Re: harmonic vs. inharmonic sounds

```Sarah,

I do not know if there is a standard definition of what an inharmonic
sound is. I do not think so, but I may be wrong. Anyway, I am going to
give you my own definition of an inharmonic sound in case it helps. I
define an inharmonic sound as a SOUND FOR WHICH THEIR COMPONENTS ARE ?FAR?
FROM BEING MULTIPLES OF THE PITCH. I found an excellent example of this
type of sounds in Patel. A. et al: ?Human pitch perception is reflected in
the timing of stimulus-related cortical activity?, in Nature Neuroscience
4, 839 ? 844. They test humans pitch perception of a stimulus built from
the 13th, 19th, and 25th harmonics of a fundamental of 50 Hz (i.e., 650,
950, and 1250 Hz). Most people perceive a pitch close to 334 Hz (+-6Hz)
for this stimuli. Since the ratio of the components with respect to the
pitch are ?far? from being integer numbers (1.95, 2.84, 3.74), according
to my definition, this is an inharmonic sound. In my case, I perceive a
pitch of around 315 Hz, not 334 Hz, but the ratios are also ?far? from
being integers (2.06, 3.02, 3.97).

Something I need to define is what ?far? means. For example, is a signal
with components 300, 600, and 901 Hz inharmonic? Given that we perceive a
signal with components 300, 600, and 900 as having a pitch of 300 Hz, and
we cannot tell the difference between the two stimuli, both should be
considered as harmonic, and therefore the component at 901 Hz is not ?far?
from 900 Hz. However, I think that instead of hard-labeling signals as
harmonic or inharmonic, we should define a continuous measure of
inharmonicity. For example, we should say that setting the third component
to 901 Hz makes the inharmonicity of the sound so low that it is
practically harmonic, however, setting the component to 910 Hz starts to
make it perceptually more inharmonic. However, those levels of
inharmonicity are small compared to the inharmonicity of the sound with
components at 650, 950, and 1250.

Arturo

> Hello list - I feel really silly asking this, but I can't seem to dig up
> a straight answer to this question.
>
> 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).
>
> I have two questions:
>
>
> 1) Is this actually correct?
> 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?
>
>
> ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
> Sarah Hargus Ferguson, Ph.D., CCC-A
> Assistant Professor
> Department of Speech-Language-Hearing: Sciences and Disorders
> University of Kansas
> Dole Center
> 1000 Sunnyside Ave., Room 3001
> Lawrence, KS  66045
> office: (785)864-1116
> Speech Acoustics and Perception Lab: (785)864-0610
> http://www.ku.edu/~splh/ipcd/Faculty/FergusonBio.html
>
>
>

--
__________________________________________________

Arturo Camacho
PhD Candidate
Computer and Information Science and Engineering
University of Florida

E-mail: acamacho@xxxxxxxxxxxx
Web page: www.cise.ufl.edu/~acamacho
__________________________________________________

```