the role of timbre in the memorization of microtonal intervals.pdf

8/11/2019 The Role of Timbre in the Memorization of Microtonal Intervals.pdf

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The Role of Timbre in the Memorization of Microtonal

Intervals

Pro Gradu

Rafael Ferrer Flores

Department of Music

University of JyvskylSeptember 2007


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bstract

The aim of this thesis /as to determine if timre has any effect in thememori!ation of melodic inter#als0 For this purpose& a test /as de#eloped in /hich )1

sujects heard an inter#al& and after + seconds of silence /ere played three options from

/hich they had to select the ori'inal inter#al0 The sound samples composin' each tar'et

inter#al& had one control and three de'rees of timral modification0 %uch modifications

consisted in alterin' the ori'inal partial structure of the sound samples0 %pectral

Modellin' and Additi#e %ynthesis techni2ues /ere used to reali!e these modifications0

Results su''est that is possile to enhance or impair the aility of e3tractin' cues for

memori!in' inter#als y alterin' timral structure0


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Synthesis.................................................................................................35

105010)Apparatus000000000000000000000000000000000000000000000000000000000000000000000000000000000000075

10507 =rocedure0000000000000000000000000000000000000000000000000000000000000000000000000000000000000007)

10508 Results00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007)10) Discussion0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007

10)05 Adaptaility000000000000000000000000000000000000000000000000000000000000000000000000000000000007.

10)0) Timre descriptors00000000000000000000000000000000000000000000000000000000000000000000000008*

- !oncl$sions%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%.&

References..............................................................................................................59

Appendix A. Instructive of the experiment............................................................67

Appendix B. Questionnaire....................................................................................68

In#e/ of Ill$strations

Fi'ure 50 Representation of sensory dissonance y =lompt > Le#elt000000000000000000000000000)5Fi'ure )0 Rou'hness and ratios00000000000000000000000000000000000000000000000000000000000000000000000000000000000000))

Fi'ure 10 63ample of dissonance cur#e computed /ith %ethares( al'orithm0000000000000000)1

Fi'ure 70 Desi'n of the e3periment0000000000000000000000000000000000000000000000000000000000000000000000000000000);

Fi'ure 80 Minima hits from +1 dissonance cur#es0000000000000000000000000000000000000000000000000000000001)

Fi'ure 0 Mean dissonance cur#e for a set of +1 different timres000000000000000000000000000000011

Fi'ure +0 Representation of timre in relation /ith the steps of different scales00000000001+

Fi'ure .0 63ample of adjustment of timral structure0000000000000000000000000000000000000000000000000001.

Fi'ure ;0 %ynthesis types000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007*

Fi'ure 5*0 Appearance of the e3perimental interface000000000000000000000000000000000000000000000000000075

Fi'ure 550 Accuracy per inter#al00000000000000000000000000000000000000000000000000000000000000000000000000000000000077

Fi'ure 5)0 Accuracy per %ynthesis Type0000000000000000000000000000000000000000000000000000000000000000000000078

Fi'ure 510 Accuracy per "nstrument Type0000000000000000000000000000000000000000000000000000000000000000000007

Fi'ure 570 Tendency of responses 0000000000000000000000000000000000000000000000000000000000000000000000000000000007+


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Fi'ure 580 Histo'ram of responses000000000000000000000000000000000000000000000000000000000000000000000000000000007+

Fi'ure 50 Adaptaility per inter#al00000000000000000000000000000000000000000000000000000000000000000000000000000007;

Fi'ure 5+0 $#erall Adaptaility00000000000000000000000000000000000000000000000000000000000000000000000000000000000008*

Fi'ure 5.0 $ne-/ay A,$?A et/een timres of t/o synthesis 'roups (ad( > (s2(000 00085

Fi'ure 5;0 $ne-/ay A,$?A et/een timres of t/o synthesis 'roups& t/o data sets81

Fi'ure )*0 9orrelation et/een eha#ioural and acoustical data000000000000000000000000000000000087

Fi'ure )50 %catter plots of rele#ant timral descriptors and eha#ioural data0000000000000088

In#e/ of Tables an# 0orm$las

Table 1. Convergence of ratios from different sources..................................................22

Table 2. Tabulated frequencies for interval selection....................................................34

Table 3. Example of selection of candidates..................................................................36

Table 4. Different combination of subsets to test syntheses type with one-way ANOVA

.........................................................................................................................................45

Formula 1. Computation of ratios for a 12 tone equally tempered system............ ........20

Formula 2. Relation of partials and steps of a scale......................................................36


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" Intro#$ction

This /ork has een inspired y the need for hard e#idence o#er the effecti#eness

of traditional practices in music education& in the area of ear trainin' /ithin /estern

culture0 Althou'h the solution for this prolem is o#iously far more comple3 than the

approach that can e co#ered in a sin'le thesis like this& an atomistic approach makes

possile to focus the prolem on the concept of timre and the memory for it0

The concept of timre encloses more 2uestions than ans/ers for the time ein'&

proaly ecause the disentan'lement of its perceptual characteristics in a systematic

2uantitati#e form is a fairly recent /ork0 The modern conception of timre has a

predecessor 'estated durin' the French 6nli'htenment at the hands of @ean =hillipe

Rameau& /ho predicted the e3istence of music uni#ersals in the inner structure of a

sin'le tone0 ,e#ertheless& the possiility to otain some scientific proof for that

conception came some years later as the result of the influence that pro#oked the /ork

of personalities like Fourier& Helmholt!& and rey& amon' others B/hom are not

mentioned here ecause the intention is to estalish a rief chain of ideas and not doin'

an e3hausti#e historical re#ie/C0

,o/adays in the analysis of timre it can e said that /e ha#e t/o main ranches in the

academic production& one is the approach that uses a #eral description for the soundin'

2ualities of a 'i#en timre& and the second consists in computin' a numerical

description for it0 The first option is the most common used amon' musicians and non-

musicians& and the second is the outcome of research in an area denominated Music"nformation Retrie#al0 This former ranch pro#ides the niche in /hich this /ork /ould

rest& since /e are interested in searchin' ojecti#e uni#ersals more than particular

differences amon' indi#iduals or 'roups0

6ar trainin' is a #ery important acti#ity of formal musical trainin' in /hich asic skills

of music literacy are de#eloped& for e3ample the necessary ailities for readin':/ritin'

music0


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minimal construction locks and creatin' a ta3onomy for its physical characteristics0


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The main strate'y consisted in sutractin' the tar'et inter#als from the timral structure

of the tones& ut the entire process is e3plained in detail in section 10501050

The te3t is di#ided mainly in t/o parts& ein' the first the theoretical frame/ork /hich

pro#ides a 'eneral o#er#ie/ and in some cases a plain summary of some /orks related

/ith music education& timre and memory0 The second is a ri'orous empirical

approach& /hich e3plains step y step the e3periment done for this /ork& from the

desi'n& participants and materials to the procedure& results and discussion0


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' Theoretical consi#erations

A sustantial amount of academic production in music analysis is focused in

/ritten music& and most musicolo'ists /ould a'ree that the in#ention of a set of

symols to code music represented the most important ad#ance in the history of /estern

music0 "t allo/ed the rapid e#olution of music ecause the separation of human and

epistemic ojects BGent > =ople& )**C0 ,e#ertheless& that code has also a disad#anta'e&

ecause it is just a 'ross representation of the actual sound itself0

The un#eilin' of structure and form is the outcome of analysis& therefore is 'enerally

admitted that music structure relies on rhythm& pitch and timre0 $ther cate'ories can

e considered as the result of the comination of these three features& as it is the case for

melody and harmony0

The set of symols /ritten in a score fitted #ery /ell to study the co'niti#e processes

in#ol#ed in music in terms of rhythm and pitch& ut unfortunately that /as not the case

for music outside those symols& for e3ample the music that makes use of timre as the

main aesthetic resource BFales& )**)& p08+C0

%i'nal processin' technolo'y is related from its semantic ori'in to communication and

codification0 This technolo'y can e seen as a ne/ /ay to represent sounds in a more

accurate /ay& for instance& it is possile to #isuali!e timre chan'es as a function of

time& /hich has permitted speculation aout music structure focusin' on timre features

