Pitches of simultaneous complex tones Citation for published version (APA): Beerends, J. G. (1989). Pitches of simultaneous complex tones. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR304393 DOI: 10.6100/IR304393 Document status and date: Published: 01/01/1989 Document Version: Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. 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If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policy If you believe that this document breaches copyright please contact us at: [email protected] providing details and we will investigate your claim. Download date: 01. Oct. 2021 Pitches of simultaneous complex tones John G. Beerends Pitches of simultaneons complex tones Proefschrift ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de Rector Magnificus, prof. ir. M. Tels, voor een commissie aangewezen door het College van Dekanen in het openbaar te verdedigen op dinsdag 4 april 1989 te 16.00 uur door John Gerard Beerends geboren te Millicent (Australië) Dit proefschrift is goedgekeurd door de promotor Prof. Dr. H. Bouma en de copromotor Dr. A.J.M. Houtsma Dit onderzoek werd uitgevoerd aan het Instituut voor Perceptie Onderzoek (IPO) te Eindhoven, en werd financieel gesteund door de Stichting Psy­ chon van de Nederlandse Organisatie voor Weten­ schappelijk Onderzoek (NWO). Contents Deftnitions 1 List of Symbols 4 1 Introduetion 6 REFERENCES 10 2 Pitch identiftcation of simultaneous 13 dichotic two-tone complexes 2.1 INTRODUCTION 13 2.2 EXPERIMENT 1 16 2.2.A Procedure 16 2.2.B Results 17 2.2.C Discussion 19 2.3 EXPERIMENT 2 20 2.3.A Procedure 20 2.3.B Results 21 2.3.C Data interpretation 24 2.3.D Discussion 27 2.4 THEORY 30 2.5 REFERENCES 33 APP. 2.A DECISION MODEL FOR CORRECT IDENTIFICATION OF 35 SINGLE NOTES APP. 2.B DECISION MODEL FOR TWO CORRECT IDENTIFICATIONS 36 OF TWO SIMULTANEDUS NOTES APP. 2.C DECISION MODEL FOR ONE CORRECT IDENTIFICATION 38 OF TWO SIMULTANEDUS NOTES 3 Pitch identification of simultaneous diotic 40 and dichotic two-tone complexes 3.1 INTRODUCTION 40 3.2 EXPERIMENTS 43 3.2.A Procedures 43 3.2.B Results 43 3.3 INTERPRETATION OF RESULTS 45 3.3.A Cochlear interference of partials 45 3.3.B Internal grouping of partials 47 3.3.C Central interference and analytic listening 49 3.4 DISCUSSION AND CONCLUSIONS 52 3.4.A Discussion 52 3.4.8 Conclusions 54 3.5 REFERENCES 55 APP. 3 THE UNDERLYING PR08A8ILITY FUNCTIONS 56 4 The influence of duration on the 58 perception of pitch in single and simultaneons complex tones 4.1 INTRODUCTION 58 4.2 SINGLE COMPLEX TONES 61 4.2.A Experiment l: two-tone complexes 61 4.2.8 Experiment 2: sequentia! two-tone complexes 65 4.2.C Experiment 3: three-tone complexes 67 4.2.D Discussion 68 4.3 SIMULTANEOUS COMPLEX TONES 70 4.3.A Experiment 4: simultaneons two-tone complexes 70 4.3.8 Experiment 5: simultaneons three-tone complexes 73 4.3.C Discussion 77 4.4 CONCLUSIONS 78 4.5 REFERENCES 80 5 A stochastic subharmonie pitch model 84 5.1 INTRODUCTION 84 5.2 THEORY 88 5.3 TESTING OF THE MODEL 92 5.4 DISCUSSION AND CONCLUSIONS 96 5.5 REFERENCES 97 APP. 5 N-TONE COMPLEXES 99 Summary 101 Samenvatting 104 Curriculum vitae 108 1 Definitions Definitions are taken, as much as possible, from Acoustical Terminology of the American Standards Association, 81.1, 1960. Where applicable, definitions are given with respect to a harmonie complex tonewith frequenciesfi = m/0 and fz = (m+1)/o, m = 2,3, ... Analytic pitch perception Pitch perception in which a sound is perceived as composed of its partials (/I, fz) and in which one perceives only the speetral pitches. Complex tone In general: tone composed of more than one pure tone. In this thesis: harmonie complex tone DUferenee limen The increment in a stimulus that IS just noticed in a specified fraction of the trials. Dichotic presentation Presentation in which a subject re­ ceives different information in left and right ear. Diotic presentation Presentation in which a subject re­ ceives the same information in left and right ear. Fundamental frequency Frequency of a sinusoidal quantity which has the same period as the pe­ riodic quantity (Jo). Harmonie Partial (h, fz) whose frequency is an integral multiple of the fundamental frequency (Jo). 