bart61r. u an

important event. Many descriptive analyses of particular works ofhia have appeared, but here for the fint time

in the

English

language it an. authoritative and convincing exposition of the theoretical principles which the compoaer worked out for himaelf but refrained,

at

far

u

is known, from expounding to

anyone during hiJ lifetime, either

in

writing or by word of

mouth. Thus we owe both the author

and the publisher a

ainccre debt.

Mr. Ern6 Lendv"; has diJcloacd the fact that Baa Bart6k, iD

biI early thirtiel, evolved for himIelfa method ofintegratin, all

the dementi ofmuaic; the scaIea, the chOrdalltructW'tl with the melodic motifs appropriate to them, together with thC"'pfOa portiODl of length as between movements in

•

whole work,

main divisions within a movement such at exposition, develoP"" ment and recapitulation and even balancing pbrucs within

aecti01lJ of movements, according to ODC single basic principle,

that of the Golden Section. Some luch mathematical proportion wu fin. proposed .. an "cathetic principle by Chalde.... in the

vii

3rd miUe:nnium D.C., taken up by the Gree:ks two thousand years later and rediscovered during the Renaissance:, but never systematically applied to music at any time. (There exists onc single string quartet movement by Haydn, composed in Ie:ngth according to Golde:n Se:ction proportions, but this is morc of an intellectual quirk of the compwer's than a principled pro­ cedure.) Bart6k discovere:d a way of deriving the basic pentatonic intervals A-G-E and the first inversion of the major common chord E-G-C from the Golden Section in its prac­ ticable fonn of Fibonacci's series of whole numbers. From there Bart6k proceede:d to the e:stablishment of two fundamental scales, dCKribed by Lendvai as "diatonic" and "chromatic", containing respectively seven and eight notes inside the octave. Within thiJ framework Bart6k applied his theory of "tonal axes" as the basis of tunality. It is an implied thesis of the book that the pentatonic scales of the earliest folk music, the modes of oriental ilDd medieval art and folk mwic and lastly, the major and minor scale idiom of European art music of the 17th, 18th and IDth centuries, are stage.! on the road towards Bart6k's complc:te integration of the deepest fundamentals of tonality with perfect formal proportion. During the past finy years there have been various scienti­ fically orientated attempts within musical theory to show the way forward to the composer and to help him to find a finn foothold in the period of chaos which followed the dis­ integration orthe major and minor scale period at the beginning of thU century. The most important in order oflheir appearance have been Asaviev's uMusikalnaya Forma kak Prouess" and Ulntonatsia" (1930), Hindemilh's "Craft of Musical Composi­ tion" Vol. I (English Ed. 1937), Deryck Cooke's "The Language of Mwic" (1959) and Emest Ansermct's "Lea Fondements de la Mus.i.que dans la Conscience Humainc" (lg61). To these major worD should now be added Lendvai's exposition ofBart6k's mwical theories. Though these five work! YlU

propagate theories which are mutuaUy contradictory in onc respect or another, they arc all in agreement on onc fundamental proposition. namely, that tonality, that tonal relations of,ome kind or another are an CSlIential framework for any COll$truction of tone' which can be rightly considered

all

a work of musical

art. Asaviev', Cookc', of the major, minor and chromatic scales",- Ansermet', exposition of the space between the notes making up the octave at

a "structured Ipa-CC, divided unequally at the perfect fifth

and perfect fourth". and now Bart6k'I tonal axes, operating within his particular "diatonic" and "chromalic" scales (the latter not the chromatic scale of twelve semitones) arc all based upon the admission that there exists a h.ierarchy of intervals, proceeding from the essential nature of musical tones themselves, which may nOI be disregarded if music is to result from composing or the putting together of tones. Some readers may wonder why I have not included among the important theoretical writings of this century Arnold Schoenberg' (1941), the argumenta.tion of which in support ofru. method of composing with twelve tones which arc related only with one another (now known as serial dodecaphony) advances it, in the author, ' theory".·· A study of the theoretical paragraphs of this cssay dispels any such illusion. The whole justification orlhe method of composing with twelve tones depends upon the roHowing two sentences: "The tenn emancipation of thc dissonance refen to its comprehensibility. which is considered equivalent to the consonance's comprehensibility. • Cooke: Tht �, f1.! Mwi&, page xii

.

