F 19 b ud i: ,t £ Lv 9 7 Rdrt 99 Lld Mw pc q Lu U pu w p Av
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A
m
W w 0 9000
Pn d In
Br
n
Contents
T Ppl 5le
p lion
T S
i
'
Ap I
Ap n
'
0
t Sye
Introduction
T pbon of .dy of mc ofBa an mrt evt Many dipv aa of prc wor o have ap, u hr for h me i he Egh lag aoiv ad convincg ion o tl pnpl whch te ome wked o o bt r, f om dng t nyone dng lifm e i ng o by wor of moh we owe th aor pbher a debt 6 Ldv" e ct at 6 aly evolve fo a meh oigan h m omc; h chOdcW te mc mo apppa o m, tg h Cp rO o gth wn moveme whole wok, mi vsio wi a movm sch poio dvloP ment a ptao ven bng pr witn 01 f movem, accordg o D sge c pnpe at f he Go Secon me ch maema p w a "h pcipe b ad n he
3rd miUium k up by t Gr two thoud y lt ad disvd d Rassa bt v sysmatiy appid to musi y m. (h is oc sil s qu movmt by Hyd, ompod i Ig aordi to God So ppoio, b is is morc of iipd po ittu quik o t omp' du.) Ba6k disvd wy o div h bai at as A-G-E ad rst ivsio o t mjo ommo od E-G-C om God Stio i is pr b o o Fiboi's i o wo umbs From tk prodd o bm o tw fdmt s, dKbd by Ledvi "dioi d om, oig spivy v d igt o id th ov Wh J mwor Bk ppid hoy o "on xs s b o y. s impd e of k ha h ptto s o h r fk mui, mods o i d mdiv d ok mi d ay h mo d mio s diom o Euop t mu of h 17h 18h d Dh s g o h rod ow Btk' omp io o h dpt damals o oaity wih pr oml proporio urg t pt ya t v b vou sii ay od mp wii musia thoy o sow wy owd to t mps ad o p im to tod i t pod o o wi oowd t igo o mo d mio piod bgii o u T mst imrtt i od oi pp v b vivs Muaaya Fom ka Pro d tosia (90), Hidms "Ct o Mui ompoi o Vo (Eli Ed. 197) k Cook's T au o Mi 9 5 9) d E Asm's Fodms d Mqu da i Humic (1. o s mao wo soud ow b ddd dvis xpsiio oBrs mi ois Thouh v wo
I
roagate oes wch are mutuaUy contradicory n on reect or anoter, tey ar all n agreeen on on fundaentl rooson. naely t onaly, a onal laos ofoe knd or anote are an ental faework for any CO$ucton of tone' wc can be rgly codered a wok of msca ar avev k of e ajor mnor and roac sca- Anee xon of e sace beteen te notes mng u the ocave a tructured IC dvded unequaly a te erfec ft and fc fo. and now Bat6k tonal ax oeag n s arcar donc ad croac l (te latter not te cromaic le of welve seton) ar al bed uon e admon tat ee x a eachy of ntv roceedng from e ssenl natre of muca one temv c ay nO be dgarded f uc to rsl from comosng or te utng geter of on Some reade may onder y ave no ncluded aong te moran eoretca rng of s cenuy Anod Scoenberg 194, e agmetton of c n uor o metod of cong it twelve ton c ar related only wt one anote now known as seal dodecapony advance n te aor teo·· A study of e teoretcl agra o ths ssay di any uc luson e woe con oe meod of ong t ele on deends uon e oowng o ntenc: Te en eancaton of h donance ref o s compreesblty. wc coderd euvalen to te cosonnce coprnbly A syle based on
pg
M • hn: S!
p cD C and ron a O t o e t y le isel f m But DOt U C; t ent &d p) - . Tr nn ught not u ft wee et Dne. Ad in any Ite euna o f a o cente d Do foow om y poy l poo d i mey doa of mI be A Uch t toly o the c vdity whch he c for � nd hoe h y hdy me icwo mo e mnt hra wri w mon ave M fa I m wre no pter o( oay, or oe h prodd ay prf of hrivality A se work or m Te dale chpo of the nS of ct, Ter W d AOnO, Ppie der eu Mu (19) am t� apa om Bk d Sky oy bg B" d W a foow hy 1 b y H _ .
-
.
-
-
"
.
N d cn t VCD C be U i aot v ojvy and dcr e large wrb tue "Wek< d g �8u, wc uld b ly t "wor mat l A i be t : it i t dd t f e nt fvew ofo m t po cit-at of John C not wn a momnt' cdan. • : S 10) •• : w p g "
c
In cuo, e pubio of ndv'• k oy wcomd. od be uded ot ony by Bk ave-men adre lethe the oher ! 6ght but by Ude mpio wh ay ot he prt o nfo e m wrd, ad w b a amwork or e eae rk whic ot a cce mixture of e at y ent i vogue amo o o othe que bU a ogicay ne devepmet m e m of pt p h6ght e gg of B nd by Lai, ipia o ven u my ot he e wch pVQ e mt dey accept
Aa Bs Rdu 19'_
Tonal Pncpes
Th St
"Every h he gb o Itke i in e of a piow it Do ony the igh ut i mu.t em fm i, Bark once dd H onaem out of ncon m unter· pd evoluon can foloed fm e of foal oep ou e mo of Viene and he ne-old of oma o By a ay of omion tem can he sen proi of ial p hon to hmony
o
he non of he fouh d dg
6) he lonhip aiv mjo nd mino key () he oerone o 4 e oe of eadin Do C) he ope enon of e domnn uoinan U e dui of ona nd dane prncipl
u
() o w o u B I! m e of. L C e () n F, h fo h ubo G he d, he o D A, he de lv of e oic, fU oc DJ d subo bon E, d d nd of e do, £OD d o F con o e fucol
u u
e uen " of y
O 'U
"aae mna n
1y
SDOMNANT AXS
DOMNANT AXS
TON AXS
b
Ch n he fume C, E� (=D#), # (G�) hae a fuc b he am E, G, B� (), C (D�) hae f he me D, F, � (G# B hae fuc I ha he a chr f he eehJ b e fc h f n, wh may m e a mc (eg C mj , E� mj C
b
It should oed h, at c moe eNitve raop bew the o n he "coun e.g C a F tho tae n to each oer, e.g. C ad A A le alway ierchageable wth s unle wiou any chage funcon· Te lecountele raiop i the t daenta cUra picpe Bar' sc n to th .m age fo eady he e fo of BlwrI C w cocev econtee teios. I ss a the dak F# le to he b ght C jor cord (he relm o Bluebe) d des agn he gy F# The cou o Sol fo, TU Pi 4 P"n r fom he dep he heighs: fom F '0 C, the beginng d end of he work n Fg 5 he F and C enr (bs 0-5) erent he toic, t G and D en fo the end b. 8) t domnan the A a D en (. 1217 he b doian countel The B mao oc o e Yil CO i relaced the develoen b y coe oe F (b 5) Sy the F maor c of te D/i eplce by i e develp men (b. ). T moveen of Mw/r Stgs Pc" kl" hae e foowng stcture BEOHO
ML
D
I
A
A
1
C
II
F A
E� b 6) F# (b. 063) C b 46 E� b. 83)
IOWK
I
C
F , A
C aUl o c, A-F e of . b vu i t way: AA�D. t D ,< b A D o ..p A vmoM/_S P_-c (Me. I t76 18), w u o IB'-EAD'C & C� • A
FBAGI'C$(C)F"·
+
table tah yet another lsn. A fu oemcnU on the ton AEIF# Thw e and oveeD are uped y the pnip brah" A ad E�; e mdde ovemen hoever, y the onda h a ofod aity ranh C an F# Thw eah depnding on hther e op te e th e ounte e or the prnip branh i the ondary branh
Cqueny the onen o e banh
te are a oo:
- enterpoe _ pinipa +onda bran Y't TS e
(no dion) 1 dieion) 2 die) dieio)
Te Slo Moveent o the o T Pmd FA opying ih bd on he bdoinant t te taio o ia io The oa ag i prnipal thee ytia te gnnng and end ped by the Band F otr i.e. the banh 88 5
of h
mc a ral
D ad un (.e. e bch o e e ae o e angng-f E) e dd·
•
&
y
(C t.) dom
7 6
- Ha
The mely ottung the ore the movement enred aund the subdomnant The 0 onng d c are replaed the mddle ofhe eme by e ounele D Eve min mctr and moivi int evov aound te omat
The two mlod y t he Itre te movement. one hem beg aahed the prnp F. e or t te da G ban o the ubdot The ond eme o he be mewha more ntria Athough he twevtne mely touh eve dege e hroma ae hee e ad D ouner doub o nali n we (gning middle end) and the boken-u F mjo d C mjomnor ounC
7
daib, App. I, p 99 ( A o oluon o aoni g la o o at t o m Fo
ncy pg lo onnuao ( in a h omplon) o Euopa uona musi oa hat h m wit i a au in e y Vinn "Ga I i e d y ah 1 hsm Th ron n m w iud i pa y o o I-IV-VI fy mval m mi at i a om oy In C to:
SUBM F
DO G
C
Th h o h y a aks o pm oay h C my b y i v A F y i lav nd h G y i lav E
C
A
Roma hoy u makg unt o up av Na y oy jo ad o ky o kcygtu my b lav g C mjo A o C E majo)
C
A 8
E
One more step omlet the yem The exted e applcato of reatv to the stem The tem imli e ogitio o e a at h ommo reaive or A ad E� s o oy C, but F# (=G); tha D ad A� o oly have F a ommo relaive t ad that E ad B ot oly hve G t alo C# =D ommo rev
U
F
C
G
A E� '/
/ A� D '/
/' E B� '/ C
F#
B
well now Bar6k howed a reerne for he
o Ued major-mor hords s Fg 32 For stac o C toay :
e o remas ag eve te C major show te ave hod repaed e reve A or o wh e majo oay he eav C mor techqe r Bat6' m:
C majomo
/
A mor
E major
Th tte ods ma emlod maormo o whh bg! he ysm a I s elave of A maor (F mor ad that o E� mor G� mao) mt a a t o earmoi dece FG� 9
/ A mn
C mjo�mnor
" "
A m
Emar Emnr
F# mn =Gmr
dmn nd lubdmnnt o he em.·
ev pped hmony, ga u e
( ) The h Che em luatd by e Ay rving m e te eac e t frm vetne-a dena e n he ncipe necnnecn between s D the vn. TUl te nn f C nt y G bt te nex verO E nd Bee
• y & I e �F U a H u O B d, B B 6 F P 7 Y b t T FB b B P. No I o \ . W t t n l tt B y m M C a cor O c c oa & a p. w . A Q U a b 1
•
•
•
oi raioi xn o c C n BIO Snce he DT laoshp corrns· avely he T an he SD eabp ovron ataon wen he T a he D el.
