Simulation Of Functions Of Composer and Musicologist On Electronic Computer

:a.n.Za.ripoT

Institute o~ General and Pedagogical Pa7cbolog, Aca~ o~ Pedagogical Sciences, usaa, lloacow

Al!lt.ract

A aetbod o~ ai aul.·'tion em an elect.roaic co~~pute.r is described, iD wbich a aet ot ~o.mal1sed Taluea o~ panaete.ra is :tiDd iD oo1".re8PC))l4eDoe to a oe.rtaiD. .reaea.rcll ob3eot. file tollowi.Da ooapute.r p.rog:NU are oonat.ruted ~or ihe 0011p0ai tiOD. o~ 80AI ~lodies, harwmd. sation ot ulodiea ~· o~ h·"'D1sat1ou (tllis prog­ .r-. acta u an ezwhe.r) and OOIIPOa1t1em ot aua1oal ft.riatiou. fte latter .realises a OOitp»DeD.t ot he11Z'iat1c act1't'1 t7 - traupoa1 tion ot the 1DT&r1at ~ora (atruotve) to 41tterat OOD.t·ts. !'laese propaa OOD.:tia the )QpothesN oonceJ.'Id.Dc ce.rtaiD law used-b7 ·· iD o.reat1Te wom llll.tuit1Teq. ~ Iaake an ob3eot1n STaluatiem o~ aaohine aua1c and co~~pa.re it with oow:pose.r auic a spe­ cial e~t llu be· OOD.duoted b7 a aethod wJiiola el1Jdna~es the ~lUDCe o~ the P&7cholof.oal set (ld.aa) ot the ex­ perts. hap es ot eo~~pute.r ulocl:lee are siTe 1a a auaical DOt;ation.

I 1. ID. the s~ ot ce.rtaiD PS7o.bo­ log1oal ob3ect the ~ollow:t.na p.ro'blea a.ri­ seaa to what extent the Jr:D.owlec1ge o~ o.r 1Bto1'1l&t1on em the ob~eot, produced oon­ so1ousl7 (e.g. o'btaiD.ed ia a ps7oholod.­ oal el!Per.l.aat) is .releftDt to the lllld.e.r­ atandiq o~ this ob~ect. ID. other worda, 18 th:la Jr:D.owledp n:tt.l.o1ant to iaitate the ob3ect?

It ia DOt al-.;ra that iD his heu.rie­ tic act1'f'1t7 aa ues onq OOD.Sc1oub­ -p.rocl1lced pa.raaete.rs. Wbea 4eal1D.s .t. f;h d1~cu1t p.robJ..a he iDt.roclacea euboOD.­ sciousq addi t10D.al taoto.ra that he em­ DOt be aware ot 1 altho11g!a the7 otta plq­ an eaaential .ro.~.e.

:llect.roDio-co~~puter a111ulat1on is a .reliable aethocl o~ Ye.ri~ li1Pothesea OOD.Cem1ag law 80Te.r.D1Jal .reau.rch o'b3ect;. Siaulation 1a .rep.rodn.otioa o.r 1111tation o~ ce,.rtaiD aspects ot the ob3ect UD.de.r etuq, that is those upecta tbat iDte.reet :the .reaea.rche.r. ID. co11pute.r a1au1atioa the aaohiDe prosr· iDcludee .resuJ.a,r1tiea obtaiD.ed 1D ~· ot ez­ periaental data. !rhe eo~~puter, D.&tural.:q does aot use aDJ'thins aboTe that, SJQ"­ tld.Dg that is au.bocmao1ou.

81aulat1oa is ca.rrt.ed out iD three stages a

1) On ana:Q'ais o~ the ob3ect; the law o~ ita structure are ~oUDd o·t. Be­ aides, the law and principles o~ the straotuzoe and cleve~t o~ tu ob;Ject aq be ~o1'1111lated em tu baais o~ h1PO­ the'tioal OOllcepticma o~ this ob~ects.

1. S;JDtheds is .reproduo*lem o.r iai­ tatiem o~ the ob3ect an an electroaic co~~pute.r .t. th the ull» o~ a p.rosra wllioh 1.Dclude8 the law cU.scoTe.red em dnrtns anal~ a.

