bartok - bela bartok an analysis of his music 1971

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Contents

T Ppl 5 le

plion '

i c

T S

t Sye

Ap I

Ap n '

0



Introduction

T p b on of . dy of m c ofBa an

m r t ev t Many d ip v a a of p r c wor o have ap , u h r for h me i he E g hl ag a o i v a d convinc g i on o t l p n pl wh ch t e om e w ked o o

b t r , f om d ng t nyone d ng lif m e i ng o by wor of mo h we owe th a or p b her a

debt6 Ldv" e ct at 6 a ly evolve fo a me h o i g a n

h m o m c; h chO d c W t e m c mo app p a o m, t g h C p r O o gth w n moveme whole wo k,m i v sio wi a mov m s ch po i o d v loPment a p t a o ven b n g p r wit n01 f movem , accord g o D s g e c p n p eat f he Go Sec on me ch ma ema p

w a " h p cip e b a d n he



3rd miU ium k up by t Gr two thou dy l t a d dis v d d R a ssa b t vsys mati y app i d to musi y m . ( h i s o csi l s qu mov m t by H yd , ompo d i I ga ordi to Go d S o p po io , b is is morc of i t tu qui k o t omp ' i ip d p o

du .) Ba 6k dis v d w y o d iv h ba iat a s A-G-E a d rst i v sio o t m jo

ommo o d E-G-C om Go d S tio i i s pr

b o o Fibo i's i o w o umb s From t k pro d d o b m o tw f d m ts , d K b d by Le dv i "di o i d om ,o i g sp iv y v d ig t o id th o vW h J m wor B k pp i d h o y o " on x s s b o y.

s imp d e of k ha h p t to s

o h r f k mu i , mod s o i d m di v d o k m i d a y h m o d mi o s diomo Eu op t mu of h 17 h 18 h d D h s

g o h ro d ow B t k' omp i o o hd p t dam als o o a ity wi h p r o m l propor io

ur g t p t y a t v b v ou s i ia y o d mp wi i musi a th o y o s ow

w y o w d to t mp s a d o p im to t o d i t p od o o w i o ow d t

i g o o m o d mi o p iod b gi io u T m st im rt t i o d o i ppv b vi v s Mu a aya Fo m ka Pro dto sia ( 9 0), Hi d m s "C t o Mu i ompo io Vo I(E li Ed. 19 7) k Cook 's T

a u o M i 9 5 9) d E A s m 'sFo d m s d M qu da i Hum i c( 1 . o s ma o wo s ou d ow b dd d dv i sxp si io o B r s m i o i s Thou h v wo

Y



r agate es w ch are mutuaUy c ntradic ry n nre ect r an t er, t ey ar all n agree en n n funda ent lr s n. na ely t nal y, a nal la s f e

k nd r an t e are an ent al f a ew rk f r any CO $ uct nf t ne' w c can be r g ly c dered a w k f m s ca

ar av evo kf e aj r m n r and r a c sca - An e ex n f e s ace bet een t e n tes m ng u the c ave

a tructured I C d v ded unequa ly a t e erfec ftand f c f . and n w Ba t6k t nal ax e a g n s ar c ar d n c a d c r a c l (t e

latter n t t e c r ma ic le f welve se t n ) ar alb ed u n e adm n t at e e x a e a chy f nt v r ceed ng fr m e ssen l nat re f mu ca ne t em v c ay nO be d garded f u c t r s l

fr m c m s ng r t e ut ng get er f nS me reade may nder y ave n ncluded a ng t e m r an e ret ca r ng f s cen u y A n dSc enberg194 , e a g me t t n f c n u r met d f c ng it twelve t n c ar related nly w t nean t e n w kn wn as se al d decap ny advance n t e

a rt e ·· A study f e t e ret c l agra th s ssaydi any uc l us n e w e c n e me df ng t el e n de ends u n e w ng

ntenc :T e e n e anc at n f h d nance ref s

c mpre e s b l ty. w c c der d e u valen t t ec s n nce c pr n b l y A s yle based n

M • h n : S! pg



p cD C and r o n a

O t o et y le isel f m

But DOt U C ; t e nt & d p ) - . Tr n n ught not u f t we e et D n e. Ad in any I t e e un a o f a o cent e d Do fo ow omy p o y l p o o d i m e y do a

of m I be A Uch t to l y othe c v dity wh ch he c for nd h o e hy h d y me icwo mo e m nt h r a

wri w m on a veM fa I m w re no p ter o( o a y, or

o e h pro d d a y pr f o f h r i vali ty A

s e work or m Te da le ch p o of the nS of ct, Ter W dAOnO, Pp ie der eu M u (19) a m

t apa om B k d S ky o y b g B"d W a fo ow hy 1 b

. P y H _. ' - - . - - . . - " . J P · I . s p m _ -, + t

, _ " ; 2 1 .

N D Y a ' o dc n t VCD C be U i aot-

v o j v y and d cr e large wrb

tu e "We k< d g8 u, w c uld b l y t "wor ma t l A i b e t : it i t dd t f e nt fv ew of o

m t p o c it- at of John Cnot wn a mom nt' c d a n .

• : S 10)•• : AI, ,_ . w p g

"



Tonal P nc p es

Th S t"Every h he gb o It ke i in e o a p iow

it Do on y the igh ut i mu.t em m i ,Bar k once d d

H ona em out o nc on m u nter·p d o evolu on can o lo ed m e o

o al o ep ou e mo o Vien eand he ne- o ld o oma o

By a a y o om i on tem canp ho n to he s en pro i o i alh mony

he n on f o he ou h d d g6) he l on hip a iv m jo nd mino key ( ) he o er one o

4 e o e o eadin DoC ) he op e en on o e dom n n u o inanU e du i o ona nd d an e pr ncipl



( ) o w o u B I ! m e of . L C ue ( ) n F, hfo h ubo G he d ,

he o D A, he d e l v of e o ic,fU u o c DJ d subo u bo n E, d dnd of e do , £OD d

o F co n o e fu c o l

e uen "

of y



" a a e O 'U m na n 1y

S DOM NANT

AX S+

TON AX S

DOM NANTAX S

Ch b n he fu me C, E (=D#), # ( G ) ha e a fu c b he am E, G, B ( ), C

( D ) ha e fb he me D, F, ( G# B ha e

fu cI ha he a

ch r f he e e hJ b e f ch f n , wh may

m e a m c (e gC m j , E m j C



It should o ed h , at c mo e eNit ver a o p be w the o n he"coun e.g C a F tho t a e n to each o er, e.g.C a d A A le alway i ercha geable w ths un le wi ou any cha ge func on ·T e le counte le r a io p i the t da enta

c Ura p i c p e Bar ' s c n to th .m a ge fo eady he ne fo of Blw r I C

w co ce v e co nte e te io s. I s s a the da k F# le to he b ght C jor c ord ( he re lm o

Bluebe ) d d e s ag n he g y F#The cou o Sol fo, TU Pi 4 P" n rf om he dep he heigh s: f om F'0 C, the begin ng dend of he work n F g 5 he F andC en r (bs 0-5)e r ent he to ic, t G and D en f o the end b. 8)

t dom nan the A a D en ( . 12 17 he bdo i an counte l

The B ma o o co e Yil CO i re laced thedevelo en b y co e o e F (b 5) S y the F ma or c of t eD /i epl ce by i e devel pmen (b. ).

T move en of Mw/ r Stgs P c" kl" ha e e fo ow ng st cture

IOWK

I1

III

BEO H OAC

FA

M LE b 6)F# (b.063)C b 46E b. 83)

DA C

F , A

• A C aUl o c, A- F e of

. b vu,i t way: A A D . t D ,< b A D o . . pA vmoM /_S P _-c (Me. I t. 76

18 ), w u o I B'-E A D ' C & CF B A GI' C$ (C ) F"·

+



table t a h yet another l n. Alfu o emcnU on the ton A EIF# Thw e andove eD are up ed y the p n ip bra h" A a d

E ; e m dd e ovemen ho ever, y the ondaran h C an F# Thw ea h h a o fo d a itydep nding on h ther e op t e e th e ountee or the pr n ip bran h i the ondary bran h

•

C quen y the o nen o e te are a o o :

b an h - e nterpo e_ p in ipa + onda bran Y't T S e

(no di on)1 di e ion)2 di e ) di e io )

T e Slo Move ent o the o T P md

b d on he bdo inant F A o p ying i ht e t a i o o s i a io The o a a g t

i pr n ipal the e y t i a t e g nn ng and endp ed by the Band F o t r i.e. the b an h

8 8 5



of h mc a ral

D a d un ( .e. e b ch o e e a e o e ang ng-f E) e dd ·

" P B _ . " I

L-S"C,ONn .Bnl. -

& y • - Ha(C t.) dom 7

6



The mel y o t tu ng the ore the movement en red a und the ubdom nant The 0 o n ng dc are repla ed the m ddle ofhe eme by e oun e le

