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  Received April 2017 “What can they have to do with one another?”:Approaches to Analysis and Performance in John Cage’s Four 2 * Drake Andersen ! #: he e$amples for the %te$t&only' P() version of this item are availale online at:h+p:,,www-mtosmt-org,iss.es,mto-/0-12-3,mto-/0-12-3-andersen-php 4#5W!6(7: John Cage8 indeterminate m.sic8 performanceA97 6AC : n this st.dy8  eval.ate the sonic possiilities of John Cage’s Four 2  %/;;<' y comparinge$isting performances of the piece with alternate renditions generated comp.tationally and y handspeci=cally for this analysis- Four 2  8 one of Cage’s .mer Pieces8 is f.lly determinate with respect topitch8 instr.mentation and overall d.ration8 .t a>ords the performer the e$iility to choose thed.rations of speci=c so.nds thro.gh time&rac@et notation- he di>erences in the m.sical res.lts etween vario.s performances8 oth real and virt.al8 prompt a disc.ssion of the performancepractices of the piece oth as o.tlined y Cage and as .nderstood y scholars and performers-Accompanying this te$t is a comp.ter program with which readers can edit and play ac@ their owninterpretations of Four 2 - ol.me 128 .mer 38 (ecemer 1</0Copyright B 1</0 7ociety for .sic heory 1. Introduction D/-/E he time&rac@et notation that John Cage employs in his .mer Pieces permits performersto prod.ce di>erent renditions of a given composition y choosing the position and d.ration ofso.nds within a e$ile time range- %/'   hese wor@s8 from late in Cage’s career8 are typically f.llydetermined with respect to pitch8 dynamics8 instr.mentation8 and total d.ration- Fowever8 theirrelative e$iility and Cage’s own poetics of non&intention have inhiited analytical disc.ssion ofsonic relationships8 even tho.gh the possile variation of the so.nds themselves is highlyregimented- %1' D/-1E n this st.dy8  analyGe the sonic relationships in one s.ch piece8 Four 2  %/;;<' for mi$edchor.s8 y approaching the wor@ from three interpretive perspectives: a onte Carlo sim.lation of 1 of 23  many %virt.al' performances of the wor@H real&world performancesH and fo.r imaginedperformances8 designed int.itively y the a.thor to reect distinct interpretive priorities emodied y fo.r invented cond.ctors- %2'   hese divergent strategies prod.ce characteristic res.lts thatemphasiGe competingIand sometimes contradictoryIconcerns in the performance of Cage’s.mer Pieces- a@en as a whole8 they contri.te to a more complete acco.nt of the m.sicalpossiilities of Four 2 -D/-2E )irst8  descrie the methodology of the onte Carlo sim.lation and s.mmariGe the dataotained therein to estalish some characteristic li@elihoods in the piece- n the ne$t section8 introd.ce each of the =ctional cond.ctors’ interpretations thro.gh a score&li@e transcription and rief analytical narrative- hese interpretations were generated y the a.thor to ill.strate speci=cpossiilities within the piece- any aspects of them are statistically .nli@ely8 .t are incl.ded hereto provide a more comprehensive .nderstanding of what is possile in a performance of Four 2 - hesim.lation data and =ctional cond.ctors’ performances are then eval.ated alongside real&worldperformances8 transcried from commercially availale recordings-D/-3E his comparative approach responds to J.dy ochhead’s s.ggestion to “DapproachE the m.sicfrom the perspective of what performers do8” as well as concerns e$pressed y Ale$andre Popo>regarding how to acco.nt for di>erences etween comp.tational sim.lations and liveperformances of Cage’s .mer Pieces %ochhead /;;3 8 13/H Popo> 1</2 8 1<8 13'- he live performances vary in some ways from the sim.lated performancesH accordingly8  proceed with adisc.ssion of the performance practice of Four 2  ,  and the .mer Pieces in general8 in order toacco.nt for some of the di>erences- he variety of performance practices in .se s.ggests roaderK.estions ao.t the e$tent and meaning of indeterminacy in the .mer Pieces8 which  address inthe concl.ding section-D/-LE Example 1  gives the soprano part of Four 2 - he soprano part consists of three so.nds8 eachpositioned within a .niK.e time rac@et- Cage’s time&rac@et notation speci=es two windows oftime for each so.nd: one in which each so.nd may egin and one in which each may end- %3'   he=rst rac@et8 consisting of an )3 s.ng on the vowel “e8” allows for the so.nd to egin anywhere etween <’<<” and /’<<” from the start of the piece8 and for the so.nd to end anywhere etween<’3<” and /’3<”- his means that8 for e$ample8 an M<&second so.nd eginning at <’/<” and endingat /’2<” wo.ld e permissile8 as wo.ld an M&second so.nd eginning at <’L/” and ending at <’L;”-n other words8 the time&rac@et notation allows for a wide range of d.rations- %L' D/-NE A .niK.e feat.re of these rac@ets is the overlap etween the starting and ending windowsIin this case8 etween <’3<” and /’<<”- his internal overlap allows for greater