B


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trainin' relies on the fact that it is not the ear that it is actually trained& ut the co'niti#e

schema /hich takes the form of an ima'e in the rain of each indi#idual0 Thus to train

the ear can e e3plained as the impro#ement of precision in music ima'ery /ithin a

particular tonal schema& ecause efore readin'& /ritin'& performin' or analysin' music

one has to make an ima'e of it in the mind B=itt > 9ro/der& 5;;) ordon& 5;;+C0

The perception of different timres must lead to the ac2uisition of different ima'es& ut

is there a set of characteristics in timre that can imprint in mind etter than others 9an

/e find a 'ood set of timres to impro#e the ear trainin' "s timre a rele#ant feature in

the optimi!ation of learnin' music "s there any especially commendale instrument to

teach the most asic aspects of tonal schema

Althou'h research in musical timre has a relati#ely short history& there is crescent

empirical e#idence of its rele#ance for the perception of music0 "n traditional music

education in the /estern culture& the most closely related topic to the study of timre

can e found in the courses of orchestration& ut the approach is ounded to its aesthetic

ori'ins& /hich undoutedly is the result of many years of e#olution in seekin' for

functionality for the senses BHelmholt!& 5;87C0 ,e#ertheless that ar'ued functionalityhas een reached throu'h unconscious processes& and the stress in peda'o'ical

applications has een left unattended0 There are of course e3emplar efforts like the

/ork of @a2ues-Dalcro!e& 4odIly& and $rff& /hom specified in their peda'o'ical

methodolo'ies the timres to e used in the early sta'es of musical de#elopment

B9hoksy& Aramson& illespie&


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cate'ories accordin' /ith the span of retention of percei#ed phenomena0 These three

cate'ories are not isolated locks of processin'& instead& they actually /ork to'ether at

any 'i#en instant& and this interaction recei#es the name of /orkin' memory0 The first

cate'ory is the echoic memory& and it is related /ith e#ents happenin' in no more than

fe/ seconds0 The second is referred to as short-term memory and studies the

phenomena happenin' after the echoic memory and /ithin a time span of appro3imately

. seconds0 And the third is the lon'-term memory& /hich can e considered the most

stale ecause the 2ualities of the information it Kretains& that can e reconstruction of

e#ents that had happen in the past eyond the domain of short-term memory& or

conditions that had een rehearsed se#eral times0 Lon'-term memory is also related

/ith the idea of schema& /hich is a kind of superior learnin' controllin' the perception

of ne/ phenomena BLeman& 5;;8 %nyder& )***C0

2.1 Music education

Learnin' has t/o sides one is the iolo'ical fact of 'enetic herita'e& and the

other has to e /ith the sophistication of strate'ies to take ad#anta'e of that 'eneticherita'e0 Music has these t/o sides /hen it is learned B=apouek& )**1C& and for that

reason there is no need to recei#e any special instruction to understand music& althou'h

in order to communicate particular /ays to or'ani!e sounds /e actually do0

"n /estern culture for e3ample& the de'ree of systemati!ation of music has e#ol#ed in

schools speciali!ed in the teachin' of music& and music education is suject to certain

con#entions depicted in the contents of the curricula and in the role of music and

musicians in e#ery society0 Ho/e#er& amon' the o#ious differences et/een each

society& one idea has een preser#ed since the foundations of /estern cultureE not all the

indi#iduals in the society are supposed to ecome producers of music& therefore& it can

e e3pected that amon' the three main musical acti#ities composition& performance and

analysis B9hoksy& Aramson& illespie&


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4olosick

method B)**8C& use a recorded piano to play the e3ercises0 Also recent #ersions of

soft/are dedicated to ear trainin' use synthetic sounds reproduced /ith a M"D" capale

de#ice& for instanceEar Master 5B)**+C0 Gut a'ain& the documentation related /ith the

2ualities of sound source or timre is poor or une3istent0

As stated y %looda B)**8C& ear trainin' is an area in /hich teachers are used to


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discuss Nde#elopin' a 'ood earO& althou'h from the scientific point of #ie/ most

peoples ears function e3cellently& and there is nothin' one can do to enhance their

functionin'0 The idea is to find out /hat needs to happen in the rain to produce the

eha#iour that musicians /ould associate /ith a N'ood earO Bp05+C0 For that effect& the

music learnin' theory de#eloped y 6d/in 60 ordon B5;;+C fits #ery /ell in his ook

entitled Learnin' %e2uences in Music the main focus of attention is in the concept of

audiation0 ordon e3plains that audiation happens /hen /e assimilate music that /e

ha#e heard or performed& and also /hen /e assimilate and comprehend in our minds the

music that comes from a symolic representation of it Bp07C throu'h this description of

the concept it is easy to understand that the term audiation refers the same phenomena

that 9ro/der > =itt B5;;)C descried as Nima'ery in musicO0 They attract the /ork of

He B9oncernin' "ma'ery& 5;.C to e3plain that Nima'ery representation is the

acti#ation of the same central neural systems that played a role in the ori'inal e#ent& ut

this time in the asence of the ori'inal sensory acti#ityO Bp01*C0 "ma'ery is linked to

perception& and in the particular case of timre it has demonstrated a hi'h correlation y

usin' eha#ioural and neural data BHalpern& atorre& Gouffard > @ohnson& )**7C0

'%"%' Intervals

The plain definition of a musical inter#al is referred as the distance et/een t/o

tones& ut this definition rin's some comple3ities if one think aout the perceptual

meanin' of a distance in the /orld of sounds& and e#en more if /e in#ol#e the nature of

a tone0 %o in order to disentan'le a functional definition of inter#al that /ould e useful

for the present project it ecomes necessary to rin' the concept of pitch as a

Nmorphoporic mediumO B%hepard& )**5C0 Gy usin' this concept& and just as e3emplified

y %hepard& it can e ar'ued that the specific #isual idea /e ha#e of a trian'le does not

chan'e if this trian'le chan'es its position in space /hich implies that #isual space is

also a morphoporic medium0 "n the same sense& the percei#ed pitch space has

morphophoric 2ualities in a manner that ideas of auditi#e forms& such as the trian'le&

can e sketched0 Furthermore& melodies could e re'arded as those forms& as could e

scales& /hich from a reductionist point of #ie/& are nothin' else than sets of inter#als0

"n this thesis& the aim is to in#esti'ate ho/ different timres affect the memori!ation of


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inter#als& so it is useful to think aout inter#als as sound units /ith particular

morpholo'ical characteristics0

The most rele#ant issue in the perception of inter#als is related /ith the re-co'nition of

patterns& ut ho/ this phenomena takes place in#ol#es a physiolo'ical system and its

capailities0 A tone in a musical conte3t outside the controlled en#ironment of a

laoratory& should e concei#ed as the sum of multiple pitches& /hich e3cite the

hearin' system in a manner that makes it to con#ey an analysis of such pitches& as /ell

as a reduction of them into a sin'le most salient feature kno/n as pitch0 Further

e3planations on ho/ this analysis > reduction takes place had re#ealed that many areas

on the physiolo'ical and neurolo'ical domain are in#ol#ed& and these had een

e3tensi#ely studied durin' the past )* years BGurns& 5;;;C0 For instance& it is kno/n

that humans are ale to discriminate appro3imately 5&7** different fre2uencies& in

discrimination tasks that in#ol#e the comparison of sounds at t/o fre2uencies in

immediate succession BHandel& 5;.;C0

Accordin' to the model descried y Deutsch B5;;;C& pitch is only one sudi#ision of

the ar'ued analysis reali!ed y the hearin' system& /hich is processed and stored inparallel areas /ith inter#al si!e and timre& amon' other patterns like loudness and

duration0 Furthermore& it is e3pected that these ar'ued sudi#isions ha#e interaction

et/een them in fact some e#idence su''est that the perception of inter#al si!e tend to

e distorted dependin' on timral #ariations B


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chan'ed too much in nearly )** years althou'h the former includes a note /hich makes

an e3plicit reference to the spectrum of the sound& the similarities consist in that oth

descrie /hat timre is not& rather than postulatin' ojecti#e facts aout /hat timre

actually is0 Another 'roup of pulications correspond to those 2uoted y Huron B)**5C

as theoretical approaches& in reference to the /ork of %la/son B5;.8C and McAdams

B5;;8C)0 %chaeffer(s Trait des objets musicaux B5;.C could also e considered as an

antecedent of this 'roup althou'h his /ork could e descried in 'eneral terms as a

ta3onomical approach created for music peda'o'y purposes0 A third 'roup constitutes

perhaps a foundation in the field of music co'nition due the disco#erin' of a

multidimensional perceptual space for timre Brey& 5;++

Toi#iainen B)**+C& /hom had een de#elopin' a computational approach that can e

re'arded as a compendium of 2uantitati#e timre descriptors& /hich are taken from the