•• Schoenberg: S!fo GIIIJ Idt4, page log.

A

style based on this

premise treata cIiuoDaDceI like CODlO"IOcel and rCQounca a conal ceIltre...•

Of coune diIIoDaace it equivalent to CONOlWlce iD the wue

that both at< perfecdy pemWaible But cWeonaac:e it DOt the aame

U

insreclienll of muoicaJ arL

CODlOunce ; it b.. different

&COUltical""d ph)'lio1ogicaJ eft'-. Therefore diooonancc ought not to be treated u ifit were identical with coDlOoance. And in

any CIIe the renunciati oo of a tonal centre does Dot follow from

any pmiolll1y .lated proposition and ia merely a dogmatic aaertioo of the compoteTI

belief. AA IUch it ia totally without

the acicntilic validity which he c1aima for i� and therefore hia aaay hardly menta

inclwioo amoDg the important theoretical

writings which are mentioned above. M far .. I am aware no lupporter o( atonality, aerial or

otherwise. h.. provided any proof of ita thcoretic:a1validity AI a

possible framework (or muaica1 art. The formidable champion

of the Vienna School of thia century, Tbeodor Wicxngrund AciOnlO, iD Ilia uPhiloeopbie der neum Muaiku (1948) aauma tha� apart fiom BartOk and Stravinaky, oaly Schocaberg, Bc" and Webcra and their followcn are worthy

10

be taken

."" .. ....P'*'" .. _-

.10. 13

g---

0.

---

b� '5

Put coocilcly, given the twelve-tone I)'Item and ttac three fuoctioDl dUI is the .ni.1l)'1teDl that can be realiJed by means of

disWlCC divilion.

Viewed historically, the axil system re8.ccll the ag�ld

struggle betweea the principlea of Ioll4li!1 and lpi-disUwl, with the cradual aac:endancy of the laller which finally reaulted in the free

and equal

tteatment of the chromatic twelve nOle!!.·

Here we have to draw.liDe between Bart6k', lwelve-tone sy1.em and the Zw6lftoDDlusik of Sc:htiDbug. Sch6nbcrg

.nnihilalel and dWolvCl tonality whereu BartOk incorporatea

the priocipJa of harmonic

thinking iD a perfect is tQ

penetrate into BartOk', creative genius

aynthcsis. To diIcover

the

natural affinities and intrinaic possibilities. inhereDt in the musical material

•

• The iatrod� of the tbIa .-

.6

tempered Kale mark.cd. about the middle or

Form Principles

Golden Section Golden Sec:tion (".cetio aurta", and henceforth CS) means the division of a distance in IUch a way that the proportion of the whole length to the larger part corresponcll geometrically to the proportion of the larger to the smaller part, i.e. the larger part is the geomdrie mun of the whole length and the .maUu part. A simple calculation shOWl that if the whole length is taken

aI

unity, the value of the larger section is 0.618

(

, A •

(1-") Plo.

t:

• • •

1

'4

x=x: (I-x)

(ICe upper formula on page 78), and hence the smaller part is 0.38•• • • Thus, the larger part of any length divided into CS is equal 10 the whole length multiplied by 0-6,8

• . •

'7

Bart6k'. method, in hie construction of form and harmony. ;, c:IooeIy COlUlCCted with cbe law of cbe GS. TbiJ ;, a formal element which ia at least as significant in Ban6k'. muaic as the 2 + 2, 4 + 4, 8 + 8 bar periocb or the overtone harmonisation in

cbe Vieaneoe dasai �, '1''''1. l

'f""h

(If we turn the cone upside down, we can also sce the system of two spirals along the junction lines of the scales). Each of the spiral Iystenu contain all the scales of the cone. There are cones in which the numben of the spirals present still higher series values: 3. 5. 8, 13, Il l .