3) :Bsto:laatian o~ the aac.biae .reault;a cODSiats iD 4etva1 n1 ng the e:nct 0~ acle~c7 o~ tU .adel to the s~ o'b3ect, that ia tlae extat o~ a1ailar1t;;r betweea aub1ne Ul4 :aa...n act;1oaa o.r .re­ aults. !his is the ~ c.r1te.rioa o~ a) pe.r:tectiem o~ our aJ.ao.ritla 1 b) oo.r.reot­ ness o~ the a~ted P%"1ncipua o~ aiav.­ latian, ad c) extat o~ k:Dowledp o~ the s~ ob3ect. At tllis stage our 14eu em the l&w o~ the o'b;Ject are Te.rifte4.

~ iD elect.roDio-ooapute.r aiaula­ 'tiem it ia ob3ect1nq ooDU!Wecl .. tlae.r tu aaold.ae (the p.rosr·, to be ·.re ezact) poasNse8 au:rftcient mowle4p ~ iaitate ob3ect OR the s~.

stnlatiem sboul4 be cU.s~ahed :O:t;=!~:!;l=.t~~h i:n ~:3eo:~4ecl

bpe.riaenta iD ailra.latiag aoae :tuao­ ticma o! ooapose.r and auaioologist an "U.ral.-2" and --6 ooapute.ra ...re co~ ted iD three stases oo.r.reapcmc11.D£q. hnhe1' the7 are ocmaeaq 4eso.riie4. ~r ao.re detailed ~om.atiem em tlle reaea.roll utboda and .renlts 11M .reacle.r is .r~e.r­ .red to the aut)M)zo's IIOIIOSl'&ph (1) and ar1iicles (2,3).

I 2. Let us ezw1ne a aetbod o~ d­ aulatiOR o~ auaioal cc.poaiticm baaecl oa altp.ri tllaisatioa o~ the law Ul4 1"Ulea ot 0011p0ai ticm. 81.a11lat1GR is baaed oa a p.roba'bU1t;r p.roc ... nb3ect to deftn1te .regularities.

~ utbod o~ o.rgazd.zation o~ the also.ri tla 18 baaed em the p.rinciple o~ ld.e.ra.rcq o~ Ta.rioua auaioal concepts · Sen.ral oonceptiou JIU8t be 1.Dt.roduoe4 J:ae.re.

klq a1181cal coapoa1t1on 1a cba.racte­ .rised (both &;JAtacticalq ad seuntical­ q) b7 a oe.rtaiD set o~ pa.raete.ra P 1 , P2, · ·., Pk~ ·· , ·'bo~ lan ad aeana or OOIIpOeiuoa. ~he pa.r·ete.ra aa;r 1D41catea .rage o~ ulo~t ·e-:;:1. cliatributioa o~ b'eqwmc1ea or iDt , naber o~ degt'ees iD an octan, etc. BYe.r;r Pk paraaeter &88lDieB aeTeral T&luaa P1r1, Pk2, ··· , P0 t.. ~. ~ 'ftl"le o~ a pw::ra­ Q"1ier ia a U%1JI1te n·be.c or naerical atructve, a concrete law o~ cllatrilnation o~ b-eqwmciea o~ interral and set o~ chorda - out o~ an asgregate o~ thoae pemiaaible in the progr·. ~ t,pe o~ oo11p0ai tion aeaa the qual1 tatin charac­ teriatica, or certain 41atinsuiah:llis aWII:­ cal ~eaturea t:tPical o~ an agrep.te o~ ooapoaitiOJLB (i't;Jle, PDH1 .-otional tezaor, etc.). !he t1P· a&7 be "4a.o1D.£ auic" "klts", Straus ·lts", "w.ldih", "aelocUoUDeaa" · etc.