/ork of many researches in the area of music co'nition0 The nature of the tool makes

possile the processin' of a sound y modules that emulate the physiolo'ical and

neurolo'ical particularities of the human auditory system& thus pro#idin' an accurate

idea of ho/ the sound is Nmakin' senseO to the rain0 These descriptors could ha#e any

#eral laels ut their 2uantifiale result makes them e3cellent in terms of reliaility

ecause the measurement /ill al/ays e the same for a particular sound sample0 These

measurements represent the est solution to make connections et/een data e3tracted

from an audio si'nal and eha#ioural or neural data 'athered from people& ecause they

pro#ide 2uantifiale 'round to formulate statistical inferences0


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'%'%" Timbre an# scales

'%'%"%" S+ectral sha+e

To concede that timre can e computed from a sound si'nal implies that /e

posses a special /ay to represent the sound phenomena /hich is useful& amon' other

thin's& to apply different forms of analysis on it0 This representation also kno/n as

di'ital sound is essentially an arran'ement of inary ciphers encodin' a sound /a#e0

Althou'h there is a standard principle& /hich consists in encodin' the situation of a

'roup of particles in small portions of time and space& there has een a considerale

increment in the amount of mathematical al'orithms that seek to achie#e this principle

in a more efficient /ay0

Gy ha#in' a representation of a sound /a#e in a i dimensional form& /e can fi'ure out

that the /ider the /a#e means more displacement of particles and so more ener'y 1& and

the amount of repetitions of a /a#e in a fi3ed time span is related /ith the fre2uency of

that sound Bor pitchC0 Gut this analysis of periodicities of a /a#e only /orks in an ideal

scenario& ecause the truth of music relies in the comple3ity of its /a#es& in such a /ay

that if /e /ant to 'o eyond the superficial kno/led'e aout #olume or pitch& it

ecomes necessary a more detailed analysis& one that perhaps y lookin' for

periodicities in the superficial periodicities /ould re#eal a three or multidimensional

form to represent the sound0 This prolem of decomposin' a comple3 /a#e into the

sum of its simpler components /as sol#ed y @ean-Gaptiste @oseph Fourier B5+.-

5.1*C& and this decomposition applied to sound is kno/n as spectral analysis0

"n a detailed analysis of the spectrum of a sound& it can e oser#ed that there are

certain components that has more po/er than others& such components are referred as

principal components of the spectrum& and the distriution and differentiated po/er of

these components are uni2ue for each sound& ut some part of this components remain

unchan'ed in sounds that come from the same source& thus dra/in' a certain shape0

Timre could e re'arded as this non-#ariant shape dra/n y the principal components

in the spectrum0 "n other /ords& timre can e found in the spectrum of a sound ut this

3 or volume of particles displaced


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imply that the spectrum /ill not contain rele#ant information concernin' other 2ualities

of that sound& like pitch for e3ample0

This is actually a confirmation for the predictions of @ean =hillipe Rameau B5.1-5+7C&

/ho askedE N9an it really e that /e hear three sounds e#ery time /e hear oneO& in

relation to the spectral components he could hear& and se#eral of his collea'ues could

not0 $r it /as not the case that they /ould not really hear them ut as a matter of

perceptual 'roupin' they heard not the principal components& ut the timre itself

BFales& )**8C0

'%'%"%' !onsonance 2 3issonance

The special se'mentation done y Rameau made him suspicious aout the role

of those components for the entire harmonic system as it /as concei#ed at his time& and

the /ay the rules of composition had een settled alon' years of e#olution as a

conse2uence of constant e3perimentation in the 2uest for an aesthetic ideal0 This

disco#erin' made him and his successors to ha#e a ne/ consciousness aout the inner

structure of a sound& thou'h this could not e pro#en y scientific methodolo'ies until

the time of Helmholt! B5.)5-5.;7C0

"n his /ork Die Lehre von den Tonenmfindungen, Helmol!t estalished the

mechanical and physiolo'ical asis for the concepts of consonance:dissonance& y

analysin' the phenomena of soundin' t/o tones simultaneously& keepin' one at a fi3ed

fre2uency& and soundin' the second at different fre2uencies0 "n that /ay he claimed that

the difference et/een consonant and dissonant phenomena /as related /ith the

difference of their fre2uency& ut specifically /ith the sound produced y the

comination of the spectral shape of one tone /ith the spectral shape of the other if the

principal spectral components7 of one sound resemled the other under a certain

threshold B11 H!C& then the inter#al8 could e considered dissonant& and if this

resemlance /as outside this threshold& and additionally had a numerical relation close

to an inte'er then inter#al could e considered as consonant0 This /as later studied and

rectified later y =lomp > Le#elt B5;8C& /hom added that such threshold /as in fact a

4 also referred as overtones or partials.

5 see a definition in section 2.1.2.


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'%'%"%- Relations bet4een timbre5 consonance an# scale%

The concept of sensory consonance and dissonance is important to understandho/ timre is related /ith a musical scale& for instance the e3periment aout sensory

dissonance conduced y =lomp > Le#elt B5;8C& that used of a pair of sinusoidal /a#es

one at a fi3ed fre2uency and the second increasin' the fre2uency& thus dra/in' a cur#e

represented in fi'ure 50 "n this fi'ure it is possile to oser#e that the peak of

dissonance happens /hen the inter#al is close to the minor second& and then slo/ly

decreases0 "t can e also oser#ed a lael for the different sensations that are e#oked in

this kind of phenomenaE t/o sinusoidal that are #ery close in fre2uency /ill e heard as

eatin' each other& /hen the eatin' is too fast& then a ne/ sensation of rou'hness is

percei#ed& and /hen they are more distant& the rou'hness Bor dissonanceC disappears

and /e start to distin'uish t/o tones0

igure !" #epresentation of $ensory dissonance by %lompt & Levelt '$ethares, !((()"

Fi'ure 5 also informs that there are no harmonics present& meanin' that there are no

other components in the spectrum of this sound& so it can e ar'ued that this is a #ery

particular timre /hich mi'ht e difficult to find in a musical conte3t0 %o /e /ould

like to kno/ /hat /ould happen if the e3perimental tones are not simple sinusoidals&

ut more comple3 tones& for instance a tone composed of si3 main spectral components

/hich are inte'er multiples of the fundamental fre2uency B)8* H!0C the 'raphical

representation of sensory dissonance for that e3periment also run y =lompt > Le#elt is

sho/n in fi'ure )0 Here the line of reference in the hori!ontal plane is not the 5) tone


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e2ually tempered scale& ut the fre2uency #alues& and an e3tra information is pro#ided

in the points of minima of the cur#e that indicate ratios of fre2uencies0

igure *" #oughness and ratios 'adapted from $ethares, !((()

These ratios are coincident also /ith an old musical scale calculated y =ytha'oras

B8.* - 8** G9C& and /hich are also coincident /ith some of the steps of the 5) tone

e2ually tempered0 "n Tale 5& these #alues are taulated to illustrate this coincidences0

Table !" +onvergence of ratios from different sources"

%ethares B5;;;C pro#ides an al'orithm to compute a cur#e of perceptual dissonance

from a sound si'nal& so it is e3pected that from this approach most of the components of

the spectral shape are included in the computation B%ee fi'ure 1C& thus pro#idin' a etter

accuracy in terms of the relation that a particular timre /ould ha#e /ith a scale0 "n this

cur#es of perceptual dissonance& /hich %ethares calls just dissonance cur#es& the same

principle of fi'ure ) can e applied& /ith the difference that the e3act #alues from the

minima points can e otained ecause they are estimated throu'h an al'orithm0 Fi'ure

1 sho/s in thexa3is the fre2uency ratios& and the 'rid in the ack'round sho/s the

position of the inter#als of the 5) tone e2ually tempered scale0 The numerical #alues in

theya3is are aritrary& ut the idea is to sho/ a measure for the percei#ed dissonance0

Musical NamesUnison just fifth octave

1 1.06 1.12 1.19 1.26 1.33 1.41 1.5 1.59 1.68 1.78 1.89 21 1.2 1.25 1.33 1.5 1.67 2

1:1 5:6 4:5 3:4 2:3 5:3 1:2

minorsecond

majorsecond

minorthird

majorthird

justfourth tritone

minorsixth

majorsixth

minorseventh

majorseventh

12 - tet

Pythagoreanratios


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igure " Example of dissonance curve computed -ith $ethares. algorithm