I - XXI • I - I .l • \- 11 • c(-l -

�x

'/,

/'

�I U 11

.piul

'fM" "

_p'." !i >pi,,"

"

"

\

,

,

s

G 'XV

----4-_ 6 F xlII

XIV

9

-'

I�(

,

,

6

PlO, 26b

33

Similar anangemenu

can

be o1»erved in sunftowen, daisies,

ananu, etc., also in the convolutions of the stems of IcOlves on numerous plants. Frequently the serial numben 2 1 , 34, 55. 8g and even 144 and 233 are encountered in these spiral sy�lcms. For exampl�, the sunflower has 34 pdals and its spirals have the values of 2 1 ,

34, 55, 89.

144.

It is interesting to nole that the as is alwayt usociated only with O'IIUIU matter and is quite foreign to the inorganic world.-

• The irralional number in me formula of CS precludes its occurreace in cryuaJ·forms.

34

The Use of Chords and Intervals

Chromatic System The study of these proportions leads us immediately to the question of Ban6k's use of chords and intervals. His chromatic system

is based on the laws of GS and especially, Fibonac:ci's

numerical series. Calculated in semi-tones: 2 stands for a major second, "

11

minor third,

5

3

11

IJ

perfect rOUM, .

8

..

11

minor sixth,

13

n

an augmented octave, etc.

For the present, the musical tissue may be imagined as buih up exclusively of cells 2, 3, 5,

8, and 13 in sile, with sub-divisioDJ

following the proportions provided by the above series. Thus,

8 may be broken up only into 5 + 3. (The possibility of a division into 4 +4 or 7 + I is precluded by the s)'Jtcm.) me

This cell division can be well observed in the: finale of the: DiDtfI;mmu. The principal theme appears in the course of the movement in five variations: in Fig. 27 we have grouped them according to size, and indicated with each variation the characteristic division. The initial form oflhe theme is 3 + 'l 5. Cl

1 " i ' r ·-; '

.!

I, . . . ..

FlO. '27

Since the fifth line (in Fig. 27) continues on the previous one, in its fourth bar the melody rises not by a minor third (3), as in the previous line, but by a perfect fourth (5), thus conforming to a CS augmentation. Fig. 28 gives the successive themes in the first movement or the SonallJ for Two Pianos tJnd Ptrtwsion. The range of the leitmotif is 8 semi-tones, divided by the fundamental note C into 5 + 3 semi-tones. The principal theme compriso ' 3 semi-tones divided by the fundamental note C into 5 + 8. (Sec also Fig. 6....) The first phrase of the secondary theme extend! 36

1 3 semi-tones, from C down to F#i while the second phrase, 2 1 semi-tones from 8 down to D. The melodies follow each other in CS order: Leitmotif 3+5=8 Principal theme 5 + 8 - 13 Secondary theme 13. 21

rlo 28 • .

From the point of view of harmonic architecture. this exposition a.lso bean witness to a systematic arrangement. The principal theme gcu its magical tone-colour from a pmlalonic harmony II.B·-4

37

(see Fig. litga),· the formula of which is lit + 3 + lit. In the middle of the principal theme there comes an ostinato built 3 + 5 + 3, A� major-minor (se. Fig_ 2gb): C-EIJ-AIJ-B, the fourth, EI:J-Ab, is further divided by an FI into 3 + 2. Parallel fourths (5) and minor sixths (8) join the sc:condary theme (see Fig. litgc). This is sc:en clearly also in the recapitulation from b. lit92. Finally (see Fig. litgd) the closing theme is accompanied throughout by parallel minor sixths (8) •

) (U')

•

:: ..

:

J .., ..

