source file: mills2.txt
Date: Thu, 6 Feb 1997 16:40:06 -0800

Subject: Re: Reply to Matt.

From: Matt Nathan <mattn@ix.netcom.com>

Charles Lucy wrote:

> I stand semantic correction. I had always understood "partials"
> to mean multiples of a frequency. i.e frequency multiplied by an
> integer.

I think there must have been some historical confusion in this
area; besides "harmonic", we're also left with the term 
"overtone" (which Helmholtz urged us to avoid about a century ago). 
The term "partials" seems to have straightened it out though. I'd 
like to know who coined it (Helmholtz, Ellis, someone more recent?). 

Here's a snippet which uses the terms in context.

from _The Acoustical Foundations of Music_, Backus, Norton, 1969
[my comments] in brackets
/italics/ in right slashes
.. shows deletions
begin quote 
"
Chapter SIX 
TONE QUALITY

..
We are now concerned with what is called the /quality/ of 
a tone--sometimes referred to as /timbre/--the characteristic 
of a tone that can distinguish it from others of the same 
frequency and loudness.

/Partials and Harmonics/

..The individual simple tones [sine waves, also called pure 
tones] making up a complex tone are called /partial tones/ or 
simply /partials/. 

For...discussion...we shall...assume that the vibrational 
pattern repeats exactly for an indefinite number of cycles.... 
For such a tone the constituent partials must be...integer 
multiples. Only if this is true will the waveform be the same 
for consecutive cycles.... 
 Partials related in this simple way...are called /harmonics/. 
The partial having the fundamental frequency is called either 
the /fundamental/ or /first harmonic/. The partial having a
frequency twice that of the fundamental is the /second harmonic/,
and so on.
 ...
The term "overtone"...introduces...confusion...it is best not to use it.

/Nonperiodic tones: Noises/

..For tones whose wavefom does not repeat each cycle, the 
partials need not have frequencies that are integral multiples 
of the fundamental frequency, and so are called /inharmonic/. 
"
end quote

> My problem with the term harmonics is that I have failed to find a
> better term to describe those notes that you hear as you touch
> an open guitar string gently at specific "audible" points.
> (Remember, my first indtrument is guitar)
> So what do we call those positions, without implying that
> they MUST only occur at integer frequency ratios.

The places which you touch are called "nodes". The tones you
get I think are still called "harmonics" by string players (and 
are notated with a little unfilled circle above the note), which 
shows there's still potential for confusion. Note that
these "harmonics" which you get by touching the string are still
complex tones, which are composed of partials which may or may
not be "harmonics" (simple tones related in whole numbers). As 
long as you show cleary which context you're writing of, we 
should be able to understand each other. Don't make the fallacy of 
blurring the multiple meanings of a word in arguing some theoretical 
point. 

BTW, the musical examples on your lullabies web site are rather 
beautiful, even if your theoretical proposals seem unrigorous. 

Matt Nathan

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