It will 1Mt eatabliabed in ua~ a n·ber o~ 0011p0&1 tiona o~ .-e t»· that DOt all the par .. tera are eQia&U:r characteristic o~ the aole t1P&· I~ a­ par .. ter unaea cmlJ one (uatllltial) Talu w ahall r~er to it u a ····­ tial par ... ter, o~ wbioh tben llq' be aeTer&l in ft'81"1' t,pe o~ ooapoa11o1on. U a paraeter uaaea 41Uer.t Tal·· 1A 41Uer..t ~aitiou o~ one tDe 1t ia 1nesa·t1a1 aad w ahall oa1l it- a ·iaeaun~.t;:-·ter · .an ···Vial parader ror aaaic ia, ~or ilaataoe, tlae UUUl"ep ... oh ia 1A ·lts '/4 and 1A oharleaCOil 4/4. .an e~le ~ a inu··­ tial par ... ter ~or w.lts ia "n·ber o~ 111U1treaaed 110tea" · .an ····id.al pareaeter ~or a a.&Bian ~olt aoaa 1a "··~ce" (MTeMilt o~ tu aelodic ~igve vp or do· b7 a ~ .. 48greea with ret·'·tlllt o~ tu .... r:utJa ad intanal relatiou), w1 th tlut Tal· o~ "abaezaoe o~ aeqaece". ~ the eaatllltial Tal.ua o~ paraeten are the 1A41aptiiU&-le characteriatica o~ the oo11p081t1ou o~ a glTC t,pe.

Let · · M (P1, p2····· Pk, ··· ) be an ordaHd aet o~ Tariou paraetera. ~ a1aulat1oa o~ a !r t,pe o~ OOli!POBi­ tion 1a baaed oa 1lbe Laaptioaa aJl7 t;J­ pe o~ 0011p0ai tion ia characterised 'a.7 a

4efin1 te set o~ n.luea o~ par .. tera

·c = · (P1ao· P2bc' ···· Pkee' ··· ), where ~ec 1a a definite Talu o~ para­ Mter .Y.: Hleoted boa a ll1llt1ta4e o~ pemi~le Taluea. Ineastllltial parae­ tera are daaipate4 1A sero Talua. ~ the qualitatin oharacter1a1oioa o~ tM coapoaition (!rc t,pe) 1a aet 1liP in oor­ reapondace to a ~omal.-qwmt1tat1n cha­ racter1at1c (aet o~ Taluea o~ Mc parae­ ten).

!o dav.late 0011p081 tiou o~ a ~­ ni te !c t»· certaila n·ber· - encod84 n.lues o~ df:r(·tera - are ~ed into tu oorreapon cella o~ the oo.p~ter'· 1181101"7. In t · ~ the O:!er ia uaigud a certaizl liat o~ and ..... o~ oo11p0ai tion b7 wbich the OOIIIPOai tion produced aut be sonmed. !rhe ftD4 oo­ clea autouticalq "aet-vp" or ~om tlle progra. Out o~ all the progr-ed Talu­ ea o~ each paraeter Olll7 one, aaaiped, Talue ia selected. I~ t:be Talu o~ a_ pa­ raeter wu not Slftll, thell 4u.r1.ng the

1. aa..Poa1t1oll o~ aeloUM 1a 111aa­ late4 1A tlae ~om o~ a auioal perio4 1a ke7 ~or or lllllor. fllle aoada o~ tile uloq anu tu ftlM o~ ita ~ov u­ peotaa ~.,_o, aelocllo, lauwoD1o a4 atructural. ~· nlea Mtaltl1U tM ft1"1ou claratiou, in~e1'ftl-p1toh · rel&- tioa.a, atable ad. -.~able N.U o~ tM aoal!J npet1t1ou o~ aelodio ad ~:a.­ llio nprea u wll u tM aepataticm o~ tM aeloq into 1~· aeparate ooan­ raota - plarUea, -~·· !!M aeleo1oioa o~ tlae ~om or 0011p»aitioa (a period. o~ 8 or 16 bara) 1a 110tin.ted b7 a tM1re to aaJte a liON data1le4 atuq o~ tlle r.­ lea o~ tM aeloq wld.oh 1· a t1111Uecl auical ~··· o~ 111D1aua exttlllt ( 1).

2. A cCJIIIPOBition in aona Z'UtJa 1a progr-84 - a aequaco o~ claratiou oor­ reapcm41Jaa to a de11n1te poe1oio aeiorea a aeqaeaoe o~ atre.-4 ad aa'Reue4 ·7l&bl.U o~ a PG·· A ooald.nation o~ t:bia pros:ra with a prosraa ~or ooapoa1t1oa o~ a aelo~ pro"fides tlae posa1b111t;r o~ aiaulatiOA o~ 80DC aelocU.es to a SiTeD te:d 1D vane, or a soq (see ( 1)).

