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Aspen no. 8, item 7 aspen no. 1 no. 2 no. 3 no. 4 no. 5+6no. 6A no. 7 no. 8 no. 9 no. 10 index

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Notes on Continuous Periodic Compt Realizations Foraccompanying audio, listen to item 5

NOTES ONTHECONTINUOUSPERIODICCOMPOSITE SOUNDWAVEFORMENVIRONM

ENTREALIZATIONS OFMAP OF49'SDREAMTHE TWOSYSTEMSOFELEVENSETS OF

GALACTICINTERVALSORNAMENTALLIGHTYEARSTRACERYBY LAMONTEYOUNG

MAP OF49'SDREAMTHE TWOSYSTEMSOFELEVEN

http://ubu.com/aspen/aspen8/audio8.html#drift

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SETS OFGALACTICINTERVALSORNAMEN

TALLIGHTYEARSTRACERYconsists ofa totalenvironmental setoffrequencystructure

s of soundand light-acollaboration of mywork withlightprojections anddesignscreated

by MarianZazeela.Althoughthe workis asection ofTHETORTOISE,HISDREAMS

AND

JOURNEYSit isdifferentfrom theprevioussectionsand willhave its

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subsections, eachof whichwillreceive

anindividualtitle. Amajordifference is thatall workon thissectionhas takenplacesince Ibegan towrite2-3PM12XI663:43AM28 X11 66FOR JOHNCAGEFROM"VERTICALHEARINGORHEARINGIN THEPRESENTTENSE"which Ihavesincerevised

under thetitle THETWOSYSTEMSOFELEVENCATEGORIES

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AM 3 X 67. I haveconcentratedprimarily

onselectedintervalsfromcategoriesAl, 131,and A2,B2, X=5from thelatterwork.

THE TWOSYSTEMSOFELEVENCATEGORIES appliesto sets ofconcurrentgeneratingfrequencies whichareintegralmultiplesof acommonfundamental andoutlines ameans forachievinggraduateddegreesof controloverwhichfre uenci

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es will bepresentwithin acomplexof such

concurrentgeneratingfrequencies andtheirassociatedcombinationfrequenci

es.Generatingfrequencies aredefinedto he theprime, orzerothorder;combinati

onfrequencies fromwhich allhigherordercombinationfrequencies arederived.

The nthorder (N0)combinationfrequencies aredefined

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to be thesum anddifferencefrequenci

esproducedby alllowerordercombinationfrequencies. Thiscontrol isachieved

bycategorizing sets ofconcurrentgeneratingfrequenciesaccordingto the

specificgenerating andcombinationfrequencies to beexcluded.

Considerthe

premisethat indetermining therelationship of twoor morefrequenci

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es ebrain canbestanalyzeinformation of aperiodicnature.Sincechords inwhich anypair offrequencycomponents musthe

represented bysomeirrationalfraction(such asthoserequiredfor anysystem ofequal

temperament)producecompositesoundwaveforms that areinfinitelynon-repeating, only an

infinitenumberoflifetimesoflisteningcouldpossibly

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preciseanalysis oftheintervallicrelationsh

ip.Consequently thehumanauditorymechanism couldbe bestexpectedto analysethe

intervallicrelationshipsbetweenthefrequencycomponents ofchords inwhichevery pairofcomponents can berepresented bysomerationalfraction,since onlytheseharmonicallyrelatedfrequenciesproduceperiodiccompositesound

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waveforms.

Assources

for thefrequencyenvironments Ihaveselectedsinewavessincethey haveonly one

frequencycomponent. Theseareproducedbyfrequencygenerators tunedboth byear and

with anoscilloscope whichcontinuouslydisplaysthegeneratorfrequencyratioswith

lissajousandintensitymodulated ring

patterns.Mostrecently I

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havebeenusing aMoogSynthesiz

er withultra-stablevariablefrequencysine waveoscillatorsdesignedfor mywork.

To myknowledge therehavebeen nopreviousstudies ofthe long-termeffects ofcontinuou

s periodiccompositesoundwaveforms onpeople.(long-term isdefinedto belonger

than afew hoursin thiscase.)

My pastwork inmusic

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withsounds oflongdurationslowly led

in thisdirectionuntil itbecamepossiblefor me todevelop asituationallowingthe studyof truly

continuous soundsbyestablishingcontinuousfrequencyenvironments withelectronic

instruments. I havemaintained anenvironment ofconstantperiodicsoundwaveforms at my

studioand homecontinuously sinceSeptember 1966.The onlyexception

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s avebeen thatIsometimes, but notalways,turn offtheequipment when noone willbe in theenvironment at all,and whenlistening

to othermusic.Also, Isometimes turn itoff to testtheacousticalsituationforspurious

(incidental) sounds,and tostudy thecontrastsof suchextendedperiods ofsoundwithperiods of

silence.