R oic C omian E omian B� ,uonan A� ubon D
R � U E an B� G#a D D anA� an G� #
omian sbomia bon
� oic
G F #
n
E�
rbc wh 1
c
If we add le o dduce he mplee
oveoe, i.e. th, he we tem fm h elao
( I the plC cadece, ha of V-I, e role play by d ve o wch pce he pl he doa ow the oc e Doe pl o r the sevh owa the thd deee of he oc, e he leadg oe B rlv OD C ad the Kveh F o E o E�
t
10
na ve o aop o ech oh. The ohalf he tave a ed b he ihagy wh chagg e val ThU e F laoPp covted o w Bk), he he F FB oe ( fue he _E# um the le he leag oe pg ow he F iead of , whe he eth B pl towa A# o A ead C. So, ad o he Qd o C jo e e eq oic F ajo o o eegC
0
rlon rd by BrtOk fo a dd o sc. Th cusanc o an d G'C dc mgng G-F# v w a Bar6 ddn" (e) Stng fom h tnc ct C w rach h dmant n on dtion ad th udomiant in h oh, i ad A a danc a h w d h doinn G pwds d th sdominan dwwd. Rgrdg 1 raos w gt th domn G B� in th upp nd h sudoma F, A, D in h ow dicon
D
DD
what happs if h pdum cov th latitud a o? I c h diaos md pws ad dow wad m, oh dig a F G, and w w o ak o h domna h h oh wud hav aum h domia fncion y cindnc, howv, a t· ao of hi fco ak pac dona ad subdoa mgg a dd iciv i h iaco of h ops oc unty baac savd nd h ftion s jniay tha of h toc. h copo is : may h dtac w h oc C ad s cd E i h o ad y A i th oh dico; yg in tionJ na ton p hy hav t b inttd n No mor han fo nc po cn srsd ic h na A AC povid o uh is of bcon 3
Fy wh hod a a a o d< �B iU C (DW the d and whch he u dot f? Rea B, C o a dg ovaion the D int . wch mi8h corrnd dedene bt ot t i opte. Anyway uona no B e doan uncon C n Uoable wh hey reated the n counel
( Thu, o he oc coal inronnecon ierg t e IU of doa d doa prtd evely by e d IV ad V bt i he of C he uonant by A� (ad oee) the don by E (and i cotere). r nohing ew hee or , the d dary theme E Behov' WGUi $ (0 majo or the s Sow Movemen n A1 of (C ). The movme of B' Fs' J" have folowig eyuene: EA in e toionabdonatoc Hower, e ae ao he em as o xp why k agmented ao e dio-VV-I (or pl App. 11 p 103) it a new approach o he yt. ge y apted at twelveoe m o a og tedey o ret o relao. At lao mt iaby ed by e dio he ave, or o he irce 6( B y dving the otave welve u pa we ge hrom ale; in o eq par we have e whoe·ne ae; our equal par gi he od o e d n e he agmtd ad y by didng he tve no two pa we ave at
t
t
c
'4
u
t we lude he whoe-e Fo the P of b: whoetone prdue the chromac e by nteckng we u Eve toal tem pup cenre odnate reao dependet he cenre Tang agn epeted mt he toc cente he hee fuco it hee tey by he dege dn the cle of eua p e n he auetd trad A. roperti nhet h y ae ble for he E aug a dt funcon and A� a uoant fuco eaio he oc Each e mn not rt heir utuo by e unterl i.e. heir ttc eqaen. Thus, C y be eplaced by F E by B� and A� by D If we dvide he tweve-one chmac e prorionly between he hree fnco each funcon hae four nd h we keep the tane pncpe ged dinhedseenth lans, dig e le in four equ p. Accordingy EFA beong o he rage of he toc EB to that of he donat E mn note and AB to hat o he ubdominant A mn ote , the tonal syt rng from a dviso ohe chomac ae ino equa par agre competey ith the system
BDOMNNT ON
0 3
DOMNNT
5
coy, given t twvne Item an t thre fco e .) at c b re by mea of dW von Vied hrcy, he a m re8c he g�ld gge e e pinpl o ! and lp-Ul wh e adu end of e ae wic fy rt n te f a eua tt of t chromc twve nO· He we ve to rwDe twn Bk', wlve-tone 1e e Z6to o Dbug Sh6ng WvC whe Batk noe e pJ o n tg pet n To nte no Bk', ceve ge i ove he and nc sb nhret n he m ae Pt
•
• T i� o p Ke m abut the m . .6
Fom Pncples
Gold Golden Seon "co ata and heneoh CS) me e divion of a dane in IU a way a e proon o he whoe eng o e arge p opon geomery he popoon o e age e smae pa .e. e age o e woe leng and e mau p e geom p A simpe aaion sOW if e woe eng aken ny he vae e ge eon 018
4
x=x: -x
e ppe orm on page 78 and he e sme p 038 s e age par o ny eng divided no CS is eq 0 he whoe engh miped by 08 '7
o hmony ; y h w o GS. a om Bk'.