This e#idence su''ests that in the e#olution of scales from the pure aesthetic

perspecti#e& it has een al/ays an intuiti#e and perhaps unconscious influence rou'ht

y the physiolo'ical attriutes of the auditory system0 Gy manipulatin' dissonance

cur#es /ith different settin's it is possile to understand that dissonance:consonance is

only one approach of many possiles& in fact in section 10501050 a numerical approachused for our e3periment is e3plained0 The relations that can e estalished et/een

timre and scales are infinite& ut depend stron'ly in the le#el of resolution y

considerin' only fe/ components of the spectral shape& /e 'et only fe/ sudi#isions of

the octa#e& ut if our le#el of resolution is hi'h and /e use in the computation each

salient periodicity found in the spectrum of a 'i#en timre& the numer of consonant

points increases dramatically0 This mi'ht e 'ood reason for ans/erin' /hy there is a

sustantial amount of musical scales in the /orld& ecause the le#el of resolution for

e#ery culture is different& and perhaps this resolution is related /ith other areas of

auditory perception as for e3ample those related /ith human speech sounds B%ch/art!&

Ho/e& =ur#es& )**1C0


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2.3 Memory

'%)%" three sta1es in one

"n this section is riefly re#ie/ed a three sta'es model presented y Go %nyder

B)**5C in his ook entitled NMusic and MemoryO0 This model di#ides the memory in

three main sections accordin' to their capailities to process information /ithin certain

time span0 These are the sensory& short-term and lon'-term memory0 This ta3onomical

approach does not imply that the rain is actually processin' information in three

different parts& ut rather those three con#er'e in one referred as /orkin' memory0

'%)%"%" Sensor6 memor6

"n the sensory memory Balso called the echoic memoryC& the auditory

information is or'ani!ed in a #ery asic /ay0 The input consists of impulses from ner#e

cells produced in the ear and each of the Kfeatures like pitch and spectrum is e3tracted

y a 'roup of neurons that are speciali!ed in a iolo'ically si'nificant form to respond

to that particular specific feature0 These e3tractors may e estalished 'enetically

ecause they appear to e innate and no learned or different for different species0

%ensory memory is the most asic kind of auditory cate'orical perception B6#ans&

5;.)C0

At this point the information ecomes cate'orical& /hich means that it is no lon'er a

continuous sensory representation0 An auditory e#ent is a asic form of association& and

it occurs /hen particular features occur to'ether& for e3ample the perception of a note

duration& timre and pitch0 "n the echoic memory some asic non-#eral representation

Bima'in'C happens& and also the matchin' of lon'-term memory content to current

perceptual e3perience called pattern reco'nition0 Haituation is a special form of

reco'nition that occurs at a less conscious a/areness le#el0 "t is a phenomena that

makes the output of the neurons less acti#e o#er time& /hen their input is repeatedly an

identical stimulus B%nyder& )**5& p0 )7C0 This decreasin' of acti#ity is also called

adaptation response in other /ords& if a the same impulse like an amient noise is


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25

repeated o#er and o#er a'ain& it is unlikely that e#ery ne3t repetition attracts our

attention0

'%)%"%' Short7term memor6

%hort-term memory lasts from three to fi#e seconds on a#era'e& dependin' on

the no#elty and comple3ity of the material to e rememered0 "t differs from the lon'-

term memory in that does not cause permanent anatomical or chemical chan'es in the

connections et/een neurons0 "t is a type of memory process /hit a certain de'ree of

speciali!ation& so there is proaly more than one short-term memory& for instanceE for

lan'ua'e& for #isual oject reco'nition& spatial relations& non- lin'uistic sounds and

physical mo#ement Bp0 7+C0

%hort-term memory has a close link /ith t/o conceptsE rehearsal and chunkin'0

Rehearsal is necessary to maintain information temporarily as short-term memory& it is

also necessary to store information into lon'-term memory and is a consciousness

process& tou'h it can happen also in a less conscious /ay0 "n 'eneral terms& any

repetition of elements in a pattern of e3perience constitutes a kind of rehearsal0

9hunkin' refers to small 'roupin's Bof elementsC associated /ith each other and

capale of formin' hi'her le#el units it is the consolidation of small 'roups of

associated memory elements and leads to the creation of structured hierarchies of

associations0 %hort-term memory is associated /ith the le#el of melodic and rhythmic

'roupin'& this is the le#el at /hich the Ulocal order of music is percei#ed Bp0 8)-8C0

This types of memory are our primary /ay of comprehendin' the time se2uences ofe#ents in our e3perience& althou'h the capacity if this memory is #ery small +V)

elements /ith conscious rehearsal& 1 or 7 elements /ithout conscious rehearsal& )8

elements /ith repetition patterns that fit time limits of short-term memory0 "n terms of

time span& it #aries from 1 to 8 seconds to 5* to 5)& dependin' on the type of

information Bp0 8*C0


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'%)%"%) Lon17term memor6

Lon'-term memory mana'es patterns and relationships et/een e#ents on atime scale lar'er than 1 to 8 seconds0 Memories need to e unconscious in order to

lea#e room for the notion of present& they are thou'hts that are formed /hen repeated

stimulation chan'es the stren'th of connections et/een simultaneously acti#ated

neurons0 The connections et/een 'roups of simultaneously acti#ated neurons are

called associations& and this process is referred to as cuein'0 There are three types of

cuein'E recollection /hen /e intentionally try to cue a memory remindin' /here an

e#ent in the en#ironment automatically cues an associated memory of somethin' else

and reco'nition& /here an e#ent in the en#ironment automatically acts as its o/n cue0

Lon'-term memory is not at all static& ut hi'hly dynamic0 The creation of lon'-term

memories is often refereed to as Ncodin'O& rememerin' is a process of reconstruction

rather than reproduction Bp0 ;-+5C0

'%)%"%- 8or9in1 memor6

The process in /hich semi-acti#ated lon'-term memory ecomes hi'hly

acti#ated and conscious& and short-term memory fadin' in from perception and out Bto

prime ne/ memory associationsC is called /orkin' memory0 The conceptual difference

consists in& /hile short-term memory can e understood as stora'e& /orkin' memory

must e considered as a process0


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27

aspects of the spectral shape had een altered BGer'er& 5;7C& and also /hen the

e3perimental task demands the reco'nition of timre under different conte3tual

situations B4rumhansl& 5;;)C0

$ther approach that seems #ery promisin' to study the effects of timre on memory& is

the neurolo'ical& ecause it has pro#ided e#idence of auditory cortical enhancement as a

possile result of trainin' /ith an specific instrumental timre B=ante#& Roerts& %chul!&

6n'elien& Ross& )**5C& and plastic chan'es in the auditory corte3 in fre2uency

discrimination e3periments B=ante#&


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) *m+irical a++roach

This chapter contains a detailed description of the different sta'es in /hich this project

/as in#ol#ed to/ards the 'atherin' of data and the conse2uent testin' of statistical

inferences related to the prolem of the effects of timre on the recallin' of microtonal

inter#als0

3.1 Method

)%"%" 3esi1n

The desi'n is oriented to/ards the comparison of performance in memori!in'-recallin'

inter#als played /ith different timres& so it can e descried as a Repeated Measures

desi'n& /here the independent #ariales are %ynthesis type& "nstrument name and

"nter#al len'th& and the dependent #ariale is the de'ree of accuracy in recallin' a 'i#en

inter#al performed y a suject& measured in numer of errors0 The main test in#ol#es

analysis of #ariance of different 'roups of timral characteristics and ori'ins& ut in the

otained data is also possile to oser#e the tendency of the response& and to speculate

aout a possile learnin' function0 The decision of studyin' timre effects y askin'

sujects to focus on another task& /as made /ith the intention of estalishin' an

homo'eneous status in the /ay /orkin' memory is controllin' the attention amon' all

sujects BHall > Glasko& )**8C0

"n fi'ure 7& there is a 'raphical e3planation of ho/ is desi'ned the e3periment0 "n the

lo/er left corner of the fi'ure& there is a s2uare se'mented in )* parts& each little s2uare

represents a sound sample /ith t/o uni2ue 2ualitiesE one instrumental ori'in and one

type of timral modification B8 "nstrument types and 1 %ynthesis types plus no

modificationC0 The ri'ht side of this dia'ram sho/s three shaded ack'rounds laelled

as Gase Fre2uency& Tar'et& and %econd > third choice& /hich purpose is to illustrate that

there are three inter#als per trial& one that is made et/een the ase fre2uency and the

tar'et& and the other t/o et/een the ase fre2uency and the second and third choice0