The setsoffrequencyratioslistenedto are

Copyright La Monte Young, 1969SECTION 7 ASPENNO. 8

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playedcontinuously 24hours aday for

severalweeks ormonths.MarianZazeelaand Ihaveworkedand livedin thisenvironment, andvariedgroups ofpeoplehavebeeninvited tolisten andreporttheirreactionsto thefrequencies.Althoughin 1957 Iwasoriginallydrawn towork withsounds of

longdurationbyintuitionalone, mywork ofthisnature

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theformulation of threeprincipleswhich

suggestfurtherstudy:

1. Tuningis afunctionof time.Sincetuning aninterval

establishes therelationship of twofrequencies intime, thedegree ofprecisionisproportional to thedurationof theanalysis,i.e. to thedurationof tuning.Therefore, it isnecessaryto sustainthefrequencies forlongerperiods ifhigherstandardsof

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precisionare to beachieved.The factthat this

information is notgenerallyknown tomusiciansmay beonereasonthat onlya fewexamples

of pitchesof longdurationsuch asorganum,pedalpoint, andthe droneare to befound inmusic. On

the otherhand,astronomers haveknown forsometime thatif ameasurement orcompariso

n is to bemade oftwo orbitswhichinvolvemanyyears oftime, the

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degree ofprecisionof themeasurement will

beproportional to thedurationfor whichthemeasurement ismade. (1)

2.

Considerthepossibilitythat thenumberofcompletecycles ofa periodiccompositewaveform

is aprimaryfactor inrecognizing anintervaland/or indetermining thedegree ofprecision

in tuningonce theintervalhas beenrecognized. If thiswere thecase,

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ra oscomprisedof lowerfrequencies (suchas 52.5Hz: 30Hz=7:4)wouldhave tobesustainedfor longerperiods oftime thanthe

identicalratioscomprisedof higherfrequencies (suchas 840 Hz:480Hz=7:4),in orderto

produceanequivalent numberofcompletecycles oftheirperiodiccompositewaveform

s.

3. In thetraditionof modalmusic, afixedtonic is

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as adrone orfrequentlyrepeated,

and alimitedset offrequencies withintervallicrelationshipsestablished inreferenceto thetonic isrepeatedin variousmelodicpermutationsthroughout aperformance in aparticularmode.Generally, aspecificmood orpsychological stateisattribute

d to eachof themodes.The placetheoryofpitchidentification

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s thateach timethe samefrequencyis

repeatedit isreceivedat thesamefixedplace onthebasilarmembrane and

transmitted to thesamefixedpoint inthecerebralcortexpresumably by thesame

fiber orneuron oftheauditorynerve.Thevolleytheoryofpitchperception assumes

that asequenceofelectricalimpulsesis senttravelingalong

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specifiedneuronsof theauditorynerve.

Forfrequencies up toabout2000 Hzonly,theseproduce amore orlesscomplete

reproduction of thefrequencyof thevibratorymotion ofthebasilarmembrane in thecase of a

singlesine waveand amore orlessdistortedreproduction of thecompletewaveformfor more

complexsignals. Itispresumedthat thisreproduction willhe best

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or soun sat lowerfrequencies andless goodfor higherfrequencies sinceanindividualneuroncannotfire fasterthan 300Hz. Atlower

frequencies agroup ofneuronsworkingtogetherwould beable tosupplyseveralpulses

per cyclewhereasat higherfrequencies theycouldonlysupplyone everyseveralcycles.

Theassumptions of

placetheoryand volleytheorysuggest

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when aspecificset ofharmonically

relatedfrequenciesiscontinuous, as isoften thecase inmy music,it couldmore

definitively produce(orsimulate)apsychological statethat maybe reported bythelistenersince theset ofharmonicallyrelatedfrequencies willcontinuously triggera specificset of theauditoryneuronswhich inturn willcontinuouslyerform

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the sameoperationoftransmitting a

periodicpattern ofimpulsesto thecorresponding setof fixedpoints inthecerebralcortex.

Whenthesestates aresustainedoverlongerperiods oftime theymayprovidegreater

opportunity todefinethepsychologicalcharacteristics ofthe ratiosof thefrequenci

es toeachother. (2)

(1) Anotableexampleof the

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application of

principles1 and 3 isthe

classicalmusic ofIndiawhich hasnearlyalwaysincludedasustaineddrone andhas

evolvedandactually

practicesthe mosthighlydevelopedsystem ofmodalscales andmoods

related tomodes inthehistory ofmusic.(2) Ibid.