3. 1'he ~rogra o~ baJ.w>DizatiOD o~ a siva aelo~ 1D qaadriwiced chords ( triacJs and seYGtbchor48 1D baaio t"oa and t!:ae:lr con'Y8Z'81ou) 1aitates the solu­ tion oi" scbool problas. file progr .... conn ·~ aaterial oi" the OAe and a llal:t ·--·tva ot 1111810 college. 8uoh prob~ are solnd 1D 1l1181c college by Mans ot tu nles oi" hal.woDisatiOA out;.. l1De4 1D te:d boob oa hs~. Howver, the abseaoe ot preoise cJst1D1 iOAS ad coastnoti n procedures llaku the proo .. a oi" lw.wmiu.tioa ::rl:r 1Dtuit1n. Ba.t 1D P1'0P'- 1 "I i"o clari b' aut be 1Dt1'0daoe4 1D tlLe losloal1Dterrslat1oa oi" the vU'iou eleullta Ul4 uas ot bar­ IIOD1aat1cm. Beslua, tu soluticm o~ tu C~.o;.·:l::~;-J:~ =-~- .u (b;r certala or1tU'1a) solution.

!:be at:Notare ot the alpr;rtla ukes it c:le to aiaulate cU.ttereat t1,P88 o~ aatioa (tor iutace, cU.ttU.t 1D the e:d·t oi" coalexl.t)-) becaue a pro'Yiaioa is ode to a ~P'_. b;r ar­ ras··· oi" a set ot 'fi.l.aU oi" ·o para­ aeters, coZ'1'8spoad1al to tu set oi" rul.M 8D4 uau ot hsJ'IIOD1aat1Ga (see (1)).

4. !he prosra tor aaa.b'a1s ot> ·l· t1ou ot s~ta· problas iD hanlola1za­ t1oa ad tor deteotioa ot errors acts u eDIIiDer ad is a F.totDe o~ a reacld.Ja8 ·111t·· B;J ·erron are ··t torld.dda or ·dea:lrable seqaaoea ot ollorcJs or wicea e.g. chord,. JIOIUJeuical boa the poiat ot 'fin ot oe prop-a. n. a error lau bee detected its speoiftcs ad looatioa 1D tu coapositioa are 1Dd1oatecL !he possibilit;r ot> asa1Diu a set ot va­ lues ot ·c parDeten (tat -is a list oi" nles tU T.t.olatioa o~ wJd.oh 1D the 1D1t1al soluticm is CODS1dM-ed au error) pro"fides tor ~· oi" solutiOAS o~ pro bleas oi" Y&J:71.q clegrees ot oaple21t;r oi" ha.J:IIoDiaatioD.. ID otll.er worcJs, the prosr-e procllloes vario· reqair·eat to atuclats dter oae aoatll ot awq or on ~letioa ot" the w!lole tua ot stuq (see (1)).

s. !he aaol:d.De ooaposes one-wice variatioas oa a &lYG auical t:ta..e. OD. the basis oi" au!cal uterial tlds prog­ r· realises one ooaponent oi" hear.latic aoti"fit;r, 1D tld.s oue, traspoaib:l.lit;r, a ha~tal p.ropert7 oi" stzoacture. !'r&D8p0aitioa or traD.Ster ot invariant ~oaa is to be obsernd 1D tr~o.raation o~ aa;r nature. In t:td.a is ·bocU.ed the 1Dtegr1 t7 ot stracture which cazmot be brokeR v.p 1Dto eleaats.

Ye.1:7 one 1dum listeDiag to a tune and its va.r:tatiOA we detect the coDDec­ tion between tlla 1Dtu1 t1 nl;r. This is so because tbe variation retaiu all the aohaD.ged eleaents or the invariant· ot tr~oraatioa. Bllt 1D. variation the;r are IWiked b;r tl:ae changed r~la, .. ter, ke;r and the aelodic 11ne itself. Dese ·= eleaents one ll&ke the tua.e =­ reco sable. !he ll-lletllod o~ ainl atioa ideD ftes the 1Dnr1SD.ts and the lluk­ ing eleaents,. u well as the aechaDi· o~ tr8118p0a11il.oa ot invariants 1D the Yariatia oi" the aeloq (see (2,3)).

