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Re: Harmonic vs inharmonic sounds

Sarah,

Your astute students have identified an ambiguity in the meaning of the term 'harmonic': it has both a precise mathematical meaning (as in 'harmonic series') and a somewhat less precise psychological meaning (as in 'harmonious'). Since the spectral components of just about any sound are harmonic in the mathematical sense (i.e., they have a common denominator) you may want to reformulate your question to your students as follows: "Determine whether a given sound will be heard as a single tone having a pitch corresponding to the greatest common denominator of the spectral components."

And what does determine whether a given sound will be heard as a single tone having a pitch corresponding to the greatest common denominator of the spectral components? We have argued (Schwartz and Purves, 2004) that it all depends on whether the greatest common denominator lies within the fundamental frequency range of human vocalization. If it does, then the sound in heard as a single pitch corresponding to that fundamental frequency, and if it does not, the sound will be heard as multiple pitches or as tones with a roughness or beating. Essentially, we argued that the auditory system behaves as if it 'assumes' that any reasonably harmonic (in the mathematical sense) complex sound stimulus was generated by a human voice, and perceives the sound as having a pitch corresponding to the fundamental frequency of the vocalization that is the most likely source of the stimulus. So, a set of spectral components having a greatest common denominator greater than ~70 will be heard as having a single pitch, and a set of components having a greatest common denominator less than ~70 will not.

Schwartz, DA and Purve, D (2004) Pitch is determined by naturally occurring periodic sounds. Hear Res 194(1-2):31-46.

Cheers,

David


On Mar 12, 2007, at 12:13 AM, AUDITORY automatic digest system wrote:

Date:    Fri, 9 Mar 2007 09:41:50 -0600
From:    "Ferguson, Sarah Hargus" <safergus@xxxxxx>
Subject: harmonic vs. inharmonic sounds

Hello list - I feel really silly asking this, but I can't seem to dig up
a straight answer to this question.=20

When I present complex sounds to my Physics of Speech class, I present
different classifications: periodic vs. aperiodic, harmonic vs.
inharmonic, continuous vs. transient, etc. One of the tasks the students
will have in homework is to determine whether a given sound is harmonic
or inharmonic. I tell them a sound containing energy at 200, 300, 400,
500, and 600 Hz is harmonic because all of those are integer multiples
of the same fundamental (which happens to be missing).=20

I have two questions:

1) Is this actually correct?=20
2) If so, it seems to me there must be some constraint on which
harmonics of the fundamental are there. In the example I gave above,
I've had students say "Couldn't the fundamental be 50 Hz? Or 25 Hz? Or
even 1 Hz?" Is there a rule I can give them?=20

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~=20
Sarah Hargus Ferguson, Ph.D., CCC-A
Assistant Professor
Department of Speech-Language-Hearing: Sciences and Disorders=20
University of Kansas=20
Dole Center=20
1000 Sunnyside Ave., Room 3001=20
Lawrence, KS  66045
office: (785)864-1116
Speech Acoustics and Perception Lab: (785)864-0610=20
http://www.ku.edu/~splh/ipcd/Faculty/FergusonBio.html