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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
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.
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.
> 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
> 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
Computer and Information Science and Engineering
University of Florida
Web page: www.cise.ufl.edu/~acamacho