Oollputer nriatioD b;r tu ..... tllod llakes it possible i;o recoutraot the u­ obaDi· b;r which tu s1..-. oo.poad.tiOA was created, to i"ollow step b;r step the aole pZ'Ooess ot trastoDU.tiOA ot tile p..-. t-.e 1aw the sl ftD. variation, a4 to deoutrate tl:ae 1Dte.nae418J:7 re­ nlt· ot the couequitin stases o~ tr~ora&tiOA .and cle:tomatioa ot the Mlod7 (see (3)). J':l.pre 1 presets the ulod!es ocapose4 liD.4er tlds P'OP'-. b;r :llla.-6 coapailer ot the Ooa.P·tatioa Oe~ 1 VSSll .lca"'-T o~ Scicces. Xt wlll be DOUce4 that ·loq ·o. 1 oaplete~ oo1ao1des ( ~il i"or t:bs Ursil 110te ill tlae last bar) wltb. the popular "'lolo~ ~· 8011.1 (boa the ftla W'folp-Yolg&") b;r the So"fiet ooapoaer Dall.&eftJI:1. file s;patllesis ot tld.· uloq b;r tlle 0011p11ter c0a:t1l.'lle4 our u.-ptiona coac8l"'ddaC the aatve ot its oo:anect1ou wltll the ori­ slaal t~, tlae W18 o~ traU:toaatioa ot tld.a tllae 1ato the ulo~ ot tile "'loloqoalmqa" U wll U COD.Oea1DS tu ·eo~· o! oreatioa ot ulo41es o~ tl:d.a s;rataot:loal stnoture (tu ulo­ <q o~ · poplllar soag). ~r it i· oza.q b;r this process that a aacld.De aeloq co1D­ c1~ wlth tu slv. .. 11.-ao· aeloq co1114 laaYe bee pro4v.oed.

I 4. !he ~21111 t;r (or a1a1lar1 b') ot the aaold.De result an4 tlle s'buq ob=­ ject is the oriterioa oi" perteotioa oi" the al&or;rtla and tu degree ot bowle4se oi" tld.a ob~eot. What is ia.Porta.t is DOt the absolute ~t;r ot the ucld.De results (oi" 11118:lo, ~or one) but a auill1a USHe ot co1Do1cl8D.oe ot these result· 1d.tll tb.ee;b ect 1D the reapeots be1u studied the ~cess o~ siaula~oa. !lae probl· o en.l.U.tioa ot the aaold.D.e renJ.ts ancl ot t!:ae1r co~~pariaoa to tbe ob~eot s11lulate4 is a Yer7 coaplex one, ~oiall;r 1D the cue ot wora ot art. BYaluati.oa here i· ~luenoe4 b;r aaa;r tactors, 1Dol=:f public :oa· reacli!:Slo::::"'!: fxt.=~::t :~~eru~- cU.ce agaiut the work e'Yaluated.

!he author has de"fised a aethocl ot aociologl.cal ·T"'"·t1oa ot e'Yaluatiou aade b;r l:iatenera o~ aaobi.D.e llUIJio. ~ :problela oi" en.lu.tioa o~ aaohiae ooapoa1t1ou and t!:ae:lr coapar.lson with coaposer auaic ca oaq be dealt w1 th on the baa:l.s ot a quut10Dil81re. This probl· is tied 1D wltll 11ataers' pa7Qholos;r, tlaat is their 1Dald.l1t;r to evaluate the coapoai­ tiODS ob~ectinl;r i~ the;r lmow betorehaDd tbat aelo~ llo. 1 is aachiae-prod.v.ced, aad aelo~ :lo. 2 waa OOII,POBed b7 aaa. J Just as it is iJIPC)ssible to appraise ob­ ject1vel7 a popular aelo~. Ps7chologlcal­ l7 it is quite natural. ~here~ore to be able to aelte an obJecti.ve OOIIPariBOD the liateaers auat DOt li:Dow what the7 are evaluatiag at tbe giYeU aoaet, uchiae­ or aa.-procluced auaic.

