Re: harmonic vs. inharmonic sounds

Hmmm ... do I read confusion in this response? The confusion between the metrics and the psychometrics?

I think 'your' definition fails with narrow-band (white) noise, which may [simply] be all the frequencies [sic] between 330 and 332 Hz, and the perception is of a harmonic sound which is aperiodic. Extend this to four bands of noise 5 Hz wide, in diminishing amplitude, centered at 220, 442 and 664 Hz. This is not periodic, nor harmonic, but is pitched.

One test of "pitched-ness" I use is to play the 'equivalent note' on the piano. While I can't simulate the spectral aspect, in the first sound I play 'E' above middle C, and in the second, you might play the A below middle C. (I might however play the A below middle C, middle A and the E just above that ... this being an example of an individual's "ability" to segregate components that many people perceive as integrated.)

Sarah's question, in my view, is either (1) not well-formed, or (2) is a 'non-question'. (A non-question would be something like: "How many ears of corn are required to make red?").

The 'not-well-formed' part, I would propose, is that if 'harmonic' is defined as whole number ratios, then 200, 300, 400 is "harmonic", and 200, 300.2, 400 is inharmonic. This is the response to the "metric" aspect of the question.

The other part of the question (not explicit, and therefore contributing to the not-well-formedness) is the perceptual one .. a whole other ball of earwax.

Arturo appears not to question the aspects of 'rounding' that go into pitch perception. He writes that 2.06, 3.02 and 3.97 are "far" from being integers. I would suggest a two step reduction of the data. Step one, round the numbers to one decimal place: 2.1, 3.0, 4.0, and then to no decimal places: 2, 3, 4 ...

In the other example, depending upon the amplitude of the three components, there is a good chance that my hearing would not integrate them without some work. My response is of a statistical nature, and therefore psychometric.

`Best`

`Kevin`

`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
_____________________________________

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

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