D Eve m in mctr and mo ivi int evo v a ound t eom a t

Th e two m lod y t he I t re t e movement.

one hem be g a a hed the pr n p F. e o r t t e da G b an o the ubdo t

The ond eme o he be mewha more ntri a A though he twe v t ne

mel y tou h eve deg e e hroma a e he e doub o nali n we e a d D oun er

( g ning middle end) and the b oken-u F m jo d C m jo m nor oun C

f

7



Fo d aib, App. I, p 99

( A o olu on o a oni g l a o

o at t o m nc y p g lo on nua o ( in a h ompl on) o Eu op a u ona musi o a hat h m wit i a a u in y Vi nn "G a

I i d y a h 1 h smTh r on n m w i u d

i p a y o o I-IV-V I fy m val m m i at i a o m o y In C to :

SUB MF C

DOG

Th c cal h o h y a aks o p m eo a y h C m y b y i

v A F y i la v nd h G y i la v E

A

C

Roma h o y u mak g u nt o up a v Na y o y jo a d o k y o

kcy g tu m y b la v g C m jo A o C E majo )

8

C

A E



One more step om let the y em The exte d e appl cat o of re at v to the s tem The tem im li e og itio o e a at h ommo re a ive orA a d E s o o y C, but F# (=G ); tha D a d A o o ly have F a ommo rela ive t a d that E a dB ot o ly h ve G t al o C# = D ommo re vU

F

/ D A'/

B

C

A E' /

F#

G

/'E B'/

C

well now Bar 6k howed a re er n e for he o Ued major-m or hords s F g 32 For sta c o C to a y :

e o rema s a g eve t e C major

show t e a ve ho d rep a ed e re ve Aor o wh e majo o a y he e a vC m or tech q e r Ba t6 ' m :

C majo m o /A m or E major

Th t te o ds ma em lo d ma or m o o wh h b g! he ys m a I s

ela ve of A ma or (F m or a d that o E m or Gma o ) m t a a t o e armo i de ce F G

9



o i r a io i x n o c C nBIO

S nce he DT la o sh p corr n s· a vely

he T anhe S D e a b p ov r on at a on w en he T a he D

e l.

R R Uo ic C E an B omi an

omi an EG#a D

s b omi aomi an B D an A b o n,u o nan A an Gub o n D # o ic

G F #T

E

n omt ac rb c wh

1



If we add le o ove o e, i.e. th, he wec d duce he mple e tem f m h ela o

( I the plC cade ce, ha of V-I, e roleplay by t d ve o w ch p ce he p lhe do a ow the o c e Do e p l or the sev h owa the th d de ee of he o c,

e he lead g o e B r lv OD C a d the Kve h F o Eo E

10

na ve o a o p oe ch o h . The o half he tave ae d b he i ha g y w h cha g ge val ThU e F la oP p co v ted o

F B o e ( f ue he w B k), he he F _E# um the le he lea g o e p g ow he

F i ead of , wh e he e th B p l towa A# o Aead C. So, ad o he Q d o C jo e

e eq o ic F ajo o o e e gC

0



r l on r d by B rtOk fo a dd o sc . Th cu s anc o an d G' C d cm g ng G -F# v w a Bar 6 d d n "

(e) St ng f om h t n c c t C w r ach h d m ant n on d tion a d th u domi ant in h o h , i a d A a d anc a h w d h do in n Gpw ds d th s dominan d w w d . R g rd g

1 r a o s w g t th dom n G B in thupp nd h su dom a F, A , D in h ow di c on

DD Df

what happ s if h p du m cov th latitud ao ? I c h d ia o s m d pw s a d dow

wa d m , o h di g a F G , and w w o ak o h dom na h h o h w u d hav a um h

domi a f nc ion y c in d nc , how v , a t ·a o of h i f c o ak p ac do na a d subdo a

m g g a d d i c iv i h i ac o of h op s o c u nt y ba a c sav d nd h f tion s jn ia y tha of h to c. h co po is :

m a y h d ta c w h o c C a d sc d E i h o a d y A i th o h

di c o ; y g in t ionJ n a t on p h y hav t b int t d n No mor han fo n cpo c n s r s d i c h n a A A C p ovid o u h i s of b c on

3



F y wh ho d a a ao d < B i U C ( DW the d and wh ch he u

do t f ? Re a B, C o a d g o va ion . w ch mi8h corr nd the D int de den e b t ot t i op te. Anyway u o na

n o B e do an unc on C nU o able wh hey re ated the n coun e l

( Thu , o he o c c o al in r onnec onof t i er g t e IU do a d do a pr t d e vely by e d IV a d V b t i he of C heu o nant by A (a d o e e) the do n by E(and i co ter e).

r no hing ew he e or , the d dary theme E Be hov ' WGUi$.(0 majo or the s S ow Movemen n A1of t (C ). The mov me of B ' F s'J" have fo lowi g ey uen e: EA in e

to i o na bdo na t o cHow er, e a e a o he em a s o

xp why k a gmented a o

e di o - V V-I ( or pl App.11 p 103 )i t a new approach o he y t . ge y a pted at twelve o e m o ao g te de y o re t o rela o .At la o c m t i ab y ed by e

di o he ave, or o he irc e 6( B y d vi ng theo tave welve u pa we ge hrom ale; in

o eq par we have e who e· ne a e; our equalpar gi he o d o e d n e hea gm t d a d y by di d ng he t ve n o two

pa we a ve at

' 4



Pt co y, give t tw v e Item a t thr ef c o e . ) at c b re by mea of dWC v o

Vi ed h rc y, he a m re8 c he g ld gg e e e p i pl o ! and lp -Ul w h e adu end of e a e w ic y r t

t e f a eua t t of t chrom c tw ve O ·He we ve to r w De tw Bk', w lve-to e

1 e e Z 6 to o Dbug S h6 g n W vC whe Batk o e e pJ o n tg pet To

te o B k', c e ve ge i ove he f and c s b h re t he

m a e •

• T i o p Ke m abut the m ..6



Fo m P nc ples

Gold Go den Se on " c o a ta and hen e o h CS) me

e div ion of a d an e in IU a way a e pro on o

he who e eng o e arge p o pon lgeome r yhe p opo on o e a ge e sma e pa .e. e a ge p e geom o e w o e eng and e ma u p A simp e a a ion s OW if e w o e engaken n y he va e e ge e on 0 18

,

( A

4x=x: -x

e ppe orm on page78 and h e e sm e p0 38

s e a ge par o ny eng divided n o CS is eq0 he who e eng h m ip ed by 0 8

'7



B k'. o h mony; y h w o GS. a o mel en w i at le cant B k'. m c the

8 8 p o or he ove tone harmo a onVie le.ple le the vem t o he

e v mp 3 ba n G g a ve fo m - 3 0'6 8, i e 74

w move en : there pit a on p y 2 4

M vement I o C1 u n.t o 93 b n. and GS(93x ·6 8) again e g o pit la on ine ddle o 7

Move t o e DW eo o 563 r p t u( h um r o n eva owi g o h ir va a l im

sig a r s) Te GS o 563 563 0·618 -348 a a coi cid s

w h h r ca i ula ioI Vo VI o MikrD h CS o Fr Va a io s"ca b s o ouch th Molto piu ca mo 82 0 6 8=51

Te GS o From e Dia o a Fly com at h c imax:h dou l i h 3/ ak a 1 ar, calcula i gi 2 4 an B ok Chords w d h r capi a io h GS 80 0 618 49 c

Te 16 oduc o ba o h S aj r T Pi RP, m r pr mod l x mpl o GS co s r c o or mor pr c s ly 2 ca s it is h r ha h or a icli o h work gi s



1' 9



It nt par th ph r of th o i ( . 2-5) he s co d w thi th omi a t b B a thir pa i t t o t ubdomi a (b 1 o ) Thi thir par th mat y

s o t nt two o, o ummari :m i po i o to i F C

T m itio om a t O DUTh m ub omi a t A

t i

Co r g h ha g o tim ig at r t i mor p a ti al o a at t o 3/8 t m T who orm o i t of46 u OS i 46x0·618 8 a t ov r t part p th Dn th h m h ma io o F g 16)

a b ob r that OS a way oi i wi h t s g i a t r i g poi t o th orm

L t ow parat rom th who h part root p itio th rst 8 Now 8 618 17' t hi v p ith to p rt at th rst thi of th 18th u t th

mi a t t F g 16)