sonic indeterminacy8permi+ing8 for instance8 the e$ile placement of so.nds of e$tremely short d.ration8 and avoidingan intermediary interval of oligatory so.nd etween the starting and ending intervals-D/-0E Example 2  is a transcription of the twenty time rac@ets of the fo.r parts in Four 2  into a score&li@e format8 .sing solid horiGontal lines to represent individ.al so.nds- Phonemes and dynamicsare also incl.ded for each so.nd- As the legend elow the score e$plains8 the starting interval ofany given time rac@et e$tends from the leftmost edge of the lac@ line to the right edge of theinternal overlap o$ in the middle of each line- he ending interval of any given time rac@ete$tends from the left edge of the internal overlap o$ to the rightmost edge of the lac@ line-D/-ME !ften the time rac@ets of two s.ccessive notes in the same part overlap e$ternally8 s.ch asthe =rst two notes of the tenor part- n the transcription aove8 when these notes are di>erent8 it isgenerally clear vis.ally where the two rac@ets egin and end- Fowever8 the last two notes of thealto part overlap e$ternally on the same pitch %('H in this case8  .se a do+ed line to indicate thee$tent of the overlap- 2. Computational Simulation of  Four  2 2 of 23  D1-/E Cage’s .mer Pieces have rarely een analyGed in detail for two primary reasons: theirscores represent a m.ltiplicity of possile performances in which so.nds’ order and d.ration canvary widely8 and a teleological analytical narrative seems to contravene Cage’s description of hisindeterminate wor@s and what we @now of his compositional process-  will address the la+erconcern in the concl.sion of this articleH regarding the former8 the onte Carlo sim.lation providesa potential sol.tion-D1-1E Osing this techniK.e8 virt.al performances of Four 2  are otained y comp.tationallydetermining the random variales %i-e- the starting and end points of the so.nds' corresponding toCage’s notated constraints- Popo> 1</2 advocates this approach:9y averaging over a large n.mer of realiGations %which is achieved thro.gh acomp.ter program r.nning the determination of the parts repeatedly' we can accessthe proaility distri.tions of each pitch&class set over time8 th.s t.rning the .merPieces into stochastic processes- 9y doing so8 we solve the prolem posed y Fas@insand Weisser of coping with all the possiilities o>ered y the .mer Pieces- %Popo>1</2 8 2'D1-2E  have carried o.t a onte Carlo sim.lation of over one tho.sand virt.al performances of Four 2 H however8 efore disc.ssing the res.lts8  will raise a few speci=c points regarding themethodology- )irst8  created a specialiGed random val.e generator .sing a$ software- Completeperformances of the piece were generated as lists of time val.es %corresponding to the eginningsand endings of so.nds' .sing the interval of a second as oth the generative grain and samplingrate8 since this is the smallest .nit of s.division in Cage’s notation- As each performance lastse$actly seven min.tes8 each sim.lation contains 31< data points8 each corresponding to one secondof the performance-D1-3E r.ly random selection of val.es within the %overlapping' starting and ending rac@ets ofeach so.nd means that8 in a comp.tational environment8 a so.nd co.ld end efore it egins- oavoid this parado$8 the software chooses a starting point =rst8 then tests randomly&selected endingpoints8 reecting and discarding any that precede the starting point in time- he entire“performance” is then tested for any e$ternal overlaps8 and if any are fo.nd8 the entireperformance is discarded and a new performance is generated in its place-D1-LE Additionally8 in the software  have estalished that a so.nd is eK.ally li@ely to egin or endat any time d.ring a given rac@etIin other words8 amongst many performances of the wor@8 thedistri.tion of each rac@et approaches .niformity- his random %.niform' approach may econtrasted with that of Popo> 1</28 in which a Qa.ssian c.rve is .sed to distri.te starting andending points within the time rac@ets- %N'   his approach emphasiGes the center of each starting andending rac@et and “gives less prevalence to so.nd events occ.rring at the very eginning or endof their time interval” %Popo> 1</2 8 L'- he random approach  am employing emphasiGes all partsof each rac@et eK.ally8 enriching the analysis with a wider variety of possile res.lts-D1-0E Example 3  displays all of the pitch&class sets %pc sets'8 incl.ding m.ltisets8 otained in /<;;sim.lations of Four 2  8 organiGed y set class %sc'- he raw n.mer of seconds d.ring which each setclass so.nds8 added together in all sim.lations8 is displayed in the col.mn to the right of the pc set- he rightmost col.mn displays the prevalence of each set compared to the others %of anycardinality' as a percentage- he percentage is otained y dividing the raw n.mer of seconds y3N/8LM<8 the total n.mer of data points amongst all sim.lations %/<;; sim.lations