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29

"nside of these shaded areas there are s2uares similar to the one that is in the lo/er left

corner of the fi'ure& ut they are marked /ith numers that represent the tunin' of each

little s2uare0 %o for e3ample each little s2uare of the ase fre2uency is tuned at

)501H!0& and )* of the * little samples of the area shaded as tar'et are tuned at

)501 H!0 plus 18* cents& other )* at )501 H! plus 88* cents& and the rest at )501

H!0 plus +8* cents0 The same lo'ics apply for the second > third choice area& in such a

/ay that there are )** different samples each one /ith a uni2ue 2uality0 The top left

area presents a summary of this0

igure /" Design of the experiment

)%"%' Partici+ants

A total of )1 sujects /ere recruited y three methodsE postin' in e-mail lists&

attachin' a paper to notice oards& and personal in#itations0 T/o tar'et 'roups /ere

considered durin' the composition of the in#itations& one /as the 'eneral pulic and it

depicted the rele#ance of hearin' skills in the appreciation of music& and the second /as

directed to musicians& in /hich /e formulated a delierate challen'e for the indi#iduals

ear trainin' ailities0 The case of the #eral in#itations included also a short

e3planation aout the test0 "n 'eneral terms& sujects /ere not informed aout the main

#ariale to e studied& /hich /as the timre instead of that the test /as presented as apitch discrimination e3ercise0


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30

There /ere . female and 58 males& /ith mean a'e of a'es et/een )* and 7* years old

BMean ).0& %D 80)C0 They /ere asked to fill a 2uestionnaire after the e3periment

/hose purpose /as to collect information aout their musical ack'round and haits0

)%"%) Materials

)%"%)%" Stim$li

The desi'n of the stimuli in#ol#ed t/o main processesE selection:discrimination

of collections and samples& and analysis:synthesis0

Selection

For the selection of samples three sources /ere analysedE NMcill Qni#ersity

Master %amples )0*O B$polko >


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3iscrimination

For the discrimination of instrumental sets& the criterion /as first to find all

instrumental sets containin' the 51 samples of the central octa#e& M"D" *-+) B97-98C0

"n second place and /ith the aid of M"RToolo3 BLartillot > Toi#iainen& )**+C a script

/as de#eloped in Matla /hich /e called NAnta'onist FinderO0 This script /as aimed

to analyse the samples& y computin' a 'eneral description of them& like duration&

amplitude and timral #alues0 This script helped to discriminate those samples that

/ere not /ell processed y the toolo3 ecause of particular comple3ities contained in

their structure0 For e3ample all the instrumental sets containin' samples /hose pitch

/ere under or ao#e estimated for more than a 5*P of error y the NmirpitchO al'orithm

Busin' default optionsC& /ere discarded0 Gy doin' this& the ojecti#e /as to find

realistic sounds /hich could e easily treated in posterior processin'0 Another strate'y

included in the NAnta'onist FinderO consisted in comparisons of specific timral

descriptors& to disco#er instruments /hose #alues are in the lo/er or hi'her ends of a

comparison tale0 For e3ample& in the initial sta'es of this project /e /ere particularly

interested in ri'htness& so y applyin' this strate'y on ri'htness& in a manner that a

pair of instrumental sets& one /ith a ri'ht sound 2uality and other /ith a dark sound2uality could e included in the final e3perimental set0 This searchin' of opposites /as

also used /ith other descriptors& such as inharmonicity and rou'hness0

At the end& only fi#e instrumental sets /ere includedE French Horn& Alto Flute and

Go/ed ?iraphone from the Mcill collection& an $oe from ,ati#e "nstruments and a

=iano from the Microsoft tale0 This final decision /as difficult to make& ecause /e

/ere lookin' for includin' at least one instrumental set per analysed collection& and

ecause for practical reasons in terms of duration of the e3periment& some timres that

had attracti#e and interestin' sounds had to e discarded0

nal6sis

"n his /ork& %ethares B5;;;C e3plains in detail a techni2ue to compute the ratios

of a ne/ scale that suits est to make music /ith etter consonance for a 'i#en timre0

"n the first part of this techni2ue is in#ol#ed the computation of the spectral shape of the

tar'et timre to e3tract the most rele#ant partials and its amplitudes0 Then& /ith that


32/68


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33

igure 1" Mean dissonance curve for a set of 0 different timbres

At this point& y ha#in' the inter#als from the Ndissonance cur#e scaleO& and y

assumin' that these collection of radios represented a 'eneric scale computed from a

psychoacoustic relation /ith timre& the ne3t step /as to select /hich of these ratios

/ould e a 'ood asset to test memory /ith them0 Gut in this intend /e learned that

dissonance cur#e scale /as just one approach and possily not the est& and ao#e all&

/e needed some strate'y to discard most of the inter#als& ecause other/ise the

duration of the e3periment /ould e too lon'& thus not acceptale to our needs0

Durin' this selection of inter#als& /e aimed to discard all the inter#als that /ere #ery

close to the traditional 5) tone e2ually tempered& under the rationale that this

information /as already in the memory of our sujects& ecause of their cultural

ack'round the intended task /ould demand from them the memori!ation of some

inter#al they /ere not really familiari!ed /ith0 $ther ojecti#e of this selection process&

/as to assure the inclusion of those inter#als that /ere actually present in the spectral

shape0 %o another strate'y /as used& /hich consisted in calculatin' the ratios from

adjacent partials y simple di#ision of their fre2uencies this strate'y resulted

prolematic ecause the resultin' ratios for a particular timre& /ere #ery different fromthe results for another& ne#ertheless three ratios appeared in a consistent form amon' the


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34

same +1 timres used for the estimation of the mean dissonance cur#e& and /ere

considered useful for our purpose0 Gut from this former strate'y& 'ettin' only three

ratios /as not really satisfactory& so /e decided to incorporate a third set of inter#als&

/hich had already ein' used in music ut in a not so common or popular matter0 Gy

e3plorin' the music and ideas of authors like 9harles "#es B5.+7-5;87C and @uliIn

9arrillo B5.+8-5;8C& amon' others& /e found that they had used a )7 tones e2ually

tempered scale& so this represented another set of inter#als /ith a hi'h de'ree of

ecolo'ical #alidity0


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35

"nitially& four inter#als /ere chosenE three ecause of its incidence on the three scales

and the fourth one ecause /e oser#ed its importance for the dissonance scale0 This

fourth one& /as the third most consonant ratio in the dissonance cur#e scale Bas can e

oser#ed in the fi'ure C& ut ecause of its closeness to the Major th from the 5) tone

e2ually tempered scale& it /as discarded0 Furthermore& as it can e oser#ed in the little

tale located in the central lo/er ed'e of tale ) headed as NTar'et inter#alsO& /hich

contains the a#era'e of coincident #alues& the M"D" #alues re#ealed that the three first

#alues are almost in the middle of an inte'er M"D" #alue& /hich means that if the

distance from one M"D" inte'er to the follo/in' is half tone in the 5) tone e2ually

tempered system& three of our tar'ets /ere really close to the 2uarter of tone and one

not0 Thus the final decision of tar'et inter#als /ere threeE 18* cents BM"D" 107;C&

88* cents BM"D"807C and +8* cents BM"D"+08)C0

A minor compromise must e declared& /hich consisted in the roundin' of this #alues to

one decimal in a manner that at the end the shorter inter#al in#ol#ed in this research

/ould e the 2uarter of tone of the 5) tone e2ually tempered system0

S6nthesis


36/68


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37

in the spectrum it could reach a ma3imum of 8** Bthis threshold is specified in the

function that con#erts peaks to tracks from the %MToolo3C0 At this point is /orth to

mention that early intends on this matter of modifyin' timre& /ere aimed at displacin'

partials from its ori'inal position to stretch them y chan'in' their main fre2uency0

