Re: Plucked strings

[William Beaty <billb@ESKIMO.COM>]

On Wed, 5 Jul 2000, Leigh Palmer wrote:

> > William Beaty wrote:
> >
> > > On Mon, 3 Jul 2000, David Abineri wrote:
> > >
> > > > Am I correct in explaining string instruments, to say that a string
> > > > actually vibrates in many modes simultaneously when bowed or plucked?
> > > > That is, is it producing its fundamental along with several harmonics
> > > > all at the same time?
> > >
> > > Yes, but the phase of the various frequencies is important, with the
>
> I don't know haw many of you have heard of Ohm's law - his *other*
> law, that is, Ohm's law of acoustics. From "Science and Music" by
> Sir James Jeans (1937):
>
>  "The timbre depends only on the relative energies of the various
>  harmonics and not on their phase-differences. Differences of phase
>  produce no effect on the ear. This is known as Ohm's law, having
>  been discovered by G. S. Ohm (1787-1854), the discoverer of the
>  still better known electrical law."
>
> So James Jeans says you're wrong, Bill,

Interesting!  This makes sense, considering that the ear is a spectrum
analyzer.  The phase relationships might be audible only if they push the
system into a region of nonlinear operation.

In the above message I wasn't thinking in terms of perceived sound, I was
thinking in terms of a mental model which explains plucked strings.

The "flat-topped standing wave" would have the same spectrum as a
collection of sinusiodal harmonics.  But if we want to understand what
happens when we pluck a string, wouldn't an animation of the string
be better than just looking at the output of a spectrum analyzer?


> but I confess that my own
> experiments on this topic also indicated to me that phase affects
> timbre. I made a set of tapes intended to demonstrate Ohm's law
> and found them very unconvincing.

At certain places on the string where the set of harmonics add up to large
excursions, I'd expect that nonlinear things would occur.  Perhaps if you
keep the amplitude of the musical instrument very low, and then crank up
the gain of the audio pickup, the results would better adhere to Ohm's
law?"

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