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From: jeq@laidbak.UUCP (Jonathan E. Quist)
Newsgroups: net.music.synth
Subject: Re: Difficulty of synthesising piano sounds
Message-ID: <717@laidbak.UUCP>
Date: Mon, 10-Feb-86 19:58:27 EST
Article-I.D.: laidbak.717
Posted: Mon Feb 10 19:58:27 1986
Date-Received: Wed, 12-Feb-86 21:36:37 EST
References: <669@wcwvax.UUCP>
Reply-To: jeq@laidbak.UUCP (Jonathan E. Quist)
Organization: LAI Chicago
Lines: 59
Summary: 

In article <669@wcwvax.UUCP> ian@wcwvax.UUCP (Ian Kemmish) writes:
>(Discussion of difficulty of synthesizing a piano sound) ... I
>saw an article recently which said that Dr. John Chowning and
>Dave Bristow (on secondment from Yamaha) were working on doing
>a "proper" synthetic piano at IRCAM - and using *all* of a TX816
>(16 lots of 96 oscillators) to do it!

I've heard _a_ full-TX816 piano setup.  I don't know if it
was this one, but it was rather effective.  Among other things,
one module of the TX816 was used solely to simulate the
mechanical thunk of the hammers on the strings.

>The second problem is that the upper harmonics of a piano tone
>are *not* exact multiples of the fundamental.  This is why pianos
>are normally tuned in that funny way - slightly sharp at the top
>of the keyboard, slightly flat at the bottom.   I don't know the
>exact mechanism that causes this effect, but then I would imagine
>that the equation describing the oscillatory motion of a thick,
>massive, inhomogeneous wire under a lot of tension is quite a bit
>more complicated than the simple wave equation we all solved in
>Fourier Analysis at university! (Maybe someone in netland can even
>write it down??!)

I find it much easier to tune piano strings by the relationship
between harmonics rather than the fundamentals; perhaps piano
technicians do this to some extent as well.  (Years of tuning
a piano every six to ten months, of course, doesn't qualify
me to say;  one of the few things I've learned about piano
tuning is that there's no substitute for experience.  But,
I digress...)

The primary reason that the upper harmonics of piano strings
are not integer multiples of the fundamental, I have been told,
is that the diameter of a piano string is NOT infinitessimal,
and therefore the nodes in a vibration at a harmonic frequency
take space along the length of the string.  The result is
that the string is effectively shortened at higher harmonics,
causing them to sound sharp.  Because the ratio of string
diameter to string length is not constant over the scale,
this effect varies from note to note.

This model is mostly qualitative, and I have only heard
it from one source, but it seems a reasonable explanation.
An alternate theory would be that the tension increase per
unit of string displacement is greater at higher harmonics
than at the fundamental (due to string geometry), which would
tend to raise the pitch of harmonics.  If you think about it
long enough, though, this effect is similar (possibly identical)
to the one described above.

Okay, so I'm rambling.  (I did try to shorten the original draft. :)
If I've got the explanation all wrong, please correct me.

Enough of this, it's time for dinner.

Jonathan E. Quist
Lachman Associates, Inc.
ihnp4!laidbak!jeq
``I deny this is a disclaimer.''