The idea /as aandoned ecause the audile result /as too far from the ori'inal sample

in terms of 2uality0

$nce the list of candidates has een otained& it is possile to ha#e a representation of

the partial structure& /hich comined /ith the amplitude #alues leads to another

#isuali!ation of the relation et/een timre structure of a 'i#en sound and a particular

scale0 Fi'ure + illustrates this idea& as the structure of this sample of a o/ed

#iraphone tuned in 97)501H!0& sho/s that its timre is al/ays related /ith the first

tone of these three scales B5) tones e2ually tempered& dissonance cur#e scale and )7

tones e2ually temperedC& and in second place /ith some step in the middle& /hich is the

inter#al kno/n as perfect fifth or )E1 ratio0 The scale in the #ertical a3is is aritrary ut

it is the result of addin' the #alue of amplitude of each partial that had an almost inte'er

relation /ith a 'i#en step of a scale Bcalled candidates in the upper para'raphC 0 The

fact is that y usin' more sudi#isions in one scale& that resolution sho/s more detail in

terms of relations et/een components of the spectral shape and the precise steps of a

'i#en scale0 This matter of resolution /as riefly discussed at the end of the section

)0)05070

igure 0" #epresentation of timbre in relation -ith the steps of different scales


38/68


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39

NholesO at 8th& ;th and 51th steps& /hich correspond to the inter#als of 17;& 87 and +8)

cents of the scale e3tracted from the mean dissonance cur#e0

The final set is made of three different synthesis strate'ies plus the ori'inal sample&

/hich conform four sets of timres that in suse2uent sections /e refer as Nsynthesis

typeO #ariale0

All samples /ere e2uali!ed in loudness and con#erted from t/o to one channel& they

had a duration of 5)** ms and a linear en#elope for the first 5* ms0 and the last )**ms0&

/hich purpose is to take the amplitude from silence to the normali!ation le#el and then

ack0 For this processin' the soft/are named N%o3O y Ga'/ell B)**C /as used0

The dia'ram of fi'ure ;& is a 'raphical summary of /hat has een /ritten aout the

desi'n of the stimuli in terms of ho/ a sound si'nal has een transformed in its timral

domain0 "n this fi'ure there are t/o shaded areas in the ack'round that represent the

t/o principal processes in#ol#ed& one that is the analysis of the timral structure& and

the second represents the synthesis of the different types of #ariale0 Dra/n o#er these

t/o main areas there are darker shaded rectan'les& /hich represent sta'es of those

process& and the inner o3es contained in them refer to computational al'orithms0 The

arro/s sho/ the direction of the flo/in' of information in a manner that from a sound

sample there are three outputs manipulated and one that is preser#ed as a copy of the

ori'inal0 The ellipses containin' the e3pressions aBtC& fBtC and pBtC are there to indicate

the e3istence of three #ectorsE amplitude& fre2uency and phase& as a function of time&

respecti#ely0 The are#iations Ns2O& NadO& NaoO and NorO are used as laels to simplify

the entire analysis:synthesis process0 Ho/e#er& the rationale eyond Ns2O is that y

usin' spectral modellin' synthesis& a timral modification in#ol#in' :uarters of tone

has een applied meanin' that the partials numerically related /ith the steps .& 5) and

5th of a scale of )7 tones e2ually tempered& had een taken a/ay from the ori'inal

timral structure y lo/erin' to !ero the amplitudes of those specific partials0 The

are#iation NadO means that y usin' additi#e synthesis& a timral modification has

een done y usin' only those partials that are not related numerically /ith the steps 8&

; and 51th of the #issonance cur#e scale0 The are#iation NaoO means that the #ectors


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40

of amplitude and fre2uency of the ori'inal sample had een copied to e added as

sinusoidals0 The lael NorO refers to a simple copy of the ori'inal sample0

igure (" $ynthesis types

"n order to otain the tar'et inter#als from the ori'inal samples /e used an audio

processin' utility named N%oundstretchO y =ar#iainen B)**8C& on the samples that /ere

closest to the tar'et0 For e3ample to otain the M"D"B108C1)*0)7H!0 /e used

NsoundstretchO on the M"D"B1C155051H! and M"D"B7C1);01H!0 to transpose up or

do/n respecti#ely& then they /ere compared y ear and one of them /as discarded y a

criteria of sujecti#e Nest 2ualityO et/een oth and also y lookin' for timral

homo'eneity /ithin all the instrumental set0


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41

)%"%)%' ++arat$s

To 'ather the eha#ioural data a special patch /as desi'ned in the =ure Data'raphical pro'rammin' en#ironment B=uckette& )**C& runnin' on


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42

)%"%- Proce#$re

%ujects /ere asked to sit in front of a computer in a room desi'nated to make

#ideo conferences& /hich implies that the place has een conditioned to ha#e a relati#e

lo/ amient noise0 They /ere asked #erally if kne/ the meanin' of inter#al in a

musical conte3t& and if they do not& then recei#ed a rief e3planation aout it&

furthermore& they had to read an instructi#e Ba#ailale in Appendi3 AC& /hich purpose

/as to lo/er the possile an3iety& y in#ol#in' them in this e3perimental en#ironment

efore startin' the actual e3periment& and y 'i#in' also information in ad#ance aout

the proceedin'0

Durin' the e3periment& each e3ample inter#al /as follo/ed y other three /hich /ere

the selectale options0 There /as a silence et/een the presentation of the e3ample

inter#al and the three options of + seconds of duration0 6ach sound sample from the

dyad that formed the inter#als had a separation of 8* ms& and the separation et/een

one inter#al Bof the last threeC and the ne3t option /as +** ms0

The selectale inter#als /ere associated #isually to one 'reen circle that /as turned on

durin' the presentation of each option& to pinpoint an association to the o3 /here the

suject could make his:her choice0 The three options /ere al/ays presented #isually in

order from the left to the ri'ht& ut the audile reproduction /as in aleatory order& one

option /as a copy of the e3ample inter#al and the other t/o& /ere minus 8* cents or

plus 8* cents different from the tar'et0 %o& for instance& if the e3ample inter#al had a

measure of 18* cents& one of the options measured 18* cents& the second 7** cents& and

the third 1** cents 0 This #alues in cents represent al/ays a dyad /hich ase fre2uency

is 97M"D"B*C)501H!& for instance /hen /e refer 18* cents& the tones of theinter#al are M"D"B*C)501H!0 and M"D"B108C1)*0)7H!0

At the end of the e3periment& sujects /ere asked to fill a 2uestionnaire related /ith

their musical ack'round and 'eneral information as it is 'ender and a'e0

)%"%. Res$lts

9ollected data for each suject /as disposed in a matri3 of * ro/s 3 +


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43

columns& each ro/ contained the information for one trial& and the se#en columns /ere

dedicated as follo/sE the first three /ere used to record the characteristics of the

inter#als for the trial& in terms of its synthesis type& instrument name and inter#al len'th0

%ynthesis type could e one out of four options laelled asE (ad(& (ao(& (or( and (s2( Bthis is

e3plained in detail at the end of section 10501050C instrument type could e one out of

fi#e options& laelled asE (afltn(& (frhrn(& (ooek(& (pnomi( and (#ir(& /hich means alto

flute& french horn& ooe& piano and o/ed #iraphone respecti#ely Bfurther e3planation

aout this instrumental sources could e found at the e'innin' of section 1050105C and

inter#al len'th& /hich could e one out of three optionsE (18*(& (88*( or (+8*( cents0 The

fourth& fifth and si3th columns of each ro/ of the matri3& recorded the order of the

optional inter#al since they /ere al/ays presented randomly& so the numer * /as

desi'nated to the e3ample inter#al& the numer 5 to the e3ample inter#al de#iated y -8*

cents& and the numer ) to the e3ample inter#al de#iated y Y8* cents0 For e3ample if

columns fourth to si3 recorded the numers *& ) &5& that means that the first sample /as

the correct ans/er& the second /as the inter#al that /as one 2uarter of tone lon'er than

the e3ample inter#al& and the third one /as an inter#al shorter than the e3ample inter#al

for a 2uarter of tone0 The se#enth column recorded the option selected y the sujects&this numer /as one out of three Bfrom * to )C representin' the location of the ans/er&

thus indicatin' if the suject had selected the inter#al represented in the columns 7& 8 or

of the ro/0

"n a preliminary analysis of the data& four sujects scored out of the ran'e of the

inter2uartile& t/o of them elo/ the chance le#el and the other t/o ao#e the upper

decile0 Gecause of those reasons and in order to homo'eni!e the sample& those sujects

/ere considered as special cases and /ere discarded from the main sample0

The a#era'e accuracy for the main sample B5; sujectsC /as 808.P& sd570)5P0 A

si'nificant correlation et/een years of musical in#ol#ement and accuracy /as found