elen w i at le cant Bk'. mc the 8 8 po or he ovetone harmoaon Vie le. ple le the vemt o he e v mp 3 b a n Gg ave fom- 3 0'68, ie 74 w moveen: the repitaon py 24 Mvement I o C1u n.t o 93 bn. and GS pitlaon in (93 x·68) again e g o e ddle o 7 Movet o e DW� eo o 563 rpt u (h umr o n ev owig o hir vaal im sigars) Te GS o 563 563 0·618 -348 aa coicids
a
wh h rcaiulaio I Vo VI o MikrD h CS o Fr Vaaios" ca b s o ouch th Molto piu camo82 068=51 Te GS o From e Dia o a Fly com at h cimax: h doul i h 3/ ak a 1 ar, calculaig i 24 an Bok Chords w d h rcapiaio h GS 80 061849 c Te 16 oduco ba o h Sajr T PiR P,m rpr modl xmpl o GS cosrco 2 cas it is hr ha h oraic or mor prcsly li o h work gis
1 '9
It nt par th phr of th oi (. 2-5) he scod wthi th omiat b B a thir pa i tt o t ubdomia (b 1 o) Thi thir par thmaty o t nt two o, o ummari:
s
m i poiotoi FC ti Tm itioomat ODU Thm ubomiat A Corg h hag o timigatr t i mor patial o aat t o 3/8 tm T who orm oit of 46 u OS i 46 x 0·618 8 a t ovr t part p th Dn th hm h ma io o Fg 16) a b obr that OS away oii wih t gia trig poit o th orm Lt ow parat rom th who h part root pitio th rst 8 Now 8 618 17' t hi v pi th to prt at th rst thi of th 18th ut th miat t Fg 16)
s
ROO OSIION
l
INRSION
O iio may b to oow o o to pib ou
depending on wheher he longer or he shorer cton comes r. Le us cl one of the poibile pitiw: long section fllowed by he shor one-and he ohe negativl sho secion followed by he long one In he srucure of boh onc and domnan part he cymba soke ceaes a harp duaiy The posion of he cymbasro is n boh cases deermned by he GS, bu wheea he onic uni (a he gn "cym in Fig. 16 is divded o a to mae it P ii (I 73 xo·6B 11) he dominant pa on he conay, ecomes a gaJiv dision i cosi3 of 1 unis and is diidd 4+6) The posiive nd negive secio ompemen ach oher omhing wh is own morimage u he meengpoin of he wo (he dmnan enty) h a postive sign n oher words condesaion and dispesal of he nodes cae a longiudina unduaon the waves meeing in a posii secion s gaiv ounep found he eny o he taa (in he inveion so ha he posive secion o he oo and he negaive section of he invesion ar again joned symmecaly No only the enie fomal ac bu een he fomcells subm eniely o the sices geomeric analys Fo instance, n the domina pat we nd up o he cymbalsroe, eleven eighh posive CS pon 7) deern he posiion of no the only msa sre n he uniby means of elongaing he E� noe Th soon counerbalnced by he negaive section pn a he dedm bea in ba 101 Simiarly, he poie secon of he onic pa up o he ymbastoe s markd by the most imporan urning poin by he hird (C�n timpani entyouned in eghhs: 33 061B 20 Precly here e hemac condensaon bg ao wih he 2 eighh On he oher hnd he ompemena negaive econ of he pat following the cymblroke i ndcaed agn by he sidedum (see ig. 6)
8·-3
Summang the ave t he smale and large fm dea, thee is a symmet jing f the psiti and Iati scos. Fm h cncaenat a sng gea "ent' fn ais wheen h smae pat ae nay smmsed n a nli" man secn pc i theefe ped wh a pow dynam neae fom panm foe-fm Aaytial sde pem the onin tha the pie eton amped by ntescaton dynam nean f he matal whle the nega seion y a fang and sbdng The sets away fw the ntent and fm-conepn e mc By way satn e sbet Memen o he P a detaed analyss T PiS Exempay i the ny of pots f he expoon: e pnpa heme h a e and he ong theme a nge Icon whe the Inday theme deelped beween h tw symmetally aanged Ts the pnpa theme· (43 ng) s dded fows A +B The n f B deteed by 361827 we he w s ae ated eh he odg t 2 x 06
o
o
d
- - ) -
no "
· e o vco i oo c •
Te symmetrcal dison of te second teme cn e expd s follwng: 2+17'S1SU! (bs. 44-02) Te gomtc cen (b 7) ccods e on constrcon o the thme a. Te ngve mn seon o e closng tm (bs 131 S (see Fg 8) Wn tis, S- he s gn n 2 bcus o te ful dynmc pos secon n nt, nd t sttc ontton n 444 nt of bs 114 podcs sold be fo ise
t t 18
k e poprons of te deeopment re ymme b 4) I negte mn sconntencng e pe mn seon ot deelopment of Moement Is detemned ply by te pnt of clmx n b 1 tonc conte l secon of he p pecedng e clm nd te ston t t cmx ndcte e mos mnt tnng pon: 16 te fgto o te pncpl teme, le b 2S t etn o he st eme o he dopment (lo p ent
pii
VE
VE
h uid owrds th cim is lws mrk otv sco
fom b 019 i fls o 52 siv , 1176 .. 170 .. 1606 .. b 166 .. b 17 6 . b 1 ..
om ot of cimx o, owvr, the giv stos ow ivt oortios fom b 720 i fl o 18 gtiv b 890 . b 95 . .. b J9 b 199
h climx iself dvidd sticl ito 6 + 6 b 7788) Te gtiv mi cio oft rcitltio (bs 8350 coicide wi e wted, t were of e tmic mril, ie wit 287 Bs. 28730 fom o ge brod wv, d i sutu view sm to tt of e bgg of Moveme cf ig 6)
"
POf(
V •
GATYI
GAlr
The negave main secion of the coda· (bs. 351�20) coincd with he hemac centre o gavy o he hole coda: a he ame me he reur o he C oic, n b 379 gen a geae empas y eghy pepaaon. Coepodg o i ac a chaace h hemac cene ha an 8 + 8 bar dvio ( 3!-394) he a o he coda ( 35-3) combne a oe
• I
•
• N.D
PmY
V
t r 4 rono '5
and a ngativ sction in uit of 9 + and 5 + 9 bs. Th cond pa 3942) own in Fg. oni at h am tim a v (b 4 a a negaiv (b 39) con ly, t pitiv ction o 3954 in b 41) and th ngatv sction o 442 in 411) ar again ym mticaly ad to ach oh.
At rs ganc it may appa contradicto hat th poins o con dmind by th lws o as n min unfld by th chaging tmpi. phomo y to udad i w cod ht muic bah in mtic pultion and no in t bout murmnt o im In muc ping tim mad ralabl by bats o b who ol i mor mphtic tha th duaion o prfomanc Subjcivly w l tim lap mor vrihly in a movmnt wth a quick tim-bt and mo ugghly in a low puon. Finaly l m giv an amp o tho who poch B6 ot haing ctd th "tot and radic gsa T ton o th mat Th compt on o th PiS I Pn dividd into lows +JwU movmnt. as may thor b xptd to t bginning o th cond slow movmnt. Ou Xti wholy ud; th tim vu o th compl wk i 432 ighh nots and th as at h 3,975th which is pcisy wh th movmnt bg .
$
\
6
Fibonacc Series l of us who have played A Barbro, have been roubed by the FI minor hobbng, extending over 8 or 5 or or even a. The propoion of : 5 8 coan a eqece, aroxmaey exed n naura numb he Fibonau nmbers. A characeic feaure of equence ha eve member equa to the um of he two reding membe 2, 5 8 1 2 4 55 89 and furher appromae more an more o he rraiona keynumr of the (the of 55 and hat of 89 55) Le comare eqence wh he poron of he fugue movemen of Mw/r Slrg, P" Ce. inmo gaday ri o for·fomo hen again reced to anoianssimo The 89 bars ohe movemen divided ino econ of 55 and bas by he pea of th ymd-e movemen. rm he pon of ve of coour and dynac arcecure he form ubdivid ino frher uis
S
S
S
S
Te aqu or nr U Dumb pl
equ to th prt oflhe png
by te remov o te mte n te 34t r, nd is e gain in te ar Te secton leading up to te climx b so a dvion o + 21, nd tt rom te cim onwrds 3 + . s te onger pat come t n te risng section wie in te flng scton t i te sorter art tat peced t lone so te sectonpoin tend towds te clim Poitie ;Dd nege sectons togeer ike te rse and ll i we
= o 2
e proporton olow te bonacc ser t no ccdet tat te epoio end wit te 2t a and tt te 2 1 bas concldng te movement re divdd into 38 of w Te proportion of Movement so relect te iboncci sries (i w clclate trogot in 4/4 s and consider te occio 3/ I ba) Its oml nd corrpondng geomtl strctre i own in ig
W
Q ns
Th h mut cmpeed by a whole-bar , • cod ih te BUl a BhoYfl
8
_ ---
"
Z
,.
P.
3
The Fionacci seri reects in fct the lw of nata roh o ake a simpe exampe. f eve brach of a tree on year shoos a new rach nd thse new rches ae douled aer two yea the umer of the ranche shows he foowng yeary icrease : 2, 3, 3, 21, 34 "W foo at i compoo wrote art6k ad wa ideed directed y ata peomena to his discovey of te regurties He ws costaty augmening hs coecion o nts, iscts ad miera specimen He clled h suower fvourite pt, d w extremely ppy whenever he ound r-cones ced o is ds According to Br6 " mic i a pheomeon of ure Is formtio devoped s sontneousy as ohe liig nura organm the owe imas etc (t te Sourc of Fok Music 125) his is why the om-word o rt6s mic eminds mt direcy o aa pictures d fomion
9
G
°
T of cce, v ° s Re on on n a 75° on o ed g o pan g r atns, a a twg o an g of 175 w n o
4 s u 3 y w 3 8 w 8
A a nw a j of o aog o of as: wg g wn an ; ig 4 fn w a 2 ; wg 5 am w t wn a ad -
• Te F dvd 30
S
wn I etc
f we onsidc" the f M " d CL/uta (alys o pag 276 rum� vlto,· stt U sgy es to Fg. 4O t xa t agamat sket oft ab s o t alo alJu Ve as tt t sa s tat e nam amo t T agIs a ay o tg t t ov a pat! t ete aays oe o eae GS eo o e mad AB BC. CD DE E G
s }
. 2
sem s stgy mla at gs 16 a
e e
te sl stt
6fr A tr
k to he A tre
o vlg xmpl s psd u o h Podg om r o d ogm sps s o mov low d ·lokw lod ssm wh mb o h ps 4/� ps vs o h bo
8 >
\'11
VI
( we he coe upide dow we c se the em w spis g he ti he s) Eh he spi e e s he e Thee e co i whch the me the spis pese s highe ei vues: 3 5 8 13
x //
X
X
I�
F xII O, 26b
Silar aagemu be o1eed i sowen, da, aa et. i the ovoltio of he se of Ic o meo pla. Feqely the el mbn 2 1 , 34 5. 8 a eve 1 a 233 ae eoeed i he pia s�ms o exampl the owe ha 3 pal ad i pils v the aes o 2 1 34 89 144 tg o oe ht the is alwa sated o with O'U mae ad qie foeig to th og word.-
• e iliona numbr aJ·for
4
i
rrece i
The Use of Chos an ntevals Chromatc ystm he tudy of he prorto lead us immeiately o the quon of Ba6ks e of chord an ntea H chomac yem bed on the la of GS and pecly, Fboas merical e. Calculaed n sem-tones: 2 and for a majo econd 3 " 1 mnor thr 5 1 perft minor sxth, an augment tave, etc 13
1
or he prent the muca iue may be magned bu up exclusvely of cel 3 5, 8 and 3 n e wth sbdvoD follon the proporto provde by the ave ser Th e may boen up oly nto 5 + 3 (e pby of a plude by he m) dvon n 4 +4 or 7
b
Thi l vin ll b in h nl th DiI;u. T pip thm pr h u f h mvmn in v vatin: n Fig. 27 hav gu hm rg z, inat th h vartin h hati iviin. Th iita rm f m 3 5.