J. special e~eriaeat is aeeded 1;o llake a eociolopca~ ob~eotive evalu.­ tioa o~ tbe coaputer a co·oai tiODB &ad co11pare t!Ma with the ob~ecta o~ aiaula­ tiOD. !he purpose o~ the el!PeriaeD.t is to elild.aate the P·7cholog1cal set ('biaa) o~ the e~erts, to OOB:tuae thea ao tbat the7 will DOt li:Dow what the7 are dealJ.Ds with, whether it ia a work o~ the coaputer or ll&ll. Beaidea, that e~eriaeDt is aleo to obtaia a. ob~ective eftluati.oa o~ uohiae COJIIPOai tioaa aa compared to oollpC)ser· s worb, tbat is to i.Ddicate their qaal1t7.

Melodies o~ wll-li:Doc So"fiet ooii,PO­ aera published 1a selected SOJl8 booka ·d aelodiea oolq)Osed b7 "Ural-2" ocmputer Ullder the above p.rograae were selected ~or the e~erimeilt. 1'he aelod1es were pla;red 1D an ubitr&r7 order, Ullli:Dowa to the list__.s no were to evaluate thea b7 a fin-poiat scale and 'trd.te the aua­ ber o~ poiats 1a the blal:l.ka o~ the ~o1'11. !he e~eriaat wu ooaclucted 1D d1rterat aocio-auaical groups with app1"0Jd.aatel.:r the sae level o~ auaioal ecmcatioa. ~7 were st.dea.ts ot tbe Moscow Powr Iaat1tute, atud.ats o~ t:t:ae Gaea1Da Muio !ea­ chera !J!rah1ng IDatitute, puticipaats 1D

!=J:r(t: :if~~o~~~:r... ocmoemed. with auio peroepti.oa) saiO.l'-Sftde so.bool pupila, utMu.td.oi::!Jn~~~c-=;~;~;:~::":f=:~ theaatios o~ tlle USSJl J.ca~ o~ So1·­ oes and tlle 90al>·tati.OD Catre o~ tu J.ca~, .-plo;rees o~ ollltv.re.l utabliela­ aeDts and otb.ers - ·re tlaaD 600 p~le ill all. J. 81a1lar e~eriMD.1; ... &laO ooad.ucted. oa the buis o~ a pzropo-. H<oa4cu1; b7 tu .boae serri.oe o~ Ba41o Moscow oa J.ugu1; 25, 1973.

Juet u 1D U7 eocioloslcal s~ ob~ec­ ti" ocmoluioae were aade oa tu buis o~ n-erases o~ subJeotiTe eftluati.ODa o~ tu parti~S:ts 1D 1;Jae aus e~rta.ats. ~he proces o~ e~er.I.Jiea1;al data :riel­ dad 41:tfereat oharactU'istios (see (~)). ~be adopted aethod ws ~olllld correct u it aade it poaei ble to elild.D.ate tu PS1'­ cholodca1 ld.u w bave aeatiODed. I1; wa established 1D a aeries o~ e~.n..ats that the uchiae eolrtPOai tiODB scored 110re poiats (b7 various criteria) thaa ooapo­ ser auaio. 1'he ~ollo1t'.l.D8 table show how melodies were evaluated b7 one cr1 terioa b7 the auaicalq wll-edliCated povp o~ students Q~ the Gae&1u Inati.tutea

BTaluatiOD

fte table g1 ft8 the nuaber o~ 5-, 4-1 3-, 2-t 1-poiDt eTaluationa o~ the .. chiDe &DC1 coaposer aelodiesa All and Ao are anrase eTaluations o~ the aelod1es.

The results o~ tbis uperiaants pro­ Te the ~ollo1d.Dg ~acta 1D co-.puter siau­ lation o~ aoae t;n>ea o~ auat.c, such u COilPC)BiDa aelod1es o~ popular 801188, the resUlts obtained b;y the aacbiDe are DOt OAl;y co11parable to h1a8D works but are eTa 81J~»er1or to th· 1D qualit7. This 18 1.Dd1cat1 n o~ t;he ~act; that t;he ucha­ D1· ot creaticm ot such tome o~ auaic .baa bea 8'W41es to a Ter'7 hiP 4eSNe, and proTes the correctne .. ot the cbosa pr1Dc1plea ot a1aulat1on.

It 18 illportant to bear 1D lliDd that the aelo41e8 ot pro~e8s101l&l COIIP088Z'8 ued 1D the eJII)eriuDt are tile result ot lllluD prote8810Dal actin~ wbich is cal­ led creat1w.