Br011) p Z 0**8C0 ,e#ertheless this /as the only si'nificant relation that could e

estalished et/een the accuracy in responses and the 2uestionnaire data Bthis

2uestionnaire can e found in Appendi3 G0C0

%ince our interest /as focused in learnin' aout possile differences et/een the main

independent #ariales& /e ran a series of one-/ay A,$?A tests per independent


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#ariale0 The case of the instrument type did not sho/ a si'nificant difference& ut in

the in the case of inter#al len'th FB)&8+C107+ p Z 0*8& This result su''ests that is easier

to memori!e short inter#als than lon' ones Bsee fi'ure 55C0

igure !!" ccuracy per interval length

The case of synthesis type in#ol#es the main test of the e3periment ecause the central

hypothesis of this project ar'ued that y alterin' the structure of timre& the

performance of memory /ould sho/ a difference reflected in an impaired or enhanced

capaility to rememer the len'th of particular melodic dyads0 This /as tested /ith

satisfactory results& ecause the #ariale contained t/o susets that had not chan'es in

their partial structure& in other /ords t/o of the four susets could e considered as

Ncontrol setsO& ecause they maintained the ori'inal partial structure and in the other t/o

the spectral content suffered a modification in the timre y discardin' those particular

partials that had a numerical relation /ith the tar'et inter#als0 This /as re#ealed /hen

/e calculated a one-/ay A,$?A et/een the four susetsE (ad(& (ao(& (or( and (s2(0 and

otained an FB1&8C)0)+ p*0*;*)& and then /hen the test /as ran for different

cominations0 Tale 7& sho/s these cominations and results0


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45

Table /" Different combination of subsets to test synthesis type -ith one6-ay 789

As sho/n in tale 7& the est proaility #alue /as otained /hen the comination (ad(&

(s2( /as tested FB5&).C0*1& p*0*)*80 This result /as someho/ surprisin' ecause /e

/ere con#inced that y remo#in' some partials from the timre structure& the

memori!ation of inter#als /ould e impaired& ut althou'h oth synthesis outputs (s2(and (ad( /ere aimed to/ards a remo#al of partials strate'y& one of them not only not

impaired the performance of memory ut on the contrary it enhanced the performance

in a si'nificant form /ith respect to the performance /ith the samples that preser#ed the

ori'inal partial structure0 The plot in fi'ure 5) sho/s means& #ariance and ma3imum

and minimum points for the results of accuracy of synthesis types0 Here is possile to

oser#e clearly that the means for the accuracy in the non-altered partial structures are

almost e2ual B(ao( and (or(C& /hile for those that had a modification in their timral

structure B(ad( and (s2(C sho/ different #alues0

igure !*" ccuracy per $ynthesis Type

ad or sq F p

, , 1-28 6.03 0.0205 , , 1-28 3.3 0.0800

, , , , 3-56 2.27 0.0902

, , 1-28 2.8 0.1054, , 1-28 1.1 0.3026, , 1-28 0.55 0.4664

, , 1-28 0.08 0.78

p / .05

ao df


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46

The ar 'raph in fi'ure 51& sho/s the accuracy per instrument type0 This is only for

illustrati#e purposes ecause as mentioned ao#e this #ariale did not sho/ any

si'nificant difference in the one-/ay A,$?A test0 ,ote that y a3is has a non-

continuous scale0

igure !" ccuracy per :nstrument Type

3.2 Discussion

The results reported at this point ha#e only ac2uainted the de'ree of accuracy in the

ans/ers0 ,e#ertheless in a second e3ploration of the data /e found that y attachin'

#alues to the cate'ories& /e could oser#e a tendency in the responses0 The #alues

attached /ere -5 to the ans/er that corresponded to the tar'et len'th minus 8* cents& a

!ero to the correct ans/er& and a Y5 to the inter#al that corresponded to the tar'et len'th

plus 8* cents0 "n that /ay /e could kno/ not only the a#era'e error& ut also the

tendency of the error0 Fi'ure 57 sho/s the responses per suject& each ar representsone suject0


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47

igure !/" Tendency of responses

Fi'ure 58 sho/s a clear asymmetry to/ards the shortest inter#al& that could e due the

direction of the inter#als used throu'hout the e3periment& /hich /as from the lo/er to

the hi'her pitch0 Another e3planation for this result could e addressed to the estalt

principle of pro3imity& /hich implies that shorter inter#als are etter processed than

lon'er inter#als BDeutsch& 5;;;C0

igure !5" ;istogram of responses

Furthermore& this tendency scale /as used to find differences et/een synthesis types&

and the results for one-/ay A,$?A /ere impro#ed if compared to the analysis of


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48

#ariance of only correct ans/ers BFB1&8C)0) p*0*8;+C0 Also y editin' manually

this data to remo#e outliers& the result chan'ed to sho/ an acceptale le#el of

si'nificance FB1&8C107 p*0*)1.0

Ho/e#er /e reali!ed this tendency data /as risky to formulate inferences& ecause it

contained emedded some randomness this effect /as due the desi'n of the interface to

'ather the data& ecause there /as no means of lea#in' any option lank0 Thus sujects

/ere oli'ated to make a choice& and as they declared #erally after their e3perience&

they sometimes had to make a choice they kne/ in full consciousness it /as a random

choice0 Also they declared that these choices had to e done like this ecause durin' the

memori!ation process they ecame distracted /ith en#ironmental noise or ecause they

/ondered ho/ lon' the e3periment /ould least0 Althou'h this approach of tendency

mi'ht represent an interestin' possiility to dra/ implications for our central

hypothesis& no further analysis /as carried out /ith it ecause /e considered that some

aspects of the interface ha#e to e impro#ed to make this measure useful0 For e3ample

like tryin' the same e3periment in a completely noise isolated room& or y addin' a

countdo/n of trials in the interface& and proaly a NlankO choice0

)%'%" #a+tabilit6

"n this section /e use the term NadaptailityO a term taken from the neurolo'ical

literature to refer to a function of learnin' as a result of repeated e3posure to a certain

impulse0 %ince this thesis is also inspired y searchin' for etter methodolo'ies in Near

trainin'O& it /as important to determine if people actually learned the inter#als after

ein' e3posed repeatedly to them0 %o /e accommodated the data in such a manner that

the correct responses per inter#al /ere summed 'i#in' the numer of times that a

particular inter#al /as played for all the sujects each inter#al /as repeated )* times0

There could not e found a si'nificant re'ression coefficient in any of the inter#als&

/hich /ould indicate that from the first to the last repetition there /ould e any

impro#ement& ne#ertheless the 'raphical results are sho/n in fi'ure 50


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49

igure !1 daptability per interval

Gut in any case a tendency is difficult to determine on #isuali!ations like the one in

fi'ure 50 ,e#ertheless if /e add all responses across inter#als and normali!e the scales

y di#idin' the #ectors y its standard de#iations& it is possile to oser#e a sli'htincrement in the correctness of the ans/ers as a slope in a linear function& /hich 'i#es a

standardi!ed re'ression coefficient of *0180 This procedure is dra/n in fi'ure 5+& /hich

also re#eals other interestin' information0 "f /e oser#e the form of this #ector of

Nlearnin'O& it can e found a couple of peaks durin' the second part of the repetitions

and then a descent in the a#era'e of accuracy0


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50

igure !0" 8verall daptability

)%'%' Timbre #escri+tors

"n section 105080 /e found some si'nificant differences in the eha#ioural data& /hen

the #ariances of the data 'rouped y inter#al len'th and synthesis type /ere tested0 %o

the ne3t step /as& y assumin' the certainty of those differences& to disentan'le their

ori'in despite of the methods follo/ed durin' the desi'n of the sound samples& /hich

passed for a presumed timral modification0

For that effect and /ith the aid of the M"Rtoolo3& 57 timre descriptors /ere

computed for each sound sample in#ol#ed in the e3perimentE !ero-cross& centroid&

ri'htness& spread& ske/ness& kurtosis& roll-of at ;8P& roll-of at .8P& entropy& flatness&

irre'ularity& lo/-ener'y& rou'hness& and inharmonicity0


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51

synthesis types& thus otainin' four sets of data of 8*357& representin' the timral

description in 57 measures for 'roups of 8* samples one 'roup for (ad(& other for (ao(&

one more for (or( and the last for (s2( Bfor reference on these laels see section 10505C0

$nce this 'roupin' /as done& the ne3t step consisted in computin' a series of one-/ay

A,$?As for pairs of descriptors& to re#eal /hich descriptor of timre /ere responsile

for the difference et/een 'roups0 %o for instance& the #ector resultin' from estimatin'

8* #alues for ri'htness in the samples contained in the 'roup (ad(& /as compared /ith

the #ector resultin' from the 8* #alues of (s2( thus otainin' the proailities of

differences and leadin' to the fi'ure 5.& /here those #alues can e oser#ed0

Hori!ontal a3is in fi'ure 5. sho/s are#iations for each one of the 57 descriptors

mentioned in the upper para'raph0

igure !3" 8ne6-ay 789 bet-een timbres of t-o synthesis groups .ad. & .s2.