1'10. 29

Thus

each new harmony rises onc Itep higher in the GS order,

i.e. principal theme middle part secondary theme closing theme Asimilar correlation of motifs is encountered in the MirdlU/OUS M....,;,, :

• h .ppean abo in the melody, bI.. �n-39: AtJ-FI-EIJ-DtJ and

FI-�B.

58

PlO. 30

It is interesting to note that in Bartok's music, in spite of the frequency of paraUet., major third and major lixth parallels seldom occur, beeau�e such parallels cannot be fitted into the

GS system, being quite incongruous to it. We could even speak of the prohibition of these parallels in the same sense that parallel fifths and octaves are forbidden in classical harmony. On the

(3), perfect (8) , and even major second (2) parallels. The major third has no noteworthy melodic function either,

other hand we meet at every step with minor third fourth (5), minor sixth

the more natural, almost self.evident is the motivic role of the minor third :

39

1'10.

31

This is the reason why, whenever llart6k uscd a triau in a ChrQ1TUltic movement, he placed the minor third oIJer thc fundamental note and the major third below it, the churd thus acquiring the proportion 8:5:3.

PlO.

32.

From the synthesis of these two emerged the most typical Bartok chord, the well·known "major·minor" form, consisting of a minor third-perfect founh-minor third (3 + 5 +3). TIlis major·minor chord is often completed by the seventh of the root, e.g. an E-G-C-Eb chord with a Bb {see also Fig. 2gb}. 4"

4'

1lUs major-minor chord has a number of synonym fornu, to which we shall give (for want of a better term) the coUective

designation: type oJplla

(a) , and we shall call the different sections of it by the letters luta (tI). gam"", ()I), "114 (I> and 'psi/Oil (t). This type occun as frequently in Bartok's music as

do the seventh-chords in nineteenth-century music :

'10· 33

These chords are exclusively bu.ilt up ofGS intervals (2,

3, 5, 8),

as follows :

no. ,..

and do not contain the characteristic intervals of the overtone system-fifth, major third and the minor seventh.·

•

From here: ariles the e:blloracte:riltic "Slow " of the alpha harmoniCl.

Pcthap. the

mon

te:Nt chord in Baroque: mwic wu the dimiliish«f

Thia Ie:,won it increased in &n6k', 1I1p/14 chorda throuah merzing of two diminilhed KVCnth cho«ia.

KYenth.

4'

the

Type

Q

can readily be reduced to the relations oC the

axis

system. In order to Cecl the tonality oC a chord. we need at least two notcs! in the simplest case the root. say C. and ils fifth G. or jts major third E. when G or E respectively supports the C.· Let

us

put this relation in

GS form:

no.

35

According to the axis system. tbe tone

G (or E) may be

replaced by any other of the corresponding axis (C-E-BI:J-C#) without Changing the tonal character oC C. We can therefore substitute E. Bb or even Cl for G.

The four intervals sounding together result in the chord 6dll (�). It should be noted that the combination of the fint three intervals is no novelty to us, since it is identical with the chord of a major seventh: C-E-G-B�.

• Tonality un only be atabfuhed through the uymmetrical divuion of

the tonaIl}'ltem; in cue ofequal division wc woukl be unable to determine

the lOOt.

A similar axis substitution may be carritd out with the note C without changing its function. We can thus replace C by E�. F# or A, all belonging to Ihe same axis.

r;

:

':

';

+ •

I'lo· 36b

In

the form

-

f]

S S

ofila the first thrce intervals are summarised.

Chord alp"a is therefore practically an axis-like application of the simple

C-G, or C-E-G

relation, the only stipulation being

that the chord should be composed of two IDYns ("axes") : that of the tonic and the corresponding dominant.·

e rlQ.

37

• The two iayen (T and D) correspond to the root and overtone rclillion of claaica1 harmony. It it pertinent that also in U"aditional music, funclional

aUr;actiolU were based on thnc two layen. The authentic (e;t.delltiill)

conn«ted chords require th..t the root of the lint chord b«omes an

.wr� of the chord following. (Chusical harmony can. these CORlIIIOII

nota.)