C
Sn th ft ln in g 27 ninu n th prviu n, t furth bar h my r t by mnr t 3 n h pv lin u by a pft futh 5) th rming t CS ugmin Fg 8 gv th uiv tm n h t mvmnt Pw Th ng f h h a T Pia ltmf i 8 min, v by funamnt n C nt 5 + 3 mi- T pinal hm mrs ' 3 m-tn ivi y h fuamna n C n 5 8. (S al Fg. ) Th rt hr f h nay thm xn!
d
6
3 emo, frm ow to F# we te eo rs 2 1 emon from 8 ow o D. Te meo olow ea ote n S orer: Lmof = Pnal teme 5 Secona tme 1
om te pont of vew o aoc arccte exo o bea wt o a stemac aangeme e pncpa tme g t magl onecolou fom a pao amon .B·-4 37
+ a
( g a),· h ma hh 3 + th midd a uit 3 + 5 + 3 h ppa hm h m A� majm ( ig_ CEJA, h uh, A, h didd y a it 3 2. Parl h (5) ad mi ixh (8) h da hm F c T lrly a i h rapiulai rm 92 Fialy F ) h lig hm mad hrughu y prall m ix (
J 10. 29
ah hrmy
p hgh h GS d
pa hm dl pa scda hm g hm
Amla ra m ud .
•
FB
a i
h rU/OUS
y �9: FED
PlO.
30
It i intrg t nt that n Bartok's music, in spit f th frqucy f araU, majr trd and m lxth aras sdm r beau� sch aas cnt b d th GS ytm bg qui cgrs t . W d vn sak f th pohibition f h a i t sam n tht ar ts and tav ar riddn i c harmn On th thr ad w m at r t wih minr third 3, prfct furth (5), minr ixt (8) , ad mar cnd (2) s Th mar hrd h twth mlodic funcn hr, th mr nata am vdnt i the mtvc r te mr thid:
39
This he reasn why wheneer r6 r i ChrQ1tic moemen he ce he minr hir namenta noe an he mr hr t e cr acqiring he rrin 853.
2
rm he synhei wo emerge he mt ypc rk h he we·nwn majrminor rm niing minr hrpee oh-minr hir 3 + 5 3. mar·mnor chr is en omee y the seventh o the oot eg an -G-C-E ch ih a {ee a Fg 2gb}.
4
4'
major-min chrd h a numb f synnym fo, t wch we hal gve (f want a better em) the cUecie dgnatn: ype a and w hal ca he dint ectins f t by the etter a (I> nd ype ccu a feqeny n Batk' mic as
d e enhchrd n nineeentcn mc
These chr a excuiey b p GS intea (2 3 5, 8 ws
and d n cntn he chaacteisc ineal e ene ytemth mar hi and the min seenth·
•
Fom he a h baciic "Slw f h lh haiC. P h N chd in Bu mc w h dmish« Kt , d in &k', 1/ cd th
mo
mig tw
Type Q can readily reduced the eation oC he s In order to e the tonalty oC a chord. we need at let wo not! in he smplt case the rt say C and fh G or js maor thrd E. hen G or E rspecvey prs the C· Let put raton in GS form:
b
n 3
Accoding to the ax ystm. e tone G or E) may repaced y any other of the corrponding ax (E-B#) without hanging the tonal character oC C We can herefore uttute E Bb or even Cl for G.
he four inteas oundng together rut in the chod �) It hould e noted that the cominaion of the t three inteva no novelty to u, ince it identcal wit the chord o a maor eventh EGB
e •
i
dv divi w d
t;
gh
y be
b
A imil uiuin my cid u wi n C wu cnging i uncin W cn u plc C by E� F# , ll lngng I m
Ilo· 36b
n m a nvl ummid. Cd aa i pcclly n i-lik pplcin imp G, G lin nly ipun n cd ud cmpd t DY ("x) : nic nd cpnding dmnn.·
D) i
two ay (T an copnd o th and ovton ion aony It ptinnt tat in itioal c, funion aU;i w n h tw la atntic (di cnn« chods i ht t of t t cod b«o an of t cod ollowin Cicl hamon c h not) w, in t p£in T o S, th of C) bom a lif in V o xnh in 1 Cnncing S and h t of 1 ) o IV (') O ft o Kn in V nncting nd th oot f V bco fh in I. •
D D
e.I,
45
• VC
f .•�
t , ·.
.
_
M
'
I"
Tp tpsilon (c) sdm ed nce t tona charctr i ntabe due to he aence of G wthot which te roo doe not recive ent uo Ceain econ of e / chod have been fami to u om cic hamon: EGBC the C majo enth GB-C- i he C mnor evenh, CEF (G) i the C venth chod ed on a dmnihed ad. Nove oduced y e ntoduction of te elaive A. and imily y he C. In fact the chod UI i an invesion of he nnth chod CG�D (C to C"BC. 46
al C
Eseniay, ype an axis hamony an exampe s ake he simpes se I he majo a i eie A mi a epace by an A
C
D
3 l
an he o cho ae ombine hen an i be eqay eaae i he esing hamoie! is cho bea a g conepe eso e o e ee oa aace o s cmpoe epese by he ece o si acciehe hee a sgs o he mo a he ee sap signs o he A maj accdace e saicai o he ype i possbe o bi p a s moe eee pie:
C
l l
47
Fm a sucio of dmihed trad a "cosed eque devd nce, by the peodic epeo of the tvas we ar take bak o the tatg poi:
Ad ow w om to he ey ! Tha CS i ot a exeal tcto bu oe of the mot tc laws of muc demoad by Dpehap the most acet hum oud sytem-wich may be gadd a a pe muic expeio of the CS pip I the gus of th dest chide sogs he ot of he m10dy a ud a te gemrc mea, e. a OS Pay artuary e mos acit Co o mo petaoy ad ), t a pate eected by th mody tep of majo seco (2, mo hd <3 ad foth
la--
• te ldty toi mel t hgg cue wJy ce th mj t d ri. T qote Kl "It tht the pt h cottion e dd ll "I_ite, Acodig to ly the lg o thd the h y othe sp guio t the chd t t wi rltohirpntg te il exi f h bg
· l L
FO2
This aspct of CS arhtu s makedly n n h D whih appopay h bn aled h "Eatn opan ymphony. Th ma-p of th CS sysm an h (owd stp y stp, fo hs woa h and ompx msa nvr asd on th pmoda mn of pntaony a th oon o hs thnq Th t momnt ass fm majo sconds 2); th ond s on mno hds 3 h hd smmas ths fom emnt + 3 + + 3 + psnng a pe pntaon a h hamon of h momen a asd on 5 + 5 Fnay th mody of th oth momnt oows th pat 8 = +3 wh 3 +
FO 49
Type 0# b deved rom . Ti how Bt6 tsms a petato e nt e and glm4 tructr:
7 e.
n 4
Ts ype ofrmonie orng fm fol ong ws sugge b Btk hmself "Te Fol Son o Hun (Pro M 1928)-
'.
I
.