"n fi'ure 5.& it can e oser#ed y #isual e3ploration that most of the 57 descriptors

sho/ed si'nificant difference et/een them& so this procedure pro#ided only a startin'

point ecause /e /ere lookin' for/ard to discriminate most of the descriptors as

possile candidates responsile of the effects on memory0 Althou'h different

cominations of synthesis 'roups /ere tested in the same /ay& they sho/ed the same

silhouette of ars& so /e decided to keep this comination B(ad( > (s2(C for further


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52

analysis ecause it had demonstrated the most meanin'ful difference in the eha#ioural

results Bp Z *0*)& see tale 7C0

Ackno/led'ed that there /ere meanin'ful statistical differences et/een particular

timral descriptors computed from sound samples /ith specific le#els of modification&

the follo/in' 'atherin' /as to learn if such modifications e3pressed in acoustical data&

had some relation /ith the responses 'i#en y the sujects in the e3periment0 To reali!e

this comparison& a simple correlation et/een the responses of the sujects and each

one of the descriptors /ould fit0 ,e#ertheless there /as one prolem& ecause the

matri3 of responses /as composed of * ro/s BtrialsC& and the #ectors of descriptors had

)** #alues& one per sample in#ol#ed in the e3periment0 To sol#e this prolem& the set of

)** samples 3 57 descriptors had to e reduced& so this method consisted in computin'

means for each timre measure amon' all the pitches that /ere in#ol#ed in one trial&

thus computin' means for 'roups of pitchesE M"D"B*C-B1C-B108C-B7C& M"D"B*C-

B8C-B808C-BC& and M"D"B*C-B+C-B+08C-B.C0 (s2( synthesis typesC of descriptors& ut /ith this set of *

#alues& and the results sho/ed almost the same pattern& e3cept for the spectral roll-off at

.8P and the spectral entropy0 Gy operatin' a reduction of this nature& /e interpret that

effects of pitch /ere also reduced& thus re#ealin' statistical differences et/een 'roups

sli'htly out of that dimension0

"n the left side of fi'ure 5; it can e oser#ed the same results of fi'ure 5.& ut /ith the

scale of the #ertical a3is offerin' a !oom0 The ri'ht side of the same fi'ure B5;C sho/s

the results of the same computation of A,$?As for the 'roups (ad(-(s2(& ut /ithin the

set of #alues that had een reduced to correlate /ith sujects responses0


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53

igure !(" 8ne6-ay 789 bet-een timbres of t-o synthesis groups, t-o data sets

An interestin' issue could e e3tracted from the matri3 of responses from the sujects&

ecause it had 1 columns containin' the numer of hits for estimations the first

contained the numer of responses that estimated the tar'et inter#al elo/ its actual fit&the second& the responses that /ere estimated correctly& and the third the responses that

estimated the inter#al ao#e the actual si!e0 %o /e could compute correlations of

timral descriptors not only for the correct ans/ers& ut also for the mistaken

estimations0 Fi'ure )* sho/s the results of these correlations in the upper part& and the

p-#alues in the lo/er part each descriptor is correlated /ith each #ector of responses&

one for the trials estimated elo/ the correct si!e of the inter#al& other for the correct

ans/er and the third one for the ans/ers that indicated an estimation ao#e the correct

si!e Bas e3plained in the section 10505 the inter#al si!es de#iate y 8* cents from the

tar'et inter#alC0 ,ote that in the lo/er 'raph a line has een dra/n to sho/ the line of

p*0*80


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54

igure *4" +orrelation bet-een behavioural and acoustical data

The results otained in the analysis of this section su''est that there are at least three

timral descriptors /hich #alues ha#e a si'nificant relation /ith the responses of the

sujects& and that are also present in the analysis of #ariances as responsile for the

differences et/een synthesis types0 %o far& the spectral centroid& the spectral spread&

and the spectral roll-off are present in oth 'atherin's0 %pectral flatness attracts also our

attention ecause it correlated hi'h in the responses that underestimated the si!e of the

inter#al0 These timral descriptors are presented in scatter plots in fi'ure )5& that also

sho/s the eha#ioural data 'rouped y synthesis types0


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55

igure *!" $catter plots of relevant timbral descriptors and behavioural data

%pectral centroid is a measure of percei#ed Nri'htnessO and represents the mean #alue

of the fre2uency distriution& the spectral spread is a measure of the #ariance of the

fre2uency distriution& roll-off is a measure of spectral shape and represent the

fre2uencies under /hich certain percenta'e of the spectral ener'y is distriuted

BAucouturier& )**C0 These three descriptors and their ne'ati#e correlation could e

interpreted as the most important cues for memori!ation of inter#als /here lo/er

#alues of any of them /ould lead to a etter performance in memory& ut such


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56

affirmation should e considered in a ne/ e3periment since too many #ariales are

in#ol#ed in this e3perimental set& and /ould e sources of statistical noise0

%pectral Flatness is defined as the radio of the 'eometric mean of the po/er spectrum to

the arithmetic mean of the po/er spectrum& and is a measure of NnoisinessO B@ohnston&

5;..C0 The hi'h correlation found in the under-estimation #ector /ould su''est that

hi'h le#els of noisiness measured /ith spectral flatness /ould proaly e a source of

memory impairment0 ,e#ertheless& more empirical e#idence is necessary to make such

a claim0


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57

- !oncl$sions

%ome of the results presented here are only partial and deser#e more attention

and further analysis0 For e3ample /e could not estalish a connection for the effects of

e#ery compromise& such as the decision to round the inter#als for the desi'n of the

e3periment that /as not applied durin' the analysis:synthesis of the stimuli this

disparity could e responsile of some distortion in the results0 Also the fact that

accuracy per instrument did not sho/ a si'nificant difference from 'roups of instrument

types could e e3plained as an inconsistency in the e3perimental desi'n due the lo/

numer of cases per instrument0 $ther e3planation could e that the timres selected

did not ha#e enou'h contrast in those timral aspects that resulted rele#ant for the cuin'

of memory for inter#als& thus su''estin' a failure in the discrimination sta'e&

particularly in the script that /as de#eloped for this purpose /hich /e called

NAnta'onist FinderO0 ,e#ertheless a positi#e aspect are the results otained for the

synthesis type #ariale& /hich could e re'arded as synthetic instruments& and their

timral characteristics /ere used to alance the other inconsistencies0 Althou'h thesesynthetic timres /ere chosen from a palette of at least 5* different methodolo'ies in an

almost aritrary /ay& just y e3plorin' #isually the spectro'rams of #ery fe/ samples&

they pro#ed to e useful in the timral descriptors analysis0

The e3perimental settin' had some aspects that must e impro#ed& such as a counter in

the patch& a properly sound isolated place& and the recruitment of more sujects0 $ther

thin' that could e impro#ed is the 2uestionnaire aout the musical ack'round& to

include information on other auditi#e ailities such as numer of spoken lan'ua'es0

The entire desi'n of this project is an intend to link the perspecti#es and concepts of a

traditional /estern academic minded musician /ith the conceptuali!ation of the nature

of music from a scientific perspecti#e& and the matter of this link has een the definition

of timre0 This effort represent in our understandin' a conceptual rid'e et/een a

macro and a micro perspecti#e of the nature of musicE a sin'le tone and the uni#erse

contained in it0


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A rele#ant issue e3plored in this project is that selection of timre to memori!e inter#als

should e considered carefully for music educators in ear trainin' e3ercises& ecause it

mi'ht e that certain timres /ould optimi!e the task0 Ho/e#er this su''estion must e

supported y more empirical e#idence ecause there are many #ariales that are not

considered& such as indi#idual preferences0

Future directions for this research /ould consist in applyin' more comple3 trials& such

as harmonic dyads and triads& and short se2uences of tones or melodies& as /ell as the

role of timre and emotions in memory performance0


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the role of timbre in the memorization of microtonal intervals.pdf

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