2 Delinitions Harmonie order Lowest harmonie number of a har­ monie complex tone ( m). Harmonie complex tone Complex tone whose pure tone fre­ quencies (h, h) are all integral mul­ tiples of a fundamental frequency (Jo). Holistic pitch perception Synthetic pitch perception. Just noticeable difference Difference limen. Note Musical sign to indicate the pitch of a tone. Parti al Pure tone component of a complex tone (fb f2). Pitch 1: That attribute of auditory sensa­ tion in termsof which sounds may he ordered on a scale extending from low to high. 2: The frequency of that pure tone having specified sound pressure level which is judged by listeners to produce the same pitch as the com­ plex tone. Pure tone Sound wave of which the instanta­ neons sound pressure level is a simple sinusoirlal function of time. Speetral pitch The pitch associated .with a partial (fblJ.). Speetral frequency Partial {!1, h,). De6.nitions 3 Subharmonie Partial whose frequency is an inte­ gral submultiple of the fundamental frequency (or of the frequency of the pure tone). Synthetic pitch perception Pitch perception in which a sound is perceived as a whole and in which one perceives only the virtual pitch. Tone Sound senaation having pitch. Virtual pitch The pitch associated with the funda­ mental frequency (Jo). 4 Symbols List of symbols Estimate of a. Expected value of a. DL Difference Limen. DL for the speetral pitch of a pure tone. DL for the virtual pitch of a complex tone. Jo Fundamental frequency of a complex tone. Speetral frequency of a complex tone. Subharmonic, with frequency !J,Jl, of the speetral frequency fk. G(x;a,u) Gaussian pdf of random variabie x, with mean a and standard deviation u. Pc(m) Percent correct scores, in a one-note identification paradigm, as a function of the harmonie order m. Pc(k,l) Percent correct scores, in a two-note identification paradigm, for both notes correctly identified as a func­ tion of the harmonie orders k, l. Pc(k; l) Percent correct scores, in a two-note identification paradigm, for one note correctly identified as a function of its harmonie order k and of the harmonie order l of the other note, regardless the response to this other note. pdf Probability density function. Symbols 5 Pr[m mJ Probability of a correct harmonie order estimate, in a one-note identification paradigm, as a function of the harmonie order m. Probability of a correct harmonie order estimate, in a two-note identification paradigm, derived from Pc(k; l), as a function of the harmonie order k. Probability of a correct harmonie order estimate, in a two-note identification paradigm, derived from Pc(k, l), as a function of the harmonie order k. Pr,.[k =kj Probability of a correct harmonie order estimate, in a two-note identification paradigm, derived from Pc( k; l) for k < l, as a function of the harmonie order k (identi­ fication of the more salient pitch). Prp[k =kJ Probability of a correct harmonie order estimate, in a two-note identification paradigm, derived from Pc(k; l} for k > l, as a function of the harmonie order k (identi­ fication of the less salient pitch). R Response of a subject in a one-note identification task. Response of a subject to the fundamental with the most salient pitch, i.e., the one represented by the lowest har­ monie numbers, in a two-note identification task. Response of a subject to the fundamental with the less salient pitch, i.e., the one represented by the highest har­ monie numbers, in a two-note identification task. random variabie with distribution G(xk; ik, uk); O"k = u(fk)· random variabie with distribution G(xkzi !kh O"kz); O"kl u,.fl'\ o: :::; 1, l = 1, 2, ..