Thw, in the prU£rcssion T to S, the root of I (C) becomes a lifth D the root of 1I (U) or IV (1-') bcc;OUlCS fifth or KVenth in V. Connecting D and T the root of V (Cl in IV. or a. xventh in 11. Connecting S and becomes fifth in I.

M..... . Sir., t-... e.I., J[

45

•• V..&o.

C__fo

. ... __._._•••••••••••M�• • •

...M••• '

••_ .

1$ .gg:mWl'arall t,

...·......

I"

"

...... r

Type tpsilon (c) is sddom used since its tonal character iJ unstable, due to (he absence of G without which the root does not receive sufficient suppon. Certain sections of the tUp/uJ chord have been familiar to us from cI:wicitll harmony: E-G-BtJ-C is the C major seventh, G-BtJ-C-EI, is the C minor seventh, Bb-C-EtJ-FI (Gb) is the C iCventh chord based on a dimi.nished triad. Novelty is produced by the introduction of the relative A. and primarily by the Cl. In fact the chord IUIII is an inversion of the ninth chord: C-Fr-G-B�D� (Cll to C"'E-C-B�C. 46

Essentially, type alpha is an axis harmony. As an example Id us take the simplest case. If the C major and its relative A minor arc replaced by C minDr and A mojDr.

F10·39

and thae two chords are combined. then btta, gamma and thlte will be equally readable in the resulting harmonie!. This chord bears a high counterpole tension due to the diverse tonal character of its component.!, expressed by the diflcrence of six accidental.s-the three flat signs of the C minor and the three sharp signs of the A major. In accordance with the stratification of the elphe type it it possible to build up a still more extended elplza pile:

'10.40

47

From a succession of diminished triads a "closed" sequence is derived since, by the periodic repetition of the intervals we arc taken back to the starting point:

fll';, 41

And now we come to the very gist ! That CS is not an external restriction but one of the most intrinsic laws of music

is demonstrated by ptntatD1pI-perhaps the most ancient human sound system-which may be regarded as a pure musical expression of the CS principle. In the la-SD-mi figures of the oldest children songs the notes of the mc10dy are tuned afler the geomdric mean, i,e. after

OS.

Pentalony, particularly lile

most ancient Cornu of minor pentalony (la and re), rests on a pattern reflected by the melody steps of major second (2), minor third -BI>-B; and a "bd,mi.,." D-EI>-F-Flf-AI>-A-S-C. Everyother form agrees with one or other ofthe above rormulae. 58

I would like to illustrate the interrelations outlined. above. by three brief examples. The NotlllmD in MiJc,okomw follows the tonic-tonic-dominant-tonic structure of the new-type Hun­ garian folk songs. So its first. second, and fourth lines fulfil tonic functions. accentuated by the tune which corutitutcs a ",nU MoJ.l l:2.

Plo. 52

lu tonal

character is determined by the A-fourth step (E-A), completed by the harmonies into a complete tonic a.xU :

PlO. 53

59

The piece called FrDm llu Island of B(J/i (Mikrokosmos No. log) rests on the G#-B-D-F axis. hs scale provides a full Model I :"l (G"'A-B-C-D-EI>-F-G�) which, as apparenl from Ihe final chords can be considered as a B-fiflh· {B-Gb = B-V#} and GI-fifth (G"'E�=Ab-F.O), and as a F1,",lh (C-F) and D-f()urtll (A-D), covering the complete axis.

, �

"".. f" , �

nO· H !

Both right and left hands play separate 1 :5 models (C#-A-D-Eb and B-C-F-Gb)·· and these are characterised by ltlt'ir counlt�r· pole relations : left hand, GI·firth ·!-D-fourth, right hand, U.fifth+F-fourth. Abo the formal construction of the piece is adjuslt:d 10 the

lr trf rt ..� aher;uion. "It i. IfiJ.:hly • lie,., we menlion Iht problem o( tnJ desir:llJh: Ih,., we have

3

5yt.h:m (,If 1101:\1;0» of Iwdve equiv..klll lymbuls." WaJ :llways guid...J by tlUI.'ltions of rr:ltl..tJility That is the n::uon why we (requelltly find thr.

writet Uartvk. addiHIo: thal lll.· wllt'lI wrili"!; his

KOrt"ll.

