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From: knudsen@ihwpt.UUCP (mike knudsen)
Newsgroups: net.music.synth
Subject: Re: piano sound and stretched harmonics
Message-ID: <700@ihwpt.UUCP>
Date: Fri, 14-Feb-86 12:19:02 EST
Article-I.D.: ihwpt.700
Posted: Fri Feb 14 12:19:02 1986
Date-Received: Sat, 15-Feb-86 05:15:50 EST
References: <202@nyit.UUCP>
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Organization: AT&T Bell Laboratories
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> The stretched harmonics in the piano have their origin in the
> WAVE EQUATION, modified to include stiffness and damping.
>
> about the 12th harmonic.  The stretching is greater in the NON-WOUND
> STRINGS and probably accounts for some of the tinny piano sound
> in the highest octave.  The effect of an assumed linear damping
> 
> What is interesting is that stretched harmonics are 
> found in ANY instrument
> described by the wave equation, though they are more audible 
> in STRUCK-STRING instruments.  The non-harmonic spectrum may account
> for the warmth or harshness of real vs. synthesized musical sounds;
> 			j.p.lewis
> 			nyit computer graphics lab

I agree with the above, but this raises a question:
Should the stretched harmonics be even more pronounced
on a HARPSICHORD, because (1) the tone is brighter,
with stronger high harmonics, and 
(2) even the bass strings are not wound.

Are plucked strings less "stretched" harmonically than struck ones?
Bass harpsichord strings tend to be of brass or bronze
(less stiff than steel) but under much less tension.

I should check my Zuckermann book (The Modern Harpsichord)
to see whether harpsichord tuning is stretched like pianos'.
I don't see how it could be avoided.

	mike k
PS: I find the Harpsichord patches on most synths to be
too harsh for more than a few bars of use, tho I doubt
it is related to the stretching issue.

PPS: Stretched tuning is neither needed nor desirable
on continous-toned instruments, like organs, since their
wave equation has no damping.
(Not that anyone implied otherwise...)