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Beyond What We Say: Physical Acoustical Analysis of Pitch in Discourse SMU Physics Colloquium 24 January 2011 Dr. Sam Matteson Professor of Physics Distinguished Teaching Professor. Beyond What We Say: Physical Acoustical Analysis of Pitch in Discourse

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Beyond What We Say:

Physical Acoustical Analysis of Pitch in DiscourseSMU Physics Colloquium 24 January 2011

Dr. Sam Matteson

Professor of Physics

Distinguished Teaching Professor

Beyond What We Say:

Physical Acoustical Analysis of Pitch in Discourse

SMU Physics Colloquium 24 January 2011

Professor Sam Matteson

Department of Physics


Dr. Gloria Streit Olness

Department of Speech and Hearing Sciences


Dr. Nancy J. Caplow

Department of Linguistics and Technical Writing

Beyond What We Say—Matteson

  • Objectives—to show that:

  • Physics amply equips one to contribute to interdisciplinary research.

  • Analysis of the statistical distributions of discourse pitch tells us much about how people assign meaning by intonation.

Beyond What We Say—Matteson

  • Physics equips one to contribute to interdisciplinary research

    • Collaborators:

      • Olness—Linguist/speech pathologist interested in language recovery by asphasics; discourse analysis

      • Caplow—Linguistic, expert in tonal language (Tibetan dialects), intonation and prosody; PRAAT guru

Beyond What We Say—Matteson

  • Task: to analyze quantitatively, the pitch of the words used by 17 subjects in a spontaneous narrative recounting a frightening experience.

Beyond What We Say—Matteson

Pitch?The “height” of the tone on a sound

PITCH = F0=226 Hz?

F3 = 678 Hz

F2 = 452 Hz

F4 = 904 Hz

F0 = 226 Hz

F3 = 678 Hz

F0 = 226 Hz

F4 = 904 Hz

F2 = 452 Hz

Octave 8o

Octave 8o

Beyond What We Say—Matteson

  • Pitch is a psychoacoustic phenomenon.

  • Equal ratios of frequency sound the same “pitch distance” or “interval” apart

H:Freference=1200¢ log2 (F0/Freference)H:Freference≈3986¢ log10 (F0/Freference)

Octave 8o

1200 ¢

Semitone ST

100 ¢

Beyond What We Say—Matteson

  • Perception guides production: How we hear affects how we speak.



Beyond What We Say—Matteson

Basilar membrane


Resonances of Basilar membrane separate sounds by frequency.

Beyond What We Say—Matteson


Georg von Békésy


1961 Nobel Prize in


Demonstrated resonance

of Basilar Membrane

Photograph courtesy Nobel Foundation

Beyond What We Say—Matteson

F0=512 Hz

F0=125 Hz

Beyond What We Say—Matteson

  • Evidence for Pitch Interval:

  • Perception of pitch

  • Unison voices and octave apart

  • Mimicry studies

  • Standard practice of log F0

  • Similar width distributions when expressed as ST

  • Let’s use it and see what we can find out!

  • H:Freference≈3986¢ log10 (F0/Freference)

Beyond What We Say—Matteson



. . . Once you were in the cabin it locked, and you had to have the car key to get out. So on the last day we were on the boat (ehm). . .

Beyond What We Say—Matteson



. . . home and to bed. And I woke up and just sit in my bed [ehmm] this sharp pain went all a sudden straight up

Beyond What We Say—Matteson

H: 1 Hz


F0 -< F0 >


Beyond What We Say—Matteson

  • The Gamut:

  • Borrow terminology from Guido D’Arrezzo

Guido D’Arezzo

(c. 992-1033)

Gamma-UtΓ-Ut :: gamut = scale

E-La:: ela = top notes

Image:;; Escala_musical.jpg

Beyond What We Say—Matteson

Dr. David Bickel, Assoc. Prof. U of Ottawa Ph.D. UNT ‘97

  • Order data

  • Find half scale partition with largest range

  • Cut range in half and repeat (2)

  • Average last two points

Half Scale Mode (HSM) Algorithm—D.R. Bickel CSDA 39 (2002) 153-163.

Beyond What We Say—Matteson

Result: No consistent declination (m<0)

in spontaneous emotive narrative!

Beyond What We Say—Matteson

  • Conclusion Re: The Gamut-root:

    • Speakers establish a reference pitch,

    • The Gamut-root Γn= mode(Hn-q+1, Hn+q)

    • Γn does not consistently decline in our study.

    • Pitch changes are relative to Γn

    • Hn* = Hn - Γn

    • Question: What are the distributions of Hn*like?

Beyond What We Say—Matteson

Cumulative Distribution of Peak Word-Pitch

Beyond What We Say—Matteson

Individual Distributionsof Peak Word-Pitch

Beyond What We Say—Matteson

Distribution seems to be multi-modal with multiple peaks.

Use Gaussian Mixture Model (GMM):

with f (h) the probability density function (pdf):

Beyond What We Say—Matteson

  • Conclusion Re: Pitch Distributions:

    • Relevant pitches are relative to Gamut-root

    • Relative pitch intervals occur at preferred levels.

    • Each person has a unique Discourse Gamut.

    • Question: Do speakers make discrete transitions or do they merely “sit” on the levels when they “get there?”

Beyond What We Say—Matteson

  • Markov Chain Analysis Program:

    • Markov Chain—sequence has no “memory”

    • No long range correlations observed

    • Examine Transition Map—

      • Plot next pitch H*n+1 versus “current” pitch H*n

      • Look for structure in map

Beyond What We Say—Matteson

  • Conclusion Re: Pitch Transitions:

    • Four processes are evident:

      • Very likely to repeat same pitch

      • Very likely to return to Γn

      • Some probability to drop an octave 1200¢

      • Elevated pitch (ela) are also probable

    • Speakers do not make discrete transitions

    • Levels are due to “clustering” not stepping

Beyond What We Say—Matteson

  • More to Do:

  • What is the effect of type of discourse have on declination?

  • Are the findings of this study universal or true only for this demographic?

  • What effect does musical training and competence have on the Gamut and on transitions?

  • Answers lead to more questions.

Beyond What We Say—Matteson

Conclusions Recapitulated:

Humans make meaning by howand what they speak.

Pitch Interval His powerful in intonation analysis.

The pitch is referenced to a Gamut-rootΓn .

Declination is not universally observed.

People use a personal Discourse GamutG(i.e. scale).

Gamut G ~ subset Chromatic Scale (Just Intonation)

Transitions are NOT intervals but rather are continuous.

The Ela (εj)are distinct and may be significant.

Beyond What We Say—Matteson

Maxim for a January:

Never underestimate the power of a profound idea to change the world, no matter who thinks of it first, where or when.

Therefore, think and think deeply.

Work and work with passion, secure in the knowledge that your ideas matter.

Beyond What We Say—Matteson

  • Acknowledgements:

  • Gracious (anonymous) subjects who allowed us to listen and analyze their discourses.

  • Colleagues– Dr. Gloria Olness and Dr. Nancy Caplow

  • Graduate research assistants— Mr. Craig Steward for peak word-pitch extraction and

  • Veronica Lewis Speech Pathology research assistant (graduated) for the many hours of interview

Beyond What We Say—Matteson


  • We No Speak Americano

Beyond What We Say—Matteson