J
5/ · J _,f .
no. $
fnl I may seem uloJh tht i B6k'. mc ntatoy iJ 10 dO!y i to hromatm Bu th dao i ntra, u wh Btl6k e prmordi araio o aoy c 1, jWl l leMOI! fb ute or o pro h CS }1 • AI
We ow meo eqey eg op o Sype � 1 3 ho wc ' " I 2. e S eo ewe he hee oe o he popo Each o he e om he peo eo o a 1 :5 3 1 :2 y he e oequey, oow
f
M eag o eo d pee O e.g. C-C�F-GC
M eag o eod ad mo h e.g C-CE-GA-C
' eag mo d j eco eg C-CE-E-B-C . . ad heey, hey m cay
yem·
n 4
O
I ODFL
3
:! O
M :5 • fl i a iNed Ar fl rfe e Mee I of exap o m h en cm Lt an d RK
w
\
[LS I·J C_
PlO. 4Gb
HUC I" c.• " r a
s,l �.td
Sr, �d•.t
We au as ipa M 1:2 sin i auay pn a sap w i Fi.
i C-EE-Fj-A.
s
4 an a a the basi sa" a mai y wi ws aiy f v is s · piad chromac os ad chods cn b dmind And w ai a an pan dsvy Tee iss an ani coelati bwn ym, e ds and Mds 12 and 1 5- w da p AFE and he w G-ECB ay the axis s cete a Fi 48) and pi p n n the w an d s p Fi. 4) we spaa the poe.countepoe �e1ao CF# and AE ivy axis, w have M 15 s i Fi 8. Iw combine ns the a w a M 1:2 (s i f Fi 8
5
048
I resec o toay hese formule are inepaabe The dae ro o e ode s o ephsisd b so o a e oeniis o h o (�F#A) majo, mor, ev, d od, a we s Mods 15
1
Ts m mg n ec t i s smm e w ne em ns e is
0
x 5
o 2
h al rig in i M 1:2 away r n e noe o or cn wi no he mor d n e e Mel on oi o C } or A. Th b nOe mnor con mor ir nd m h Is awys he o, we ha e mjo ec, orh mnr x ad mjor C\ e ppr O n r r c o ;jor e n e ae a Jh ny e no may a e
And ths i h an why th mot chaacttc a mi n Dat6k a xcy by CS pinipJ ( bttm , oFg. 4).
AU (l
po. 51
Wihin th ang th tw-on cal he ern moes b contc:
.:2
a I•" EIEGAB�; a '.mi." EFGAIB; and a bd,m" DEIFFlAIAS-C Evoh fom agr wth o o othr ofh av omua 58
I old ike o ilstrate the inlton oue ae. by three ef p e Notlm in M foows he toc-toicominnt-tonic stcte of the newe Hn gri fok ong So t t econd, nd orh n f oic fncons ccented he tne hich cotitt nU M :2
2 ton chcte is etemined the Afoth ste (E-A) ometed the ho ino coete tonc
59
I
The pece caled FrDm Id / (Mom No. ss n th G#-BDF axis s scle pvdes a ful Me "'ABCD-FG�) whch, as appaen m h nal chods can e on a · ad I (G"'=AO) and as a (C) and D(ut (A-D) cvng h complte axs
{GV#}
f
·H! Bth t and lf ands play spaate 1: mol (#ADE ad BC-G)· nd hs chaatd by c po o: l I !Do U+fot A t fmal constcion of th c s aj t
3 » vk K W J / P 2 o e, w m io Iht problm o(
aher;uon. "I i Ifhly diJ: . w ave 5m of v uk s" wt dH ta · w guid y l t o f ty l' wili! h a is h : wy w q (hri vrS h »no rWUlio hi. rch o O h o t ;1 in Jionc syt a te( t i om o odg w- us" (t920) ;,k:
Th by h m
W M 1 : w ob
F-BGID as. Th t scton loss in J, nng a h obebar The mdle t mov oun B, hen G#, wh n extend D pel·point at the second double·bar e nal cho i a synhesis of D majr and F mino and may be cnsideed e sam tim pe alpha (#ACD-At).
10· 5
O trd xample s e rcapua heme of h Violn Cc,rto sng axs EGA## Is l f Ml I :� FGG#-A#B-#D Bas I ad � as on mldy) d G (mo ls of h s. Ra 6 ccmsibs he £gmma hd (E mo-mor, G#�-G ad mloy o 5-13. h 1:5 mol
&F-f·
Fr'r- r
�
6
W ave o o a id of cac cod e cor of I fuen on h GS ae e whoeone Ke cod of dnshed nh, chod n fh and h gd iad Th a jscaion Bar6k' coaics on n o far o xhs 8+88
Woeo cae Dishd h Chord n fors Agned d
222 3333 ���5 · 888
I or oe s wo whoone sc e dsngsd : he e "geica doinn cena ae of ach ohr: CD-EF-G-A and C-EF-A-B
Ba iked e whlen cds ho c, ine i ha e i wee f melin und e F 7 Blehrd' ate N. 36 TI Woo c N. 2 Mc v b. 48 v b. 5 v b. 4) Hamniain and heme nucn in fot cord ae tikinly fequnt, d the nunc Hunaan eaan mui
O hod fouh geeally aow wo omitio aording to the 2:3 p�an prnp e ot after te modl th t furh chs i he 2:3 scale wc tt ih r mir t o whh a majo scnd hn ut n ; he -_a adc h od sogs:
·9
r
b good xp of aoiton e loing them n Movement of t kw fr Sg Peon d ea The 1 5 model e baed on tw uth hod DG and A�DG 64
{
1 d
ADDG DG!G G
h GS hd and hd a nta n n tt n ie. i h n ta M TI<: t· stia ta ti a
e aa Jw Pa a P; e e
1
h u d n th ADEG wht a, ad th w th nta #G#B� OE whtn a Eah at sd n xt h u AO and GE augnd ads and h w #DB and GIE agnd tad 8 + 8 + 8 h t as n aa n hd h nat haad y h 1 ds and th an +5 +
13
3
3 gmm
Th bgg a al ot um a lcorpol laonhp upp par A a E a t lowr F a C W vw tog t fo a axal aragmt, FA Ev comt o h tucu o GS oula
Daonc s
ak' atony mpy an eat an ema iD homa thnque e the S u of the aw of The mt aati om o arOk "aton ystem the wl ovrtone) a DEFGA an e d mao a wi mno ven and aumnt ouh maor wth and ) It i a aoui ee ton derve om e naua ovtone
I
O 6] I e a Sonat for Two Pnos nd P;on, r xampe, e aus ae C-DEF#G-ABb es se av e C (C majr) r see F. 64 T ae mae y e mar r pre "ara ve a e e aumee as a e mar s (wt D;tk, t par A e mr r pere mr 3:5 :8, CE meu S m. Le us pae e prpa eme f e rm F Mvme a e a Mm se . e "rma me mp S me le s m , pee mr s eals 3--8 e "a eme pe s ae
O 1
T o spher of harmony compement each other to uch meure tha the chomaic cale can be separated into a OS sqence and an aouc cale.·
6 In he acouc ce he major hrd replace he mnor rd the agmented fouh rpac the pefec forth (�), and the maor xh repace he nor xth 8 ncdntal let me ref hr to the la gur in th oldt chidren' and pive folk mic wch b no tetch of maginain can be rgarded pdc o me debrate plannng thugh he not accrd wih th "gomi mean ie GS Liwi when teng to traona mic t ldom occ to u that the connanc of a mpe ght rut from h cincidence of th nat Wjor atral oeton: or ea impl regter th fndamenta nuber elaio in the ibaion of the p h and major third In Movement I of th 0a T P;a on the meod ad haonc dev ae deved fom the mot pte a lemen we the pncp them n the Finl mply o e natua ovton ale ovr t C jor chord Ce Fg 6) Yet ti maor tiad relaion How cn a mple maor chord produce ch expe eect? L at from another angle may a comer with a
• Bmnlc,ua
chc itcato
pretence of being uptodate avail hmself at of the major triad, whose vl sgncanc hs long so orn o and became an empty husk? Actuly he tl eect of Bar6'. music is due for the most part to his method of reducing expression to smple and prma symbols The mjor riad may n self be a holow clch but hen brought no p-ul reltion ship ith anohr system-s done by rt6kit may regan its original and poten signicance he xplnaton s ht the GS beeen o poins lways cuts ino the mt t pont wheres symmet cret bl: he overtone series is devoid of tenson because is notes are integer multles of the undamental noe's vbrtons· he thrllng eec o the majo tiad in the Finale o the Sonata s a drect rult of it being completely released rom the constraints o th S system are not only So he l (pntatony) and the symbols o the purest musc but aso elemens of stucre and formation hch n art6's interreltion regin the re only hey may onc hve posseed hs s wha I wold lke dnoe s the ementa rebrth oCmusc through the reconstruc ton o its means Let us set up the formula of the ork:
YNAMC ATC
proporton " Sforms " pentatony opening movement proporton symmetry = overtones closing movement
The cs pr be law o he OW men e oveton reRt • tb Lw o he mn � we kow hmoni oveon u
y be viao o t i t et; tC only viae o hr leJ u in i. et f he IBh-pudJ n on he .nJ o n e e e ovo omne w noe e o he oe eeme he e he oveo mif he e eo e bDmo othe out tem "lo r t o n ha he e n 6k omoR oge prm i e oou o pon Fen mm 6k m u o ae o
U
Ths mpie that th 5ymmeical priiaion of the Vinne caica cho and is hamoni sytem of ovetone aions ae phnomen not inpndent of ach ohe; they only pnt drent (hozon-vetc) pjection of h am baic conpt. Th two ytm Oct ach othr n an vr tion hip hough th nvion of CS intv coi ntev a nat vnth (.g ae obtindfom a mao ond fom B, B from a mno thi (3) a mao ixth fom a pfect fouth (5) a h om a mno th 8) a mo thrdthe mt chaaceit acout nta Theefoe no ony o they ompment t lo r ch oh ogicy Th opnng an oing of the C1t Prfn o beautifu ilutation two Kae miong ah oth t f notea GS ca (itea 2, 3, 5, 8 wih imih h an a pue acoutic c:
(
.