ROO OSI IONcI I

'ni

il •

l

IN RSION,_

O i i o may b to o ow o o t o p ib ou



depending on whe her he longer or he shor er ct on comesr . Le us c l one of the po ibil e p itiw: long section

f llowedby he shor one-and he o he negativl sho sec ionfollowed by he long one

In he s ruc ure of bo h on c and dom nan part he cymbas oke c ea es a harp dua i y The pos ion of he cymba s rois n bo h cases de erm ned by he GS, bu whe ea heonic uni (a he gn "cym in Fig. 16 is div ded o a to ma eitP i i (I7 3 xo·6 B 11) he dominant pa on he con a y,ecomes a gaJiv d ision i co si3 of 1 uni s and isdi id d 4+6) The posi ive nd neg ive sec io omp emenach o her om hing w h i s own m or image u hemee ng poin of he wo ( he d m nan ent y) h a pos tivesign

n o her words conde sa ion and dispe sal of he nodes ca ea longi udina undu a on the wave s mee ing in aposi i

sec ion s ga iv oun e p found he en y o heta a (in he inve ion so ha he posi ve sec ion o heoo and he nega ive section of he inve sion ar again jo nedsymme cal y

No only the en i e fo mal a c bu e en he fo m cellssubmen i ely o the s ic es geome ric analys Fo instance, n thedomina pa t we nd up o he cymbal s ro e, eleven eigh hno pos ive CS po n 7 ) de er n he posi ion of the only m s a s re n he uni by means of elonga ing heE no e Th soon coun er bal nced by he nega ive sectionp n a he de d m bea in ba 10 1

Simi arly, he po i e sec on of he onic pa up o heymba st o e s mark d by the most impor an urningpoin by he hird(C n timpani ent y oun ed in e gh hs:33 0 61B 20 Prec ly here e hema c condensa onb g a o wi h he 2 eigh h On he o her h nd heomp emen a nega ive ec on of he pa t following thecymb l roke i nd ca ed ag n by he side d um (see ig. 6)

8·-3



Summa ng the a ve t he ma le and large f mde a , the e i a ymmet j i ng f the psiti and I ati

c o . F m h c nca enat a ng g ea " ent 'f n a i whe e n h ma e pa t a e na y mm edn a nli" ma n ec n p c si the ef e p ed w ha pow dynam n ea e f om p an m fo e-f m

A a yti al d e pe m the on i n tha the p i ee t on a mp ed by nte cat on dynam n e a n f he mat al wh le the nega e ion y a

fa ng and b d ng The e t a way f w the ntent and f m-con ep n o e m cBy wayo at n e b e t M emen o he T PiS dP a deta ed analy

Exemp a y i the n y of p o t f he expo on: ep n pa heme h a e and he o ng theme a n g eIc on wh e the I nda y theme de el ped be ween h tw

ymmet ally a angedT the p n pa theme· (43 ng) d ded f ow A + B The n f B dete ed by3 618 27 w e he w a e ated e hhe o d g t 2 x0 6

t - -- --1 + J - - ) -no "

• · e o vc oi o o c



T e symmetr cal di s on of t e second t eme c n eexp d s foll w ng: 2+17'S 1 S U! (bs. 44- 02) T e g om t c cen (b 7 ) cco ds e on constr c ono the th me a .

T e n g ve m n se on o e clos ng t m (bs 1 3 1s g n n S (see F g 8) W n t is, S- h e

pos sec on n 2 b c us o t e ful dyn m cnt, nd t st t c on t t on n 4 4 4 n t of bs114 p od c s sol d b e fo ise

t t 18

k e p op r ons of t e de e opment re ymmeb 4 )

I neg t e m n s c on nte nc ng e p em n se on o t de elopment of Mo ement I s dete m nedp ly by t e p nt of cl m x n b 1 ton c co ntel

p i i sec on of he p p eced ng e cl m nd t e

s t on t t c m x nd c te e mos m ntt n ng po n : 16 t e f g to o t e p nc p l t eme, leb 2 S t et n o he st eme o he d opment ( lop ent



VE VE

h ui d ow rds th c im is lw s m rk o t v s c o

fom b 0 1 9 i fl s o 52 s iv, 1 176 .. 170 ..

160 6 .. b 166 .. b 17 6 . b 1 ..

om o t of c im x o , ow v r, the g iv s t o sow i v t o ortio s

f om b 7 20 i f l o 18 g tiv b 89 0 . b 95 .

.. b J9 b 199

h clim x i self d vid d st ic l i to 6 + 6 b77 88)

T e g tiv m i c io of t r c it l tio (bs 8 350coi cide wi e w te d, t were of e t m icm ri l, i e wit 287 Bs. 287 3 0 fo m o g e bro dw v , d i s u tu view s m to t t of e b g g

of Moveme cf ig 6)



and a n gativ s ction in u it of 9+ and 5+ 9 b s. Thcond pa 3 9 42 ) own in F g. on i at ham tim a v (b 4 a a nega iv (b 39 ) c on

y, t p itiv ction o 395 4 in b 4 1) and thn gatv s ction o 4 42 in 411) ar again ymm t ica y a d to ach o h .

At rs g anc it may app a contradicto hat th poin s oc on d min d by th ws o as n min unfld byth cha ging tmpi. ph om o y to u d a d i

w co d h t mu ic b a h in mt ic pu tion and no int b o ut m ur m nt o im In mu c p ing tim mad :r a ab by b ats o b who o i mor mph tictha th du a ion o p rfo manc Subjc iv y w timap mor v ri h y in a mov m nt w th a quick tim -b t

and mo ugg h y in a ow pu on.Fina y m giv an amp o tho who p o ch

B 6 ot ha ing ctd th "tot and radic g saton o th mat Th comp t o n o th $ TPiS I P n divid d into ow s + J w Ulmov m nt . as may th or b xp td to \ t b ginning o th cond sow mov m nt. Ou X ti

who y u d; th tim v u o th comp w k i432

igh h not s and thas

at h3,975th

which is p cis y wh th mov m nt b g .

6



Fibonacc Seriesl of us who have played A Barbro, have been roub ed

by the FI minor h obb ng, extending over 8 or 5 or or evena . The propo ion of

: 5 8co a n a S eq e ce, a rox ma e y ex ed n na uranumb he Fibonau nmbers. A charac e i c fea ure ofequence ha eve member equa to the um of he twore ding membe

2, 5 8 1 2 4 55 89 and fur her appro ma e more an more o he rra iona

key num r of the S (the S of 55 and hat of 8955)Le com are eq ence w h he por on of he

fugue movemen of Mw/r Slr g, P" Ce .S i n mo gada y ri o for ·fo mo henagain reced to ano ian ssimo The 89 bars o he movemen

divided in o ec on of 55 and ba s by he pea of thy m d- e movemen . r m he po n of v e of co our anddyna c arc ec ure he form ub divid in o f r her u i s

Te aqu or nr equ o h pr t oflhe p ngU Dumb pl



by t e remov o t e m te n t e 34t r, nd i s e gain int e ar T e sect on leading up to t e clim x b s oa dvi on o + 21, nd t t rom t e c im onw rds 3 + .

s t e onger pa t come t n t e ris ng section w i e int e f l ng s ct on t i t e s orter art t at p eced t lon eso t e sect on poin tend tow ds t e clim Po iti e ; Ddneg e sect ons toge er ike t e r se and ll iw e

H

=o 2

e proport on ol ow t e bonacc ser

t no cc de t t at t e e po io end wit t e 2 t aand t t t e 21 ba s concl d ng t e movement re div d d into3 8

T e proportion of Movement of w Q n sW so re lect t e ibon cci s ries (i wc lc late t ro g o t in 4/4 s and consider te occ io3/ I ba ) Its o m l nd corr pond ng geom t l

str ct re i own in ig

•Th h mut cmpeed by a whole-bar ,co d i h t e BUl a B hoYfl

8



_ - - -+-- . --- - - " "

iI Z h

, . . _P .3

The Fi onacci seri re ects in f ct the l w of nat aro h o ake a simp e examp e. f eve brach of a tree on year shoo s a new ra ch nd th se new r ches a edou led a er two yea the um er of the ranche shows hefo ow ng year y i crease : 2, 3, 3, 21, 34

"W foo at i compo o wrote art6k a d wai deed directed y at a p e omena to his discove y of t eregu r ties He w s co sta t y augmen ing h s co ec ion o

nts, i s cts a d mi era specimen He c lled h su ower f vourite p t, d w extremely ppy whenever he

ound r-cones ced o is d s According to Br 6 " m ic i a pheomeon of ure I s form tio dev oped

s s ont neousy as o he li i g n ura organ m the oweima s etc ( t t e Sourc of Fo k Music 1 25)

his is why the o m-wor d o rt6 s m ic eminds m t direc y o a a pictures d fo m ion

