aspen no.8
TRANSCRIPT
-
7/29/2019 aspen no.8
1/36
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
http://ubu.com/aspen/siteIndex.htmlhttp://ubu.com/aspen/aspen10/index.htmlhttp://ubu.com/aspen/aspen9/index.htmlhttp://ubu.com/aspen/aspen8/index.htmlhttp://ubu.com/aspen/aspen7/index.htmlhttp://ubu.com/aspen/aspen6A/index.htmlhttp://ubu.com/aspen/aspen5and6/index.htmlhttp://ubu.com/aspen/aspen4/index.htmlhttp://ubu.com/aspen/aspen3/index.htmlhttp://ubu.com/aspen/aspen2/index.htmlhttp://ubu.com/aspen/aspen1/index.htmlhttp://ubu.com/aspen/intro.htmlhttp://ubu.com/aspen/aspen8/threeDistributions.htmlhttp://ubu.com/aspen/aspen8/leadPendulum.html -
7/29/2019 aspen no.8
2/36
-
7/29/2019 aspen no.8
3/36
-
7/29/2019 aspen no.8
4/36
-
7/29/2019 aspen no.8
5/36
-
7/29/2019 aspen no.8
6/36
-
7/29/2019 aspen no.8
7/36
-
7/29/2019 aspen no.8
8/36
-
7/29/2019 aspen no.8
9/36
-
7/29/2019 aspen no.8
10/36
-
7/29/2019 aspen no.8
11/36
-
7/29/2019 aspen no.8
12/36
-
7/29/2019 aspen no.8
13/36
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 -
7/29/2019 aspen no.8
14/36
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
-
7/29/2019 aspen no.8
15/36
subsections, eachof whichwillreceive
anindividualtitle. Amajordifference is thatall workon thissectionhas takenplacesince Ibegan towrite2-3PM12XI663:43AM28 X11 66FOR JOHNCAGEFROM"VERTICALHEARINGORHEARINGIN THEPRESENTTENSE"which Ihavesincerevised
under thetitle THETWOSYSTEMSOFELEVENCATEGORIES
-
7/29/2019 aspen no.8
16/36
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
-
7/29/2019 aspen no.8
17/36
es will bepresentwithin acomplexof such
concurrentgeneratingfrequencies andtheirassociatedcombinationfrequenci
es.Generatingfrequencies aredefinedto he theprime, orzerothorder;combinati
onfrequencies fromwhich allhigherordercombinationfrequencies arederived.
The nthorder (N0)combinationfrequencies aredefined
-
7/29/2019 aspen no.8
18/36
to be thesum anddifferencefrequenci
esproducedby alllowerordercombinationfrequencies. Thiscontrol isachieved
bycategorizing sets ofconcurrentgeneratingfrequenciesaccordingto the
specificgenerating andcombinationfrequencies to beexcluded.
Considerthe
premisethat indetermining therelationship of twoor morefrequenci
-
7/29/2019 aspen no.8
19/36
es ebrain canbestanalyzeinformation of aperiodicnature.Sincechords inwhich anypair offrequencycomponents musthe
represented bysomeirrationalfraction(such asthoserequiredfor anysystem ofequal
temperament)producecompositesoundwaveforms that areinfinitelynon-repeating, only an
infinitenumberoflifetimesoflisteningcouldpossibly
-
7/29/2019 aspen no.8
20/36
preciseanalysis oftheintervallicrelationsh
ip.Consequently thehumanauditorymechanism couldbe bestexpectedto analysethe
intervallicrelationshipsbetweenthefrequencycomponents ofchords inwhichevery pairofcomponents can berepresented bysomerationalfraction,since onlytheseharmonicallyrelatedfrequenciesproduceperiodiccompositesound
-
7/29/2019 aspen no.8
21/36
waveforms.
Assources
for thefrequencyenvironments Ihaveselectedsinewavessincethey haveonly one
frequencycomponent. Theseareproducedbyfrequencygenerators tunedboth byear and
with anoscilloscope whichcontinuouslydisplaysthegeneratorfrequencyratioswith
lissajousandintensitymodulated ring
patterns.Mostrecently I
-
7/29/2019 aspen no.8
22/36
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
-
7/29/2019 aspen no.8
23/36
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
-
7/29/2019 aspen no.8
24/36
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
-
7/29/2019 aspen no.8
25/36
playedcontinuously 24hours aday for
severalweeks ormonths.MarianZazeelaand Ihaveworkedand livedin thisenvironment, andvariedgroups ofpeoplehavebeeninvited tolisten andreporttheirreactionsto thefrequencies.Althoughin 1957 Iwasoriginallydrawn towork withsounds of
longdurationbyintuitionalone, mywork ofthisnature
-
7/29/2019 aspen no.8
26/36
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
-
7/29/2019 aspen no.8
27/36
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
-
7/29/2019 aspen no.8
28/36
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,
-
7/29/2019 aspen no.8
29/36
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
-
7/29/2019 aspen no.8
30/36
as adrone orfrequentlyrepeated,
and alimitedset offrequencies withintervallicrelationshipsestablished inreferenceto thetonic isrepeatedin variousmelodicpermutationsthroughout aperformance in aparticularmode.Generally, aspecificmood orpsychological stateisattribute
d to eachof themodes.The placetheoryofpitchidentification
-
7/29/2019 aspen no.8
31/36
s thateach timethe samefrequencyis
repeatedit isreceivedat thesamefixedplace onthebasilarmembrane and
transmitted to thesamefixedpoint inthecerebralcortexpresumably by thesame
fiber orneuron oftheauditorynerve.Thevolleytheoryofpitchperception assumes
that asequenceofelectricalimpulsesis senttravelingalong
-
7/29/2019 aspen no.8
32/36
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
-
7/29/2019 aspen no.8
33/36
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
-
7/29/2019 aspen no.8
34/36
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
-
7/29/2019 aspen no.8
35/36
the sameoperationoftransmitting a
periodicpattern ofimpulsesto thecorresponding setof fixedpoints inthecerebralcortex.
Whenthesestates aresustainedoverlongerperiods oftime theymayprovidegreater
opportunity todefinethepsychologicalcharacteristics ofthe ratiosof thefrequenci
es toeachother. (2)
(1) Anotableexampleof the
-
7/29/2019 aspen no.8
36/36
application of
principles1 and 3 isthe
classicalmusic ofIndiawhich hasnearlyalwaysincludedasustaineddrone andhas
evolvedandactually
practicesthe mosthighlydevelopedsystem ofmodalscales andmoods
related tomodes inthehistory ofmusic.(2) Ibid.