Definitions needed: partials, harmonics, overtones

Does anyone have good definitions of "partials", "harmonics", and
"overtones"? Books and articles don't always seem to agree with each
other on the meanings of these words when they discuss music theory.
Alita Morrison

Alita writes:
>Does anyone have good definitions of "partials", "harmonics", and
>
>"overtones"?

Greetings,
There are no "good" definitions, but a workable approach is to label all
components of a given spectra as "partials", then use "overtone" and
"harmonic" to describe certain characteristics of these partials.
The norm in the piano world is, (or should be), that overtones refer to
partials above the first. The term "Harmonics" is gradually being used less
and less, since there is nothing harmonic about string's partials, what with
their overtones "stretched" by inharmonicity.
Regards,
Ed Foote
Precision Piano Works
Nashville, Tn

>From: "Ed & Alita Morrison" <essaim@texas.net>
>
>Does anyone have good definitions of "partials", "harmonics", and
>"overtones"? Books and articles don't always seem to agree with each
>other on the meanings of these words when they discuss music theory.

Here is what I understand:

Partial: Any sine wave component of a sound (short for "partial tone").
Harmonic: A partial whose frequency is an integral multiple of the fundamental.
Fundamental: The lowest partial of a sound.
Overtone: An informal term for all partials besides the fundamental. (So
that the first "overtone" = the second "harmonic" in harmonic spectra).

As Ed Foote pointed out, the partials of stretched strings are spoken of as
harmonic, even though their deviation from true harmonics is often
significant. While the fundamental is usually the perceived pitch in a
harmonic spectrum, the same is not necessarily true for a non-harmonic
spectrum. The fundamental of bells, in particular, is often not the
perceived pitch. It usually doesn't make sense to speak of fundamentals in
reference to noise sources such as cymbals.

A further ambiguity arises with overblown woodwinds and "flageolet tones"
in strings (confusedly called harmonics also), when a "fundamental" an
octave or an octave and a fifth lower than the perceived note is present,
but is not usually spoken of as such. Non-harmonic (also called
"inharmonic") spectra can include harmonics, but non-harmonic partials are
usually found only in transient form in harmonic spectra. I'm sure there
are other qualifications and ambiguities, but these simple definitions are
useful in most circumstances.

Bill

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)607-7600 (fax) ^
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is that inegral or integer multiple?
Harmonic: A partial whose frequency is an integral multiple of the
fundamental.

I'd hate to have to find the area under the fundamental's sine wave...
It's been a while since I have done calculus.

Musick, Magick, and Mo'f'ck
Alex J. "Azi Vajravai" Van Wey
http://members.xoom.com/Azi_Vajravai

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>From: "Azi Vajravai" <vajravai@hotmail.com>
>
>is that inegral or integer multiple?
>Harmonic: A partial whose frequency is an integral multiple of the
>fundamental.
>
>I'd hate to have to find the area under the fundamental's sine wave...
>It's been a while since I have done calculus.
>
My copy of Webster's defines "integral" as a) pertaining to integers, or b)
pertaining to integration. It is, of course, the first of those two
definitions that I meant.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)607-7600 (fax) ^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^