9



T G of c c e, v ° s R e ° on on n a 7 5° on o e d

g o p an g r at ns, a

a tw g o an g of1 7 5 w n o

_

4A a n w a j of oa o g o of as: sw g g

w n an ; ig 4 f n w a2 ; w g 5 am w t w n a ad -

•Te F u wn 3 dvd y w 3 S 8 w8 I etc

30



fwe nsidc " the f M "d CL/uta (a lys pag 27 6 r um

vl t ,· st t U s gy es t Fg. 4-

O t xa t ag a mat sket f t a bs t al a l J u V e as s t t t s a s t at e nam am } t

T ag Is a a y t g t tv a pat ! t e t e a ays

e e a e GS e e ma d A B BC.C D D E E G

A B

.2s em s st g y m la t e s l st t

at gs 16 a

e e 6fr A trk to he A tre



o v g x mp s p s d uo h P o d g om r o d og msp s s o mov o w d · o kw

o d s s m wh mb o h p s 4/ p sv s o h bo

\'11 VI

I'X ! >pi .8 > r - l 'f"h



( we he co e up ide dow we c s e the em w spi s g he ti he s ) E h hespi e e s he e Thee e

co i wh ch the m e the spi s p ese s highee i v ues: 3 5 8 13

9 6I

O, 26b

x//

I - X ul • U "1 1 p

- ! >

G

s

XX6

F xII



Si lar a a gem u be o1e ed i s owen, da ,a a et . i the o vol tio of he s e of Ic ome o pla . F eq e ly the e l mb n 21 , 34 5 . 8

a eve 1 a 233 a e e o e ed i h e pi a s mso exampl the owe ha 3 p al a d i pi ls v

the a es o 21 34 8 9 144 t g o o e h t the is alwa s ated o

with O' U ma e a d q i e fo eig to th o g wor d.-

• e i liona numbr i rrece iaJ·for

4



Use ofThean nte vals

Chromat c yst m

Cho s

he tudy of h e pro rt o lead us imme iately o thequ on of Ba6k s e of chord an nte a H ch oma cy em b ed on the la of GS and pec l y, F bo a smerical e .

Calcula ed n sem -tones:

2 and for a majo econd3 " 1 m nor th r5 1 perft

1 minor s xth,

13 an augment tave, etc

or he pr ent the mu ca i ue may be mag ned bu upexclus vely of ce l 3 5, 8 and 3 n e w th s bd v oDfollo n the proport o prov de by the a ve ser The may b boen up o ly nto 5 + 3 ( e p b y of ad v on n 4 +4 or 7 p lude by he m )



Thi l v i n ll b in h n l thDi I;u. T p i p th m p r h u f hm v m n in v va ti n : n Fig. 27 hav g u h m

r g z , in at th h var ti n hh a ti ivi i n. Th i it a rm f m 3 C5.

1" i

.!I .

S n th ft l n in g 27 n inu n th pr vi u n , t f urth bar h m y r t by m n r t 3 nh p v lin u by a p f t f u th 5) th rming t CS ugm i n

F g 8 g v th u iv t m n h t m v m nt h a T Pia d P w Th ng f hl tm f i 8 mi n , v by fun am nt nC nt 5 + 3 mi- T p in al h m m r s '3m -t n ivi y h fu am n a n C n 5 8. (S

al F g. ) Th r t hr f h n a y th m x n !6



3 em o , fr m ow to F# w e t e e o r s21 em on from 8 ow o D.

T e me o ol ow ea ot e n S or er:L mo fP n al t emeSecon a t me

=5

1

om te po nt of v ew o ao c arc ct e ex oo bea w t o a stema c a angeme e p nc pa

t me g t mag l one colou f om a p ao a mon.B·- 4 37



( g a),· h m a h h +3 + th midd h p pa h m h m a a ui t 3 + 5 + 3

A maj m ( ig_ C E JA , h u h,

A , h d id d y a i t 3 2. Par l h(5) a d mi ix h (8) h da h m F cT l rly a i h r api ula i r m 92Fi a ly F ) h l i g h m m a dhr ugh u y p ra l l m ix (

:

J 10. 29

a h h rm y p h gh h GS d

pa h mdl pa s c da h m

g h m

A m la r a m u d h rU/OUS.

• a i y 9: F E DF B



PlO. 30

It i int r g t n t that n Bartok's music, in spit f thfrqu cy f araU , maj r t rd and m l xth ara ss d m r b eau s ch a a s c n t b d thGS y tm b g qui c gr s t . W d v n s akf th pohibition f h a i t sam n th t art s and tav ar r idd n i c harmn On thth r a d w m at r t wi h min r third 3 , prfctfurth (5), min r ixt (8) , a d ma r c nd (2) s

Th ma r h rd h t w th mlodic func n h r,th m r nat a a m v d nt i the m t v c r t em r thi d :

39



This he reas n why whene er r 6 r iChrQ1tic mo emen he ce he min r hirn amenta no e an he m r h r t e c r

acq iring he r r i n 8 5 3.

2

r m he syn he i wo emerge he m t yp cr k h he we · n wn maj r minor rm n i ing

min r h r pe e o h-min r hir 3 + 5 3 .ma r·m nor ch r is en om e e y the seventh o theoot e g an -G-C-E ch i h a { ee a F g 2gb}.

4



4'



major-min ch rd h a numb f syn nym fo , tw ch we ha l gve (f want a better e m) the c Uec i ed gnat n: ype a and w hal ca he di nt

ecti ns f t by the etter a (I> nd ype ccu a f eq en y n Ba t k' m ic asd e en h ch rd n nine eent c n m c

These ch r a exc u i e y b p GS inte a (2 3 5, 8 ws

and d n c nt n he cha acte is c in e al e e ney tem th ma r hi and the min se enth ·

•Fom he a h b ac i ic "Sl w f h l h ha iC.P h mo N ch d in B u m c w h d mi sh«K t , d in & k', 1/ c d t hmig w



Type Qcan readily b reduced the e ation oC hes In order to e the tonal ty oC a chord. we need at le two not ! in he s mpl t case the r t say C and fh G

or j s ma or th rd E. hen G or E r spec ve y p r s the C ·Let put r at on in GS form:

n 3

Acco ding to the ax yst m. e tone G or E) mayrepaced y any other of the corr ponding ax ( E-B #)without hanging the tonal character oC C We can hereforeu t tute E Bb or even Cl for G.

he four inte a s ound ng together r u t in the cho d) It hould e noted that the com ina ion of the t three

inte va no novelty to u , ince it ident cal wit the chord oa maor eventh E G B

• i y be gh d vt ; div iw b de



A imil u i u i n m y c i d u wi nC w u c nging i unc i n W c n u pl c C by EF# , ll l ng ng I m

+

•- S

S

Ilo· 36b

n m a n v l umm i d.C d a a i p c c lly n i -lik ppl c i n

imp G, G l i n nly ipu n n c d u d c mp d t DY (" x ) :

nic nd c p nding d m n n .·

• two ay (T an D)co p nd o th and ov ton iona ony It ip tin nt t at in itio al c, fun ion

aU ; i w n h tw la a t ntic ( d ic nn« cho ds i h t t of t t c o d b«o an

of t c o d ollowin C icl ha mon c hnot ) w, in t p £ in T o S, th of C) b om a lifin V o x n h in 1 C nnc ing S andDh t of 1 ) o I V ( ')

O ft o K n in V nn cting Dnd th oot f Vb co f h in I.



e.I ,

45



V C f. . . • _ . M '

1 .g g:mW alt , · .

I"

•

.r

Tp tpsilon (c) s d m ed nce t tona char ct r i

n tab e due to he a ence of G w tho t which t e roo doenot rec ive ent u o

Ce ain econ of e / chod have been fami to uom c ic ha mon : E G B C the C majo e nth

G B -C- i he C m nor even h, C E F (G ) i theC venth cho d ed on a d m ni hed ad. Nove oduced y e nt oduction of t e ela ive A. and im ilyy he C. In fact the chod UI i an inve sion of he n nthcho d C G D (C to C" B C.46



Es en ia y, ype al an axis ha mony an examp e sake he simp es se I he Cmajo a i e i e A mia ep ace by C an A D

3an h e o cho a e ombine hen an li be eq a y ea a e i he es ing ha mo ie! is chobea a g co n e p e e s o e o e e e o aa ac e o s c mpo e e p e se by he e ce o si

acci e he h ee a s g s o he Cm o a he ees a p signs o he A maj

acc da ce e s a i ca i o he l ype iposs b e o b i p a s mo e e e e l pi e:

47



F m a su c io of d mi hed tr ad a "c osed equede v d nce, by the pe odic epe o of the t va s we artake ba k o the ta t g poi :

A d ow w om to he e y ! Tha CS i ot aex e al t ct o bu o e of the mo t t c laws of mu c

demo a d by D pe hap the most a c e t humou d sy tem-w ich may be ga d d a a p e mu icexp e io of the CS p i p I the la- - gu s of thdest chi d e so gs he ot of he m 10dy a u d a

t e ge m r c mea , e. a OS P a y art u ar y emos a ci t Co o m o pe ta o y a d ), t apat e e ected by th m ody tep of majo seco (2 ,m o h d <3 a d fo th