m.ltiplied y31< data points per sim.lation'- he total n.mer of val.es and total percentage per set class isdisplayed at the o+om of each o$- he o$es display the set classes in )orte order from left toright and top to o+om-D1-ME he single most prevalent pitch&class set is the n.ll setIsilenceIwhich occ.rs /2-NR of the 3 of 23  time amongst all sim.lations- he least prevalent pitch&class set is S<30;TIan instance of sc %<2LM'Iwhich occ.rs only once8 or appro$imately <-<<<<<11R of the time- 9etween these two e$tremeslies a varied collection of sonorities8 with 1/ of 3; possile set classes of cardinality <&3 represented-FUnermann oserves that8 “DtEhe increased proaility of traditional harmonic content rests .ponthe simplicity of pitch material and the red.ction of density” %FUnermann 1</3 8 N/1'- ndeed8 thereare only seven distinct pitch classes availale in the piece: the (&minor diatonic collection min.s9&at8 pl.s the raised seventh degree wri+en as oth C and (- he limited pitch material ens.resthat many of the sonorities that emerge from any given performance will e recogniGale s.sets ofthe same diatonic scale- ).rther constraining the harmonic possiilities is the fact that icN is notpossile as part of any sim.ltaneity in the piece-D1-;E Example 4  presents the same data as #$ample 2 organiGed y %m.ltiset' cardinality: then.mer of active voices8 even when two voices are singing the same pitch class conc.rrently- h.sS<//LT reects a cardinality of 38 even tho.gh in normal form it wo.ld e red.ced down to thecardinality&2 set S</LT- Comparing the total percentages in the lower&right cells of each col.mnshows that the piece is silent appro$imately /2-NR of the time %ao.t L0 seconds per sim.lation'8one voice is so.nding 2/-1R of the time %ao.t 1’//”'8 two voices 22-3R of the time %ao.t 1’1<”'8three voices /0-/R of the time %ao.t /’/1”'8 and fo.r voices .st .nder LR of the time %ao.t 1<seconds'- his data helps ill.strate the sparseness of the m.sic: in a composition with fo.r parts8te$t.res of two or fewer parts are heard over 0LR of the time-D1-/<E Example 5  depicts the prevalence of each set class otained in the sim.lations of Four 2 graphically over time8 .sing lines of di>erent colors to represent each of the 1/ set classes listed in#$ample 2- n #$amples 2 and 38 prevalence is e$pressed as a proportion of the total d.ration of thepieceH the graphs in #$ample L demonstrate how prevalence changes over time d.ring aperformance of the piece- he horiGontal a$is represents time %in seconds' and the vertical a$ise$presses the percentage of sim.lations in which a given set is so.nding at a given time- )orinstance8 in the opening seconds of the piece8 almost ;<R of the sim.lations are silent- #$ample Lais an interactive graph for which individ.al lines representing set classes can e toggled on and o> y clic@ing on the set name in the legend at the top of the graph- #$ample L is a still image givingall 1/ set classesH #$amples Lc and Ld depict only sets of cardinalities <V1 and 2V38 respectively8 forlegiility-D1-//E As #$ample 2 demonstrates8 many of the set classes in Four 2  may e constit.ted y severaldi>erent pitch class sets- Example 6  depicts all of the instances of a single set classIsc %<2'Iovertime- n the sim.lations of Four 2  8 sc %<2' was formed y =ve di>erent pitch&class sets which8 eca.se of the presence of d.plicate pitch classes8 reect three distinct pitch&class pairings- !verthe co.rse of the piece8 fo.r distinct pea@s can e ascertained: pcs %1L' and %1LL'8 pcs %30' and %300'8pcs %/3'8 and a ret.rn to pcs %1L'- he vertical a$is displays the prevalence of each partic.lar pitch&class set %as a percentage' in relation to every other pitch&class set otained among the sim.lationsat each .nit time %in seconds'-D1-/1E n addition to the prevalence of diatonic harmony in Four 2  already disc.ssed8 writers haveremar@ed speci=cally on the strong potential for triadic harmony- FUnermann descries “an.ndenialy consonant so.nd environment circling aro.nd d minor8” thro.gh which8 in relation tothe chromatic material in the =nal min.tes of the piece8 “the listener may well perceive %and Cageat least facilitates' a teleological harmonic process” %1</3 8 N/1'- While a disc.ssion of “perception”is eyond the scope of this st.dy8 the sim.lation data provides a K.antitative description of theprevalence of triads within the piece-D1-/2E Example 7  depicts the prevalence of sc %<20' over time- As efore8 the lines of di>erent colorsrepresent di>erent pitch&class sets that form triads in this piece- here are three distinct instances ofsc %<20': pcs %1L;' and %1LL;'H pcs %<30' and %<300'H and pcs %/3;'8 corresponding to ( minor8 Cmaor and A maor triads8 respectively- he =rst and third pea@s %( minor and A maor' are m.ch 4 of 23

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Jun 13, 2018
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