t oth aifyng Ihi ntraion fom anothr point of view he hmony whch appa bneath th u mloy of Fig. 64 poduce phap th geatt pie o the wok otan y m f ml mao chod E·C. 72
Thi s osss This osss or th los loss s ovetonl aios. Le a pcrc r ad majo id I e omai Fis Movm mo 8 di\isio f hc OS: ad always emgcs i te 3 +
isi rou (5) , min six 0 o tis CS od v ben nsom y iVrsi ino P" fh ad maj hiJ aoi ho pily et s sow s ods i i s fom too:
'0 68
Wa is aid eai o e o. i e S ysem om Oe downwa is eqaly id i e aousti ysem i the pp deio I s coe a "ovo od i umSae t o aie me meod odi i a dding aae my pps be to te a ha paoy is OS to s
j Ao s aus sm o p
ouwad m. is o o appis w it is osidd a oly icV;s V;s s i aousi sysm sysm owig oto unnn ic
73
cnanc cn ance) e) wheres the GS avls tsel pecisel pecisely y f those a by msicl intevals whch have been cnsdeed dsa the m the ime Palstina. Incidentally th diveity accnu the the tedeny tedeny Wt Wten en ms msc c t be be acsi acsicc and and Este t be pentatnc. mpJes ht the ea csnance ad dnance hs inveted the tw hamnywrd; the py " datc cnsnce s n dect pptn t the vetnes while the chmtc techniqe tns u hght degee cnsnnce hen al the telve semitns n he temped scae sca e ae ae a ade de t s sd d tge tgehe he- - ke he a a he sea qte Bk. Heve incedble t my sd n penttnic meldies bed n ey·e ey·e (· (·sc sce e:: nte ntels ls 8) elngig t the mst cent laye l msic the eaest dssce is epeseted by the pf (c. Fg 76 6
3
A sect Bt6k's Bt6k's msc and pehaps the mt pnd that the clsed wld the O s cntebaanced by th pen sphee the acstic system. The me alwys pe sppes the pesnce the m systm-t s nt ccidentl h e hve lwys depicted chmtc mtns in the ccle hs ee Figs. 2 4 4 ) ) n the lt lt al lt ltio ions ns ae depedet n n te snce the nata senc emeg g m ne sngle sngle rt rt he he e e t s U U tn eme
J
Th th thee ditnc system hs a fn ndament damentl l r nt ntee nd 5 Th the chmtc system a U nte. n the chmat system l eti cn be nveted tht changng the sgncance the centl nte. The pincipal theme the apitlatin in the Vin nr h a B tnlty n spie the act tht te B mj mj tnic sns sns n its hea i t te invi th tme nd e ccstm ny ny t ve vetne tne elt peceive it a havng an mn tnalty The B cente s acentaed acent aed by shimmeng shimmeng pedlpnt pedlpnt t t)) 7
I is this "mirror (see Fg. ) ) whch sho show w that that th th chrom chromatic atic technique leave t reqiemet he overton ytem o consideto ad dea lk p ad "dow bcom qt magl t The haoy which the prdg pl soud below th B ct poduc by th gao of th ovrto ytm, a ect ct f f th ob obj j of th phycal world have uddy bcom wightl a phre wher the aw of gravit ar o loge vald ( Mov I, b 1 94)
6. Ad thi is why Bart6k' CS system alway ivov e ocetrc o r( of itrval whch a cotet a o b vrtualy epaabe fom he chromac echque or xample h qod hm fom h irt Movm d of h S0 Jr T a corced i evwdeig obi (s (se e Fg Fg 8 8 lemofpricipal hem secoda theme 82 Th pricipa thm i augmetd fom bar bar om o third to fouth xth d vh iteal Ad the op of the ecoday theme pad imlary tp by step rt wh peaoc urs the wh rh ad h iterva aly ovg a boad sh (s Fg 8). W fequely d a f�shapd (e Fg. o ad rik ri k movemet of ot
pi
i
70 ad eqc poceedg by wder ad wder tp: 75
Ev en ths poce Even poce fo oow a pa e cour vy dtil howg gnttion p to th gotrc centre th o o t t (b. 2 1 7) 7),, aer which they gra gray y con conrac ractt gin. gin. On h othr hn n th atonic Thi Momnt h progrsons a qit m,6I. Th iatoni hroj�! � charactrs y a rns . th cor o i rais t rgy rgy o or o og g prio prio o ti ti wt w th h a ot· ot· nwving conancy in cotra to th CS sy sy w w h h ay of a dynamic charactr.
7 Bartk' closed chotic wor ay w b yi y th irc, whie hi op (itoi syst, by th raight e Li Dnte's D\n Coey t yo yo o the In In e, th wi ha t Pdo he tgh ay igs o rno h rro concntr concntr i i ion ion t t the they y :rri :rri\ \ at th th "ct "ct hrea thoe o th rio win ino th innit pyr.
h
h
tk coos t w a iir t; choacs ot ty associa wih th r w aoy wih h stragt n o oy sc Fig 8 h i o "on an "os is aso xre by organiation organiat ion o th thee he he n re reato ato o The bi
7
a lssial meody is the ptiod As a ru t tmes n t msic o Haydn Moza ad Beethove arc dvded to 8 + 8 brs t r two·ba "questio beg folloed 4 4 d 2 by a wbar ansr; ts fur bars ma t b osdrd as a sgl sto t ar o wc beg gve ba 5-. Tu t form dvlops s smpl Oar st d alflose ad orrpds o to uls dig o t 16bar pod prncpl of symmrcal riodato s ready dsrnd Bark's daonic mod of riting l In ot o tis j OS e posive ad negatv sectos costtt ut dert system esos ad "asers (s Fgs 6 ad ). r t law of lacc ad symmral rodsato s replaed by rgularts of Psitive ad negav secos mbr ac othr e th asnding a dscdng arts o a wave condios o orgaisao n the CS systm a inrsely reled to o te ymml prodsao o provd a proc of ergng, t otr for dvng osttt t ormr mpasss galc Ul� tm r svy t maral p C forms assume t ha o an trpd tme oc rvolvg t o a wav w t symmrca rodtio bks matal o metra ompos of le rym and stops t ontrcto of a vs
ymm
9. And what o the two y.te lk ike when examind in numbe eaon? The key�nmbe o the ovetone yem ae wlt nbe: ho of e oae 4 8 j o he h-3, 6 J2j o he mao d5 1o e Whie in he OS !yscm the key nmb inaia/:
.
=068034° .
The irrional haae beom il moe explii i e oma wtten olow (whih again oneal the Fibona eie)
The ao yem on aritial, he O� ytem on gtOmal poo (Se App 111 The haates 8 pooon only appoxmay oet and ep ible ony in iaiona nmbe (eg 8'0906 Th mino hi in pntony an be poed o be omewha age ha it in he temeed yem·
u
u
0 I may be ymbol hat in he daon ytem he paia on nge a while in the homat yem btow the damenal noe (ee g 68) I o me ntet that emann deie he mno iad om "ndetone an the mao om oe on In he e o CS hod elaon ao aid neey; the mino hi al ae n the mao th below he kynoe Ahough Riemann onept may be
o 1 T
• Te odr·nubr h mr hid n Ih lm i " 9 t patoc tc:, Tas aoy c c r id)
ce s w nsdg e e w ml nn G evs dee w e cmss f ve e de e cd Rem ded nveg d ecg e m d e we ge CAF) 8 = CA 5 = C e lemf f e eeves es m s ese evs A GF ee g 1
a aa
M ;; (
t :
each person rpent b a • In he Kore the ton.symo with whe aid ma weU "read the pol he pantomme The Mandarin ma c08n, (om the not G'-: (ApF; Gi O-A· I�) nu J;-Op th vy ginning o the wrk The hat the omimen he Od Gaant e inended or he Gir i shown o by he mi he basi hord the d Gant me than hit tim ead to the Gir sm
W m n he brief mJ Aer he nry o he Mandarin the ntton ostito ndat from the Mandarin, G'- not to he Gir tone.,mb
or aer when he
We
tring o h the Gir
the o he wo at h
A ta n he ome Vo! No pp
M
wk
pub y aho i
62 G)
79
A prtlry v alto o vr o a b ov a ma h Cmajor o ',ards C4t, wh a lu o ark
7 y o ta ymmety ente o t a· o a e:
o-o-e+lami Smry !r e o th ymm o
maor a mor ha o h aou , oo h h rlaop o h wo ym om w r h h a p o paoy paa I�mi a h b o hoy h omao Oo a r mi"o mage o h ohr rla o h ymm r ymmry t
o o
e
m /a
rk hroma ym rul pga, w o Ym authetc hmo roo h h or bin S tha o h r D pp I rao m h mo· uy a mo
'r' h h
u x
m h y a rry whr u h ubomt.