• t e ld ty t o i mel t h g g c u ew Jy c e th mj t

d ri. T q ote K l "It th t the p t

h co t tion e d d l l " I_ite,A co di g to ly the l g o th d the h ·y othe s p gu io t the ch d t t Lwi r l tohi rp nt g t e i l ex i fh b g



Type 0# b de ved rom . Ti howB t6 t s ms a pe tato e nt e and glm4truct r :

7 e .

n 4

T s ype of rmonie or n g f m fol ong ws sugg e

b B t k h mself "T e Fol Son o Hun (ProM 1928) -

' . I . J 5/. · J _,fr . I ,

a ' J J !lw m r fun ,W

no. $

• AI fnl I may seem ulo Jh th t i B6k'. m c ntato y iJ 10

dO!y i to hromat m Bu th da o i n t ra, u w h Btl6ke prmordi a ra io o a oy c 1 , jWl l leMOI!f b u te or o pr o h CS }1



We ow me o eq e y e g o p o S ypeho w c ' " f 1 3

I 2. e S e o e w e h e h ee o e ohe p op o Each o he e om he pe oe o o a 1 :5 3 1 :2 y he

e o eque y, o ow

M e a g o e o d pe e Oe.g. C-C F -G C

M e a g o e o d a d m o he.g C-C E- G A-C

' e a g m o d j ecoe g C-C E -E- B -C . .

a d he e y, hey m c a y y em ·

I ODFL On4:!O

• fl i a M :5e M ee I of wiN ed Ar fl rfeexap o an 3m h e n c m L td R K



, u



HUC I"c.• " r a

s ,l .t d " ' ._ " ' .

Sr, d •.t

l ' i f ····,



We a u a s i p a M 1 :2 sin ia ua y p n a s a p w i Fi .i C -E E-Fj-A .

s

4

an a a the basi s a " a ma iy wi w s a i y f v is s ·p i a d chroma c o s a d cho ds c n b d min dAnd w a i a an p an d s v y

Te e is s an ani co elati b w n y m,e ds and Md s 1 2 and 1 5- w d a p A F E and he w G-EC B ay theaxis s ce t e a Fi 48) and pi p n n the

w an d s p Fi . 4) wes pa a the po e.counte po e e1a o C F# and A E

iv y axis, w have M 1 5 s i Fi 8 . I w combine n s the a w a M

1 :2(s i f Fi 8

5



0 48

I res ec o to a y hese formul e are in epa ab e Theda e ro o e 1 ode s o e ph sis d bs o o a e o en i i s o h o ( F#A)

majo , m or, ev , d o d , a we s Mod s 1 5



T s m m g n e c t i s s m me w ne em n s e

i s

1 ' Ci " . 0 x

5

h al r ig in i M 1:2away r n e noe o or cn wi no ohe m or d n e e Mel 2on o i o C} or A. Th b nOe

mnor con m or ir nd m h Is awys heo , w e ha e mjo ec , o rh mnr x ad mjor

C\ e ppr O n r r c o ;jorJ h ny e no may a e e n e ae a



And th s i h a n why th mo t cha act t c a m in Da t6k a xc y by CS p in ipJ ( b tt m, o Fg. 4).

A U ( l

•

po. 51

Wi hin th ang th tw - on cal h e er n . :2

mo e s b con t c :

a I• " EI E G A B ;a '.mi . " EFGA I B; anda bd,m " D EI F Fl AI A S-C

Ev o h fo m agr w th o o oth r of h a v o mu a

58



The p ece cal edFrDm I d / (M o m No.s s n th G#-B DF axis s sc le p v des a fu l M e I"'A B C D- F G ) wh ch, as appa en m h nal

cho ds can e on a · { G V#}a dI (G"' =A O) and as a (C ) andD(ut (A-D) c v ng h compl te ax s

f

·!HB th t and lf ands play s pa ate 1:mo l ( # A D Ea d B C -G ) · nd h s cha a t d by cpo o : l I !D o U + fo t

A t f mal const c ion of th c s a j t

e , w m io Iht probl m o( t aher;u on. "I i If hlyd i J : . w ave 35 m »of v u k s "w t vkd H t a · W w guid Jy l t o f tyl ' w ili ! K l a is h : wy w q h( h r i vr S h » no rWU lio hi. rch o O

h o t ; 1 in Ji onc syt a te (

t i om o o d g w - us "; ,k: /P (t920)

Th by h m oW M 1 : w ob 2



F-B GI D a s . Th t s ct on los s in J, n ng a ho b e bar The m dle t mov oun B, hen G#, w h nextend D pe l·point at the second double·bar e nalcho i a syn hesis of D majr and F mino and may bec nside ed e sam tim pe alpha ( # A C D -At).

10· 5

O t rd xam ple s e r cap u a heme of h ViolnC c,rto s n g ax s E G A# # I s l f M lI : F G G#-A# B- # D Ba s I a d as on

m l dy) d G ( mo l s of h s. Ra 6

c c ms ib s he £ g mma h d (E m o -m or,G# -G a d mloy o 5-13. h 1 :5 mo l& F- f ·

=

F r'- r- r

6



1. . .. _... .... _ . ;

r

Ba iked e wh le n c ds ho c ,in e i ha e i we e f mel in und eF 7 Bleh rd' ate N . 36 TI Woo c N . 2Mc v b. 48 v b. 5 v b. 4)

Ha m ni a i n and heme n uc n in fo t cord a et ikin ly f equ nt, d the n u nc Hun a an ea anmu i



O

hod fou h ge e ally a ow wo om i tioa o rding to the 2:3p a n pr n p e ot after temod l

th t f ur h ch s i he 2:3 scale wc t tt o wh h a majo s c nd i h r mi r r hn ut n ; he - _a ad c h o d so gs:

· 9b good x p of a o i t on e lo ing themn Movement of t kw fr S g Pe on d e a

The 1 5 model e ba ed on tw u th ho d D Gand A D G64



1d {A D D G

D G! GG

h GS h d and h d a nt a n nt t n ie . i h n t a M e a a Jw P a a P ;TI <: t ·

sti a ta e e ti a

1h u d n th A D E G wh ta , a d th w th nta # G# B O E

wh t n a Eah a t sd n xt hu A O and G E aug n d ads and h w #D B and GI E a g n d t ad 8 + 8 + 8 h

t a s n a a n h d 3 h natha a d y h 1 d s and th g mma n

3+ 5 +3



- r C b.

Th b g g a al ot um a l co rpolla on h p upp par A a E a t low r F

a C W v w tog t fo a ax al a ra g m t,F A Ev com t o h t uc u o GS

oula



D a on c sa k' atony mp y an e a t an ema i D

of the aw of h oma t hn que e the S uIThe mt aa t i om o arOk " atonystem the wl ovrtone) a DEF GAan e d mao a wi mno ven andau m nt ou h ma or w th and ) It i aa ou i e e ton der ve om e na u a ov tone



O6]

I e a Sonat for Two P nos nd P ;on, rxamp e, e a us a e C-D E F# G-A Bb e s se

a v e C (C maj r) r see F . 64 T a e m a e y e ma r r p r e " a ra vea e e au me e a s a e ma rs (w t D; t k, t pa r A e m r r per e m r 3:5 :8,

C E m eu S m.Le us p a e e pr pa eme f e r m F

M v me a e a M m s e .e " r ma me mp S mel e s m , pe e m r s e als3- -8 e " a eme pe s a e

O 1



T o spher of harmony comp ement each other touch me ure tha the ch oma ic cale can be separated into a

OS s q ence and an a ou c cale.·

6In he acou c c e he major h rd replace he m nor rd

the a gmented fou h r p ac the pe fec fo rth ( ), andthe ma or x h rep ace he nor xth 8

nc d nta l let me ref h r to the la gur in th

old t chi dren ' and p i ve folk m ic w ch b not etch of magina i n can be r garded p d c o mede b rate plann ng th ugh he not acc rd wi h th "g o-m i mean i e GS Li wi when te ng to tra onam ic t ldom occ to u that the con nanc of a mp eWjor ght r u t from h c incidence of th n a tat ral o e ton : o r ea impl reg ter th f ndamenta

nu ber ela io in the ib a ion of the p h andmajor thirdIn Movement I of th 0 a T P;a on the

meod ad haonc dev ae de ved fom the motp t e a lemen w e the p nc p them n theFin l mply o e natu a ov ton ale ov r t Cj or chord Ce F g 6) Yet t i ma or t iad

r ela ion How c n a mple ma or chord produce chexp e e ect?Lo at from another angle may a com er with a