(:lIharmollic;: varilllllS in Ihe I»ano rWU(:liolll of' hi. orchestral worb. Ollr methOt.! of lIul..tillll "ol;l;ill:l11"l 3n

in

the Jiatonic system and tben:(ure it if

utterly useless tool when it comn to recording twdvc-Ione music"­

U;lrll,k: T/v Prohltm. ./ Mwn" MI4';c (t920)•

•• Thus by ahe merging of IWO Models 1 :5 we obtain Modd I :2.

60

F-B-GI-D axis. The first section closes in Jo', ending at the double·bar. The middle first moves around B, then G#, with an extended D pedal·point at the second double·bar. nle final chord is a synthesis of D major and F minor. and may be considered at the same time as type alpha (F#-A-C-D-F-AtJ).

1'10· 55

Our third example is the recapitulation theme of the Violin Conc,rto, representing axis E-G-A#-C#. Its scale is of Model I :� (E-F-G-G#-A#-B-C#-D). Bars I and � arc based on thc Cl. E (melody) and G (harmony) poles of the axis. Rar 6 circumscribes the £.gamma chord (E major-minor, G#-�E-G). and the melody or bars 5-13. the 1 :5 model (Il-&-F-Afl·

F---r--+-- '--r =

-----

r

r

�

6,

We have to mention alto a third type of chromatic chord­ namely the chorW of ttpuU inUmJIs. Its most frequent fornu in the GS system are the whole-tone Kale. chord of diminished seventh, chord in founhs and the augmented triad. The last has its justification in Bart6k's chromaticism only in so far as it is built of minor sixths (8+8+8). Whole-lone scale Diminished ac:venth Chord in fourths Augmented triad

2 + 2 +2+2+2+2 3 + 3 + 3 +3 �+�+�+5 · . . 8+8+8

In our tone systc:m two whole-tone scales tan be distinguished : they are "geometrical dominants". complementary patterns of each o.her: C-D-E-F.-Glf-A. and Clf-E�-F-C-A-B.

6.

Mo Blwlu�l C.dk, o,.n (11. u� ... ..... _

. ....

..

_

-.-

....._ ..

--;]

r

1

no. 57

Bart6k liked to use whole·lone chords hifort climtuu, since it has the effect. as it were, of "melting" the sounds (ICe Fig. 57 : BluehtlJrd's Castle No. 136, TIu Wooden Princt No. 123. Music Mov. I b. 48, Mov. 11 b. 56, Mav. III b. 14). Harmonisation and theme construction in fourth chords are strikingly frequent, due to the influence of Hungarian peasant music.

FlO. ss

Chords in founhs generally aUow two combinations: Ont� according to the 2:3 p�ntatonic principle, the other after the 1 :5 model. (a) or the two fourth chords in the 2:3 scale wc can treat the one, which lies a major second (2) higher or a minor third (3) lower than the uther, as lunit, and Ilu$ (:;In ill: rcdut:(:d Iu the du-so_la cadence of the older folk songs :

f10· 59

(b) A good example of 1 :5 association s i the closing theme in Movement 11 of the klwit for Strings, Percussion tJnd Celesta. The 1 :5 models are based on two fourth chords: D-G-C-F and A�-D�-GI>-Cl>-F�. 64

1 :5 models

{

AI>-DI>-D-G DI>-G!>-G-C GI>-q-C-F

PlO. 60

The GS chords and chords or equal intervals onen combine together, in pracliee. Fig. 61 shows an ostinato from Mov. l of the Sonatajor Jwo Piafl(JJ alld Peuun;oll. TII