u
FIO 74
Acuy, he mos nns haonic ncion n clssic msic is reesnd by h sdomin coms as spris tha h minor subdom£nant, ing n sst of sdomin chords is ssnilly chrcsc Co of "S nsion (inas 8
3 5
5 nd convrsly h mnn hamonis u on dJ's of h nas ovons I 8 I. mas nohin lss han ha he chnqu o nson-aaion in clsc msc is closly ld o h d pnpl o S nd cosc co rlaions: sudominn nsion is, in c CS enso", wh domnnonic rs n vo lionship. Th S in h S ysm cn dcd h l·mi o cos so fquny fond n ncn pnaonc mlodis omp wh h chnin h nd sx-fou ys of old Hunrin sn sons
tu
7
z
J 2 Ba 6ks dtonic mwc alway inspird by n omm a s en , ma mic by a ark, mever, raoal a moac ao Tis voluay br! o m e hromati experime of z a Mussoy probg he om depths of l t recll he l te n pe of Ls Gr , UnJk St, d Febre he deathm R WQnr ee<a, the ghsl Le Ga al thse ae wten n a tnesem dsane od Or t Goov sene of wee Mosorg vl imelf of a per "xi system. Al all, the homati a datn tem m a oheret rree to ides of e sme coi, one of whh neges and a he same time mlemens, t the he sttte nta n n am and den and ede ea the
k
z
• he e ualty appa he reque o h � key. Tw ras wh Mv her e
F
mer Sa9 distnce ceat • faig aly, 1 ihilAt
i. T
prograe
o
he e dy /"n rcv f mr d A j eJe w cmpemen a e, meeting n a dane mel :] e) F-A-C + AE FA--C
a® ':
[ j
e an ece w raw ag ed A j GBAC by e mb mr
8
In ome ofh work Bk so ar i he larao ad reducion o h matera, that frm ad cotet mean ad meaig o cosue am inpaabe eiy.
Fm te pecedn priip eve fther djnj rman becom sef-eviden The mai daonic tervas .e he d mjM rd ph y majo chord ilt up ue hr ever ecd deee f hch rhyme et
t
5 « Q H e E C C m
E me). Sly & u Ap m�or " he BwW: bit dnk ( F 4 he S Ce h d b mi & he oa u u h FI mor dyl,h mo u y A mo y e hU e l hmm gk he me e of # mP mj &t h e 'vc s h uc dqe eo
A
Hee we he he r the wekw Bk s�·
78 f w Pt, Swss V , Ns 13 e es p pcs Dc Dw, Mkkss N 0 ec) hs tpe, e wh ust fh ( ch wh #), ppers he sp , s w Bu' s ee 79
1
h
i
ord h a conepart e mno cho wh j vluJ.
fb G;
g DF-AC" whch ;w�y wih pan ; o Ha6k', rama wo n os (Yo mof woe B6 S ey) W he be examp om
j r , ,# d • J
1 ' " C-EOU Py e o .
hs
the
,",' i .
I
I:
At the u h
ltmotf
h uvn;J l
EG mo chor h A o e m d -A om hee di l
10· 79
Sin t ai ym mly an invin S an in dini mni y ly d
0. 8
diani i d t alpainvin i vd y p maj id d min vn i nt vtn wi wr xld4 by h�ql4 Q$):
Hweve paradoxica it may m. he cd wic a a mj id abve the ke-ne and a min thd bw i mks t mos "datonic mo oped mpsin i BatOk's muic:
t
And cmpe he cncaenin, huld b p a er of apha cna h y n hd
O
8
I appen fequey ha an ambgu ba omeime repeened b and mim by F
T s me ce in he "axs eody ofhe ee n Moveen III of Mc Str S;O Ca
We ay suase thse aye s PES (chroac syse) Penony Alpha chord 3 1 5 ode
Fos of eq;J nea. whoe-one scae dnshed even chord n fos gend a, consng of no
foows:
Acoumc PES
(donic sse) Oveone chord and cae Invron o aha Sccon tds and s wth jor ch acerc o of eqa nervas chod n s agened ad on· ssng of ajor hrds
Patcar igniance may b attbtd to the fact tht J1aY i mot haatitic o Btk' chomatic (CS) ytem ie ltroe chod pevai in hi diatoni systm. Thi dulity in o opinion, od m to xps th two mot ancient ndeavo o mi. h phyioogc ppt o o es ith th ogthmic tct o th coch ena most diy to pcv th -a-mi (2:3:5) eation t th ist stag o hih both pimitiv mi nd o impet hidns ong povid nqivo vidne. In pimiv msicte th n o mjo tnity n nctiona ttction a ite nnon· he dvm o o;c tining deive om a ite int o namy h ovetone i hi od ony hv OR no i on ith intmenta m and it no int tt ntona mi thinng hdy mo than a w ti od. nttony my b ddd om th ythgo; ton ytem-goping th net th nd otshmoni mic om the ovton s. nidentay pntatony i o md" ina oigin bing o "ozont xnt in tm hi the ovton sytm i o har oigin and ha a "veti ptil dimnion Woud it be to dang to ppe that the o penttoni nd acoti hnng e the to int o ogin o msi.· o then at6 penttd to it nm co.
"etaton do not er e omiattic aenc artk • Hnarian Fk sic 193. ti ale te t no realing
he h ••
he
role (6k: Hngian ·olk i and garan �ic, 9. On and te reuen use e or nea in or m U8 to w e o tcos artk inluene o pan mi on ern mus, 1920
a6k i n bevd at i b ble o race k k m e ce o e o et, ace anien l Ba6: okson rarch an nainai
97
T t i usti "ir ai, a o t [oc trt of t a; t o xtra ari oro yal w of oa T fomr , tfor s, xpssi a eotonal a, att oouu, imprsi a a aim support t siti osao ta S is to mt wi i ga;c mattr o Ptato wit i tsio ou r a om ito i wioU t a of uma motio aosti armo o t t a, ma op ipt of t pomo of uma if o of uma ittio-a ira um of ar i a pip (or a sr i ou to ri it aout Ptatoi a aousi trs foow otao o, Psooia ot to gas a ra on wi psi ots isorais strii to aoJ tsio Hr aa tat OS rats a dos wo t tsi ma a ars a ir tso, wi t aousi sstm is a stris to as tsio tou i oro soa It ma a tat ts osss is a orai fau o S s is , a for ams ip of Bartk tostm a tis quait is sposi fo apai of GS ogae. a iustato CS a a rot aut ifw i a imp "ot wit a pap rio wiout xptio, popotio of ts ot wil ipa omti o o· i 5
• It cid h _S0n 1 ommo ivi tue 10 i d.
_::
,:o·63
no. 85
I ppe e peagram ha as Pa I
aUdes
M Le me adm; a sace Fds my wakg u here I he drds up y rhd A: The dsees y? Bu e me h y s he hs mpeds y hw d yu cme Hw c y d sp ced MZPH Osee! The es are ry draw; Tha e age pg wad, s y see a e
r
hc
Alhough he mpotnt queton oytm and mte nno i w e d l e w be ined out. Btk' ythm s govene by ct w been own o ule i fom and hmoy The cfa he of Moveme 1 of e Sa j T Pa a P i no mll degee due o he olute" odd mete 3 tme 3 eigh we te Fnle ow i ti he o t boute even mete 2 ime eght. Movemen ee d od e itentonly nted. (B w ve mh teed i he otntiite of eve" nd odd met. I te a C Mov o Ms Vl Dv Mkk tem peented in eve�meted eu in odd hytm o ve ve.) e yhm with tong endng in Movment hve onet wt we eng in te Fne ee Fg. 87.
Y c
6 Coneqenty te tem of Movement onte s nd hoe of e Fie J fom. B e pl le evil lo wh te even d odd mete n e eiodilly lte .. d ntn n e oddmeted hem ile n ltention of ovide e ym "+ d e of the evenmeted tu.
_+_+
9
+ r:
£N + - + + + + +-
9
PO.
Tha s wy we fl te folg dims o be s eveang f Bar6k.