• B m nlc , u a chc i tcato



pretence of being up to date avail h mself at of the majortriad, whose v l s gn canc h s long so orn o and becamean empty husk? Actu l y he t l e ect of Bar 6 '. musicis due for the most part to his method of reducing expressionto s mple and pr ma symbols The m jor riad may n selfbe a hol ow cl ch but hen brought n o p -u l rel tionship ith ano h r system- s done by rt6k it may rega nits original and poten signi cance

he xpl nat on s h t the GS be een o poin s lwayscuts in o the m t t po nt where s symmet cre t bl :he overtone series is devoid of tens on because i s notes are

integer mult les of the undamental no e's v br t ons · hethr ll ng e ec o the majo t iad in the Finale o the Sonatas a d rect r ult of it being completely released rom theconstraints o th S system

So he l (p ntatony) and the are not onlysymbols o the purest mus c but a so elemen s of st uc re andformation h ch n art6 's interrel tion reg in the re onlyhey may onc h ve posse ed h s s wha I wo ld l ked no e s the e menta reb rth oCmus c through the reconstruct on o its means

Let us set up the formula of the ork:YNAM Cproport on " Sforms " pentatony opening

movementAT Cproport on symmetry =overtones closingmovement

•The c prs be law o he OW me n e oveton reRttb Lw o he m n we kow h moni ove on uy be vi a o o t i t et ; t C only vi a e o h r

le J u in i . et f he I B h-p ud Jn on he . nJ o n e e e ov o om ne w

e no e e o he o e eem e he he ove o mif he e e o U e bD mo

o the ou t tem " lo r t o n ha hee n 6k om oR o g e pr m i e oou oFen m m 6k m u o a e o p on



Th s mp ie that th 5ymme ical p ri i a ion of theVinn e c a ica cho and i s ha moni sy tem of ove tonea ions a e ph nomen not in p ndent of ach o he ; they

only p nt d rent (ho zon -ve t c ) p jection of ham ba ic con pt.

Th two y t m O ct ach oth r n an vr tionhip h ough th nv ion of CS int v co i nte va e obt in d fom a ma o ond ( a nat v nth ( .gf om B , B from a m no thi (3) a ma o ixthfom a p fect fouth (5) a h om a m no th 8) a m oth rd the m t cha ac e i t acou t nt a The efo e noon y o they omp ment t l o r ch o h o g ic y

Th op n ng an o ing of the C 1t Prfn o beautifu i lu t ation two Ka e mi o ng a h oth t fnote a GS ca (i te a 2, 3,5, 8 wi h im i h han a pu e acou tic c :

.

t o th a ify ng Ihi nt r a ion fom anoth r point ofview he h mony wh ch app a b neath th u mloyof Fig. 64 p oduce p hap th g eat t p i e o the wo ko ta n y m f m l ma o cho d E· C.72



This o s s s or th los s ove tonl a io s. Le a pc rc ra d majo i d I e oma i Fi s Mov m m o

ad always em gcs i t e 3+ 8 di\isio f hc OS:

is i rou (5) , min six 0 o t isCS o d v be n ns o m y i V rsi in o P "f h a d maj hi J a o i ho p i ly

et s s ow s o ds i i s fo m too:

i ;' 0 68

W a is a id e a i o e o . i e S ys em omO e downwa is eq a ly id i e a ousti ys em i thepp d e io I s c o e a "ov o o d iumS a e t o a ie me odi a d ding a a em y p ps be to t e a ha p a o y is OS tos

j A o s a u s s m o p ou wa dm. is o o app i s w it is o sid d a o ly

un nn i cV; s s i a ous i sys m owi g o to73



c n ance) where s the GS av ls tsel p ecisely f thoseinte vals wh ch have been c ns de ed ds a by m sic lthe m the ime Pal st ina. Incidentally th dive ityacc nu the te den y W te n m s c t be ac s ic and E ste t be pentat n c.

mpJ es h t the e a c s nance a d d nance h s inve ted the tw ha m ny w r d ; the p y "

d at c c ns nce s n d ect p p t n t the ve t neswhile the ch m t c techniq e t ns u h gh t deg ee c ns n nce hen a l the t elve semi t n s n he temp edsca e a e ade t s d t gehe - ke he a he sea q te B k. H eve inc ed ble t m y s d n pent t nicmel dies b ed n ey· e ( · sc e: nte ls3 8) el ngi g t the m st c ent laye l m sic theea est d ss ce is ep ese ted by the p f (c .Fg 76

Asec t B t6k's m s c and pe haps the m t p nd that the cl sed w ld the O s c nte ba anced by thpen sphe e the ac stic system. The me alw ys p e

spp es the p esnce the m syst m- t s n t ccident lh e h ve lw ys depicted ch m t c m t ns in the Jc cle hs ee Figs. 2 4 ) n the l t a l l tionsa e depe de t n n t e s nce the nat a se nc t n eme g m ne sngle r t he e t s U

5 Th the di t n c system h s a fndament l r n te ndthe ch mt c system a U n te. n the ch mat system le ti c n be nve ted th t chang ng the s gn cance the cent l n te. The p incipal theme the apit lati n inthe V in n r h a B t n l ty n spi e the act th t t eB m j t nic s n s n its hea i t t e inv ith t me nd e cc st m n y t ve t ne el tpe ceive it a hav ng an m n t nal ty The B cent e sac ent a ed by shimme ng ped l p nt t )7



Even th s p oce fo ow a p a e cour v y d t ilhow g g nt tion p to th g o tr c centre tho t (b. 2 1 7), a er which they gra y con ract g in.

On h oth r h n n th atonic Thi Mo m nt hprogr s ons a q it m, 6I. Th iatoni h r o j ! charact r s y a r n s . th c or o ira i s t rgy or o g p rio o ti w th a ot ·nw v ing con ancy in co tra to th CS sy w h ay of a dynamic charact r.

7 Bart k' closed ch o tic wor ay w b y iy th irc , whi e hi op ( i to i syst , by th raighte Li Dnte's D \ n Co e y t y o o the In

h e, th w i ha t P d o he t ghh rro h ay i gs o rno

conc ntr i ion t they : rri\ at th " c th rea tho e o th r i o wi n in o th in nitpyr .

t k co os t w a i i r t ;

ch o a c s o t t y associa wi h th rw a o y wi h h stra g t n o o y sc Fig

8 h i o "o n an " os is a so x re byorgani ation o the he n re at o o The b i



7

a l ssi al me ody is the ptiod As a ru t t mes n tm sic o Haydn Moza a d Beethove arc dv ded to 8 + 84 4 d 2 b rs t r two· ba "questio be g follo edby a w bar ans r ; t s f ur bars ma t b o s d r das a s gl st o t a r o w c be g g ve ba5- . T u t form d v lop s s s mpl O ar s t d

alf lose a d orr p ds o to u l s di g ot 16 bar p od pr nc pl of symm r cal riod at os read y d s rn d Bar k's d a onic mod of riting l

In o t o t is j OS e posi ve a d negat vsect o s co st t t u t d er t system es o s a d"a s ers (s F gs 6 a d ). r t law of la cc a dsymm r al r od sat o s repla ed by r gular t s of

ymmP sitive a d nega v sec o s mbr ac oth re th as nding a d sc d ng arts o a wave

cond io s o orga isa o n the CS syst m a in rselyrel ed to o t e ymm l p r od sa o o prov d

a proc of ergng, t ot r for dv ng o st t tt orm r mp as s s galc Ul t m rs v y t ma r al p C forms assume th a o an t r p d t me oc r volv g t

o a wav w t symm r ca r od tio b ks mat al o metr a ompo s of l e r ym andst op s t on tr ct o of a v s



9. And what o the two y.te l k ike when examin d innumbe ea on ? The key n mbe o the ove tone y em a ew lt n be : ho of e o a e 4 8 j o he h-3, 6

J2j o he mao d 5 1o e Whi e in he OS !ys cm thekey n mb ina i a/:v5-1

- =0 6 8034° ..2

The irr ional ha a e be om il mo e expli i i eo m a w tten olow (whi h again on eal the

Fibona e ie )

The a o y em on ari t ial, he O y tem ongtO mal p o o (S e App 111 The ha a te s8 poo on uonly app ox ma y o e t and uep

ible on y in i a iona n mbe (e g 8'0906 Thmino hi in p n tony an be p o ed o be omewha a geha it in he tem e ed y em ·

0 I may be ymbol hat in he d a on y tem he pa iaon nge a while in the h omat y em bt ow thedamen al no e ( ee g 68) I o me nte t thatemann de i e he m no iad om " nde tone an themao om oe on

In he e o CS hod ela on a o a idn e e y; the mino hi al a e n the ma o th

below he k y no e A hough Riemann on ept may be• Te odr·nubr oh m r hi d n Ih l m i " 9

t p ato c tc:, 1T T a saoy c c r i d )



A prt l ry v a l to o v r oa b o v a ma h Cmajor o',ards C4t, wh a lu o ark

7

y o t a ymmet y ent e o t a·o a e:

o-o-e + la miS m r y !r e o th ymm o ma or a m or ha o h a ou , ooh h r la o p o h wo y m om

w r h h a p o p a o y paaI mi

a h b o h o y h om a oO o a

r mi"o mage o h o h r r la o hymm r

ymm ryto o e m /a

r k hroma y m r ul p ga ,w oY m authe t c h mo r o o h h o r b in S tha o h r D

pp I ra o m h mo · u y a mo 'r ' h h

m u h x y a r r y u wh r u h ub om t.