93
l
a nal exmpe let omp the opening and cosing brs of the Sonatafor and Pemus;o.
As
S
A �
P
The openn r iv he imprion of dent, it were nto wel "hch i immenely deep or shold e ay has no ottom t ll (hom Mann) he o hveng sun of the timpan realy eem to emanae from the negave pole of ife from phase of preconions-the key of whch s FI the owt point in the ire of fts. owrds the le of he or the liped cyma sondd i e nl nd the igh ic dncing on the of the dedrum produce ointo hich mol joyfy over e o slende anl on the pas of in majo the ighet oint n e re of nd unerle f # n this way the extrme pons of the comon my erded neaive nd postive po so tht the no o mnec ed oe telf nt en develop ewn wo opposi pol he Lentowit tely owi reprented y the ot the Aegwth it
m
g
95
rtatd rhym-by Ie gl rum et. On te onc side inr, on olr, rytmispat cment. Nevre, t mo nteretng rumtne s tal imnon of te mp" work wer not nta: it rRcts t unY of Ie oet prinip o te os r an open ym ofl ir s , we t alr an be expre y I power o2 (�'=4 = 16, 16= 56; I next powr s rey too g) Te imeue of te woe work te bomentione 32 egt) i 80 o noe n ts i presy te pru of
t an b ue rom foregong t onc n te same regurty is estabise trougou many iernt imnsins o te ork troug form, key rmony, roportons rytm, ynmis, oour et Cnsieing te t 1937) n oler prtuar one may k te suppoon t Bk probby intene te fr T Po d Po to b rowning pi te Mkosmos o t Mromos 37
G/
Wt roe Brtks art py n t musi of our entu? Hi romt ytem a t oot n Esern ok musi an n pentaony out tem oe to Wrn armoni tinng H mef aitte s nbten to ok mus n e Fren mpresionists te mot sisic inuen on i a·
Th two
oour t int i olk d th n Fh muic, oe 16k (Zo£ K£ly: 9U). T co dc ttenton it kown tt ry, vr m il n oiio-hh h ld o mp tr lon t olkoe mny h Inno of pro &tg mDc Lt my mc k or if l n lm y lt o my wrb'
r
Shoud his oson i music summd u in a sing sntc it might run as olo Bart6k achd somhig tha noon hd bfo hi tim, th ymbolic hndhak btn East and Wt: shis of musc o Oint and Occidnt
Ths sa i h introduco ar o h utho' bo art6k yl" ulih in Hungarin in 953 A folloing cht ackls h dmatic" incil of Ut6ks muic, scall of h instrumna ors W mus no fgt that Ba is i ac a damac mrmnt, as all cati gniu in ho charc th bnts or ogic nd hom, a utd.
9
Appendx I feig o h &ta JM T PiaS a Per;oT, s of iC o on u w paicula of Mvm In �35-247 n aO t x; on he o h th # o runng hrug he n he D coutrpol d on the ohr hd h contng funelhpd mc pgron dgd h D picip ch nd atr t F-B cond brch
L
!
_ ·
99
The ou stions o the
sondy hm th cpiuto (b. 2933°) a bsd o th four pols of Io xi $ tht ter Otr ad er pt, pectivy corrsd wh ch ohr i thi polcoutrpole raio.
FIC 91
Th ax cosrcto o the ca s qly abguos b 41743) aoda t t ola schem the autd rncipal thee aea i \ t ad ay i E + A, o t disjoid EG-AC ormior (gamma) acopat cord5
E-CIA AXIS
O. 92 lO
T vm Mov 11 Mf S P n C e a eem
e eae EF#-C i w d b e ba dm mm wi cmiJ e A ad E� (
B
n
''
It vi h f h ccoi ics tht h EA pli f th ckn f h sucur lis A l Fi. 95 ivs s sr rk
Appd I I A few example are iven to Utre he interrelatons eunded in connection wit Fig. 13 Te orde of key of te Fsl ROc follow: C tonic, E dominan A� ubdomnant and C onic. Movement I of te ubdvded by te ve·fold ecuence of te prncpal eme
tonc (epion) D� sbomnant (t part of development A domnant econd prt of development tonic (reaptulation tonc (od
. 76 231 3 1 3 . 38
A mila aangement to be een in Movement IQr T Ps Psson:
8
I of S
C tnc (eiton . 3 E dominant t part of development 11, 95 uomnant (econd pat of deveopment b. 3 7 C tonc (ecaptulaon
In te ld eample of pae 45 te elaion are D-AJF#. Te prncpal eme n Mvement 11 of M j Sg ls partcuary coent becaue ere we nd te cuasructue and onic-tocomnant-nc con tucton of e newype Hungn folk ong. Te toc & repeened by e CF# ounterpo te domnant untel (not y ) Te econd en of e tonic povid e eact "ton answe of te CF GC ton cange nto and CF to #-C#
A ilar iain inan an nic i vin in 8 Mvmn 1 h Di" /oj A mia cunl cro F8 nc cur:
�
· 9 h rpu:
T m cn g ( B C tl) mgh juib b l h b6 mnn g qun cu n mu
wch can agin be explaned the reulaities delt wh aove. The openg a of the Mru/ Mndn ltte how he ton ad sdominan ae kd; the D# ton swings towads he uomnn nd B onterpole:
n
It s inteing to note that n Bat6's muc the three functn pa a smbol le too partarl n his stage wok. In Bubd' C t sgnanguage awas goes hand n hand wt the plt and content of the drama. Te sub dmnan h a negate meanng beng reered for the epr sion f fve and psin. All sitve movemen stt with te domnant The tatc pla of the opera and the ponJ of rt are bed on the tnc The downward pu of the acon n the MDuw Mi s aso expeed by the functonal reaon The domnant art of the pantmim in ) ets he thobbing ectement oflife where e subdomnant end ofthe work (in depic the death of the Mandarin. he ntemediate scenesnearl half f he mcepecal where the andarin saies his dere are wrtten n te tonc C Begnnng G
Clma C
nd
OMNNT TONC BOMNNT
The succen of scen folows the same ddi oderI a rpe decent frm te dmnnt heih o te sbdminant depts a f eprng the dea that the wok move towards a faful" ab:
V Od Cl-. V Yh)-3 V ()
Mrdr
Wltz
_2 Mudr
-
3 Mud
t i fo thi resn that the sene, tuated one beow the er on the above pan ae deloped from the same matel; eg the music ofhe i Murder orgnat n the baic chord of the t Visitor (Old Gallant
l
(_. " C)
In th" plot of h cene ollow TD gre: XOIION
MIDDL PART
( '
W all this is inveely line, incessnd going Plue rinc Pince Foest Stem Mking of te oll Dnce of te Woen ince Scene (No. 0) . Scene No. 8 3 Scene (No. 13 Conuio I.
964 •
DOMNANT UBDOMINANT ONIC DOMNANT DOMNANT ONI
DOMINANT UDOMINANT ONIC ON
Woe rine No. 1 49 ncess n the Sre Denoueet
• A detail anaysu or h wrk
ONIC
ONIC
REAPTATON " e o expiion
o exe ee follow e ceeDce of te nc·
up
ai
DOMINAN DOMINAN ON
ucure of
w pblishd in th ao' " Drlk's
Damagy": Stage wrks ad Can.ata orana (Editi Mic Jlap
08
E- AX
A ,
$
.
Aen III
m
ex oden eon n onye onue gmrily
t nnt b obid mte i y i. by ma o rao um Te kymbr o CS (mir o . Hee the Eudoxu" otuo, wi empe qe d ee
o
6 103
n nohe d on he Phoe popoo
P. 0
Th ypo < o h Kp ag bn a g ag to h hot c 0618 . ° 9 3
)
6 �
a a ca o gol con a
b gh abo
foow
I
Te mbs of he OS hain can be obaind by subrato hus he OS o ·618, a o e lae: 1 -.6=0'82, c · "'3 0; '3 3 (46 Bu OS an a ao be obaned by nvouion = 0 .2- 38; o' 06 04, e Te n oe ue mee i oe ini p d eiy in he Te ue eig i
g
v
.
07
W e ad ma a own a au oes m wh C me n e iumee e Te hs Pyam n Ey revas e olw sru
.
0
n se a old ale • K Kcppisb a E. B
and so
'
e ynam qay of t Panon n Aens ows muc o s OS meno, and at s wy we eel t buldng soarng uwad, a we.·
Wle Goc arcecr aourd ang o 5° Renaanc at, olowng t Gree moels, owd a rdcon fo te golden age Te crce ad een gen a "eaely ymsm we uare ay o Bcau t Gotc concet ujct artly aar to any concens t forcd t sqa o n a ace win t ccumfence of e ccle contst to mate o ae d ea ad an eqlbrum n Ge an Reasanc a foe n
I
• Zg
ee e e le led qe. Hee e iae e ubeded b e e de le
a
e e �
Ck ct
0
"