FIO 74

Ac u y, he mos n ns ha onic nc ion n cl ssicm sic is re es n d by h s domin com s ass pris tha h minor subdom£nant, ing n s st of

s domin chords is ss n i lly ch r c s c Co of" S nsion (in a s

358

5nd conv rs ly h m n n ha moni s u on dJ' sof h n a s ov on s I 8 I. m a s no hin l sshan ha he chn qu o ns on- a a ion in cl s c m s cis clos ly l d o h d p n pl o S nd co s c cor la ions: su domin n nsion is, in c CS ens o", whdom n n onic r s n v o l ionship.

Th S in h S ys m c n d c d tuh l ·mio c os so f qu n y fo nd n nc n p n a on cm lodi s omp w h h chn in h nd s x-fouy s of old Hun ri n s n son s

rfl[f J D1J JjJ!

7



J 2 Ba 6k s d tonic mw c alway inspir d by no m m a s en , ma m ic by a ark, m e ver ,r a o al a mo ac a o Tis volu a y br ! o

m e hromati experime of z a M usso yprob g he om depths of l t rec ll he l te np e of L szGr , UnJ k St , d F ebre hedeath m R WQnr ee<a, the gh s l L e G a alth se a e w ten n a t ne s em d s an e od Or ts ene of Go ov z w e e Mo s org v lim elf of a per " xi system .

Al all, the h omati a d at n tem m aohere t k r re e t o ides of e s me coi , one of

wh h neg es and a he same time m lemen s, t t hehe st t te nt a n n a m and den and e de ea the

•he e ual ty app a he reque oh key.

Tw ra s wh mer S a9 M v her e di stnce c eat • f aig al y, 1 ih ilAt i. T pro grae o

heF / " n r c v e d yf m r d A j eJe w c mp emen a e , meetingn a d an e m el :] e ) F-A -C +A E F A - -C

a®' : [

j

e an ece w r aw a g e dby e mb m r A j G B A C 8



In ome ofh work B k so ar i he lar a o a dreduc ion o h mater a , that f rm a d co te t mean a dmea i g o co s u e a m in pa ab e e i y.

F m t e p ecedn pri ip eve f ther djJ nj rma nbecom se f-eviden The mai d a onic terva s .e he

d mjM rd ph y t majo chord iltup u e h r ever ec d de ee f h ch rhyme et

• •

5me). Sly & u E Ap m or "he S he « Bw W: bit dnk ( F 4 QH e E C e h d b Cmi

& he o a u u h FI m or dyl,hy e Cm m o u y A m ohU e l h m m gk h e -me e of # m P mj &I t h e ' vc

s h uc dqe e o

A



He e we h e he r the we k w B k s ·

f A78

f w P t , Sw ss V , N s 13

1 e e s p p c s D c D w ,M k k s s N 0 e c )

h s t pe, e w h ust f h ( ch w h #), ppe rs he sp ,s w B u ' hs e e 79

ord h a co n e part e m no cho w h j v luJ .g D F-A C" wh ch i;wy s wi h pa n ; o

Ha 6k', rama wo n o ( Yo mo f w o e B 6S ey ) W h e b e examp om f b G ;

1 ' " . ,", ' i . Ih s At the u , , # d I: the j rh e o l tmotf C-E O U Py h uv n; J l •E G m o chor h A J

o e m d -A om hee di l



10 · 79

Sin t a i y m m ly an inv i n S an in di ni m ni y ly

d

0. 8

dia ni i d t alp a inv i n i v dy p maj i d d min v n i n t v t n w i w r x l d 4 by h ql 4 Q $):



H weve paradoxica it may m. he c d w ic a a m jid abve the ke -n e and a min th d b w i m k s t

mos "d atonic mo ope d mp si n i Ba tOk's mu ic:

\ I L&UI, I

And c mp e he c nca en i n, th uld b p a er of apha c n a h y n h d

O 8

I appen f eque y ha an amb g u ba ome imerepeened b and m im by F



T s me c e in he "ax s e ody of he e e n Move enIII of M c Str S;O C a

f f I:,z - ft : F

We ay su a se th se a y e fo ows:

s PES

(chro a c sys e )

Pen onyAlpha chord 3 1 5 ode

Fo s of eq ;J n e a .who e- one sca e

d n shed evenchord n fo sg en d a , con s ng

of no

Acoumc PES

(d onic s s e )

Ove one chord and ca eInv r on o a haS cc on t ds and

s w th jor chac er c

o of eq a n erva scho d n s

a g en ed ad on·s s ng of ajor h rds



Pa t c ar igni ance may b att b t d to the fact th t1a Y i mo t ha a t i tic o B t k' ch omatic (CS)y tem i e ltroe cho d p evai in hi diatoni syst m.

Thi du lity in o opinion, o d m to xp s th twomo t ancient ndeavo o m i . h phy io og c pp to o e s ith th og thmic t ct o th cochena most di y to p c v th - a- mi (2:3:5)e ation t th i st stag o hi h both p imitiv m i nd o imp e t hi d n s ong p ovid n q ivovid n e.

In p imi v m si c t e th n o m jo t n ity nnctiona tt ction a ite n no n · he d v m

o o ;c t in ing de ive om a ite i nt onam y h ove tone i hi o d on y h v O R n o io n ith in t menta m and it no i nt t t

n t ona m i thin ng h d y mo than a w t io d. nt tony m y b d d d om th yth go ; tony tem-g o ping th n e t th nd o t s h monim ic om the ov ton s .

n identa y p ntatony i o m d" in a o igin b ing o" o zont x nt in t m hi the ov ton sy t m i ohar o igin and ha a "ve ti p ti l dim n ion

Wou d it be to da ng to pp e that the o pent toni

nd aco ti h n ng e the t o int o ogin o m si .· o then a t6 pen t t d to it nm co .

•" e taton do not er e omi a t t ic a enc artkHnarian F k sic 193 . t i ale t e t no re a lingrole ( 6k: Hngian ·olk i and gar an ic, 9 .On he hand t e reuen use e o r n e a in o r mU8 to w e o t c o s art k hein luen e o p an

m i on ern mus , 1920 ••a 6k i n b ev d at i b ble o race kk m e ce o e o e t ,

a c e an ien l Ba 6 : o k son r arch an na i na i9 7



T t i usti "i r a i , a o t[o c tr t of t a ; t o xt r a ario ro y al w of o a T fomr ,

t for s , xp ssi a eotonal a , atto ou u , impr s i a a aim support t s i ti o s a o

t a S is to m t wi i ga;c matt r o P tatowit i t sio ou r a om i to i wi oUt a of uma motio a o sti armo o t ta , ma op i p t of t p om o ofuma if o of uma i t tio -a i ra um ofa r i a pip (or a s r i ou to ri it a out

P tato i a a ous i tr s fo ow o t a o o ,P s o o i a o t to ga s a r a on w ip si o ts isor a is stri i to a oJ t sio H rt t si ma a a t at OS r at s a dos woa ar s a i r t s o , w i t a ous i s st m isa stri s to as t sio t ou i o r o so a

It ma a t at t s os ss is a or a i f a u oS s i s , a for am s i p ofBart k to s t m a t is qua it is spo si fo apa i of GS oga e. a i ust at o CS a aro t a ut if w i a imp " ot wit a pap ri o

wi out x ptio , p opotio of t s ot wil i p aom t i o o · i 5

• It cid h _S0n 1 ommo ivi tu e 10 i d.



=: =:_ : :, :o ·63

no. 85

I p pe e pe agram ha aU des a s Pa I

M Le me adm ; a saceF ds my wa k g u hereI he dr ds up y rh d

A: The r d s e es y ?Bu e me h y s he

h s mped s y h w d y u c me H w c y d sp c ed

MZPH O se e! The es are r y draw ;Tha e a g e p g wa d,s y see a e



Al hough he mpo t nt que t on o yt m and m t e nnoe d l hce Y c i w wbe in ed out. B t k' ythm s gove ne by ct w

been own o ule i fo m and h mo y The cfah e of Moveme 1 of e S a j T Pa aP i no m ll deg ee due o he olute" oddmet e 3 t me 3 eigh w e t e F n le ow i tih e o t b o ute even met e 2 ime e ght . Movemen e e d od e i tent on l y n ted.

(B w ve m h te e d i he ot nti it e ofeve " nd odd met . I t e a C Mov

o Ms V l Dv Mk k t em p e ented in eve met ed e u in odd hyt mo v e ve .)

e y hm with t ong end ng in Mov ment h veo n e t w t we en g in t e F n e ee F g. 87 .

6

Con eq ent y t e t em of Movement on te snd ho e of e Fi e J fom.

B e p l le ev il l o w h t e even d oddmet e .. d n e e iodi lly lten t n n e odd met ed hem ile n lte n tion of" + d _+_+ ovide e y m

e of the evenmeted tu .

9



l



Shou d his os on i music summ d u in a sings nt c it might run as ol o Bart6k ach d som hi gtha no on h d b fo hi tim , th ymbolic h nd hak

b t n East and W t: s h is of mus c o O i ntand Occid nt

Th s sa i h introduc o ar o h utho ' b oart6k yl " u li h in Hungari n in 953 A folloing

ch t ackl s h d matic" inci l of U t6k s mu ic,s c all of h instrum n a or s W mus no f g t thatBa is i ac a d ama c m r m nt, as all c atig niu in ho char c th b nts or ogic nd h o m, au t d.

9



Append x I

fe i g o h &ta JM T PiaS a Per ;oT, s ofi C o o n u w pa icula of Mv m L In

35-247 n !aO t x ;on he o h th # o ru n ng hrug he nhe D cou t rpol d on the o h r h d h con t ngfun el h p d m c p gr on dg d h Dp i cip ch nd at r t F-B cond br ch

D _

< " 1 ·If , J. . t ,rH d rE I'J 4l 1" ; .!"c f·- I .

99



T he ou s tions o the s ond y h m th c pi u t o(b . 29 33°) a b s d o th four pol s of Io xi $

th t t e r O t r a d er p t , pectiv y c orr s d w h

ch o h r i th i pol cou t rpole r a io .

FIC 9 1

Th ax co s r ct o o t h e ca s q l y a b guo sb 417 43 ) a o da t t ola schem the

au t d r ncipal the e a ea i \ t a da y i E + A, o t disjoi d E G -A C or mi or

(gamma) a co pa t c ord5

E -CI A A X I S

O. 92

lO



T v m Mov 11 M f S Pn C e a e em

e e a e E F#- C i w d b

e ba d m m m w i cm i J e A a d E (

n B ' '



App d I IA few example are iven to U tr e he interrelat onse unded in connection wit Fig. 13

Te orde of key of t e F sl ROc follow: C tonic, Edominan A ubdom nant and C onic.

Movement I of t e ubd v ded by t e ve·foldecu ence of t e pr nc pal eme

ton c (e p ion) . 76D s b om nant ( t part of development 231A dom nant econd p rt of development 313 tonic (re ap tulation . 38 ton c ( od

8A mila a angement to be een in Movement Iof SIQr T P s P sson:

C tn c (e it on . 3E dominant t part of development 1 1, 95

u om nant ( econd pa t of deve opment b. 3C ton c ( ecap tula on 7

In t e l d e ample of pa e 45 t e ela ion are D-AJ F#.Te pr nc pal eme n M vement 11 of M j S g

l s part cu ar y co ent becau e ere we ndt e cu a s ructu e and onic-to c om nant- n c contucton of e new ype Hung n folk ong . T e to crep e en ed by e C F# ounterpo t e dom nant &unte l (not y ) T e econd en of e tonic p ovide e act "ton answe of t e CF GC ton c angento and C F to #-C#



(M)

A ilar ia i n inan an nic i vi n in 8 Mv m n 1 h Di" /oj A mi a

c un l c r o F 8 n c c u r :



· 9

h r p u :

AC 'F

T m c n g ( B C t l ) m ghju i b b l h b 6 m n n gqu n cu n mu



w ch can ag in be expla ned the re ula ities de lt w h

a ove.The ope ng a of the Mru/ Mnd n l t te howhe ton a d s dominan a e k d; the D# ton swingstowa ds he u om n n nd B o nterpole :

n



It s inte ing to note that n Ba t6 's mu c the threefunct n p a a s mbol le too part arl n his stagewo k . In Bub d' C t sgn anguage awas goes hand

n hand w t the pl t and content of the drama. T e subd m nan h a negat e mean ng be ng re er ed for the e prsion f fve and p s i n. All sit ve movemen st t with t edom nant The tat c p l a of the opera and the po n J of r tare b ed on the t n c

The downward pu of the ac on n the M Du w M is a so exp e ed by the funct onal re a on The dom nantart of the pant mim in ) e ts he th obbing e c tement

oflife where e subdom nant end of the work (in depicthe death of the Mandarin. he nte mediate scenes nearlhalf f he m c e pec al where the andarin sa i eshis de re are wr tten n t e ton c C

Beg nn ngGOM N NTCl maCTON CndB OM NThe succe n of scen folows the same d di o der Iar p e de cent frm t e d m n nt hei h o t e s bd minantdept s a f e pr ng the dea that the wo k move towardsa fa ful" ab :

V Od C l - . V Y h)- 3 V ( )WalZ _2. Wltz -Mrdr _2 Mudr 3 Mud

t i fo thi re s n that the s ene , tuated one be ow theer on the above pan ae de loped from the

same mate l; e g the music of he i Murder or g nat nthe ba ic chord of the t Visitor (Old Gallant



(_. "C)

l In th " plot of h W all this is inve ely ( 'cene ollow line, incess nd going upT D gr e :

XOIION

MIDDL PART

P lue ONIC

rinc DOM NANT

P ince UBDOMINANT

Foest ONIC

St e m DOM NANT

M king of t e oll DOM NANT

D nce of t e Wo en ince ONI

I . Scene (No. 0). Scene No. 83 Scene (No. 13Con u io

ONIC

DOMINANT

U DOMINANT

ONIC

REAPT ATON " e o exp i ion ON

DOMINAN

DOMINAN

ON

Wo e rin e No. 14 9ncess n the S re

Denoue e t

o ex e e e follow e ai uc ure ofce e D ce of t e nc ·

• A detail anaysu or h wrk w pblishd in th a o ' " Drlk'sD ama gy": Stage wrks ad Can.ata orana (Editi Mic J lap

964•08



E- AXA ,

$ E I

_ h

.



A en III

ex oden e on n ony e on u e g m ri lyt nn t b ob i d m t emi y i. by m a o ra oum Te k y mb r o CS ( mi r o .

Hee e mp e o the Eudoxu " o t u o , wiq e d e e

, -

J

103

,

\

\6 \

n nohe d on he P h o e popo o

P .0



Th ypo < o h K p a g b n a gag to h hot c 0 618 . ) ° 9 3

- 6

a a c a o gol c on a b gh abo fo ow



T e m b s of he OS hain can be ob ain d by subra t ohus he OS o I ·618, a o e la e : 1 - . 6=0' 82,c · " '3 0 ; '3 3 ( 46 Bu

OS a n a a o be ob a ned by nvo u ion = 0. 2- 38 ; o ' 0 6 0 4 , eT e n o e u e mee i o e ini p

d e i y in he g T e ue e i g i v

. 07W e a d m a a own a a u oes m wh C me n e i um e e eT e h s Py am n E y rev a s e o l w s r u

'

. 0and so n s e a old a le

• K Kcppisb a E.B

'



e ynam q a y of t Pa non n A ens ow s muc os OS men o , and at s w y we eel t bu ld ng soar ng

u wa d , a w e.·

,

"

W le Go c arc ec r a our d ang o 5° Rena anca t, o low ng t Gree mo els, ow d a r d c on fo t egolden a g e T e c rc e ad een g en a " ea e ly ym -

sm w e uare a y o B cau t Got cconce t u j ct art ly a a r to a n y conce ns tforc d t sq a o n a ace wi n t c cumfe nce ofe c cle I cont st to mat e o a e d ea ad

an eq l br um n G e an Re a s anc a fo e n

• Z g



n he ti be ween the th ee i e in t e b e Jetteymb h w OS e t n

Z in d ri d OS om th p t n f the hu n b dyn 1 l t I I ;L [ mb t

Ei t in p nne hi m Potemk n n u h w y thhe p e pon o pe e n t v ty n he n i oe on o e h a and h e f h ghe t t ty n t epo ve e on.

A o ng to En ten OS p i at o wh h oppoethe n t te t e eve pment o wh t oo .

No e emen n be p ope y join w t ut he a od one he wo n on y be un ted y the m i tion o

lin t o l the in h t o e i mo t beu ifu whi m ke omp e e w o e o t e n f t e e ement un ed by t."

P t Tim .

bartok - bela bartok an analysis of his music 1971

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