Klarinet Archive - Posting 000477.txt from 2000/08

From: Bilwright@-----.net (William Wright)
Subj: [kl] inharmonic (anharmonic) vs. decay vs periodic vs recipe
Date: Thu, 17 Aug 2000 12:30:05 -0400

It seems to me (but I am not presenting myself as an expert in this
stuff) that we are confusing different aspects of waveform with each
other because of imprecise definitions:

<><> The sequence, f, 2f, 3f, 4f, 5f, etc is called the 'harmonic
series', and sounds that can be analysed in this way -- periodic sounds
-- are called 'harmonic'.

No, 'harmonic' means that the _FREQUENCIES_ of the component sine
waves have whole number relationships. Thus sine waves are periodic,
but not all periodic waves are harmonic.

<><> This applies just to *sustained* sounds. Any *sustained*
sound is periodic.

'Sustained' usually means that a continuing energy source is
replacing whatever energy that the wave is losing through damping and
radiation. A sustained sound need not be either periodic or harmonic.

<><> What we've been talking about here in this thread is the
difference between sustained sounds, like oboes, clarinets and organs,
and *un*sustained sounds, like pianos and bells. Because pianos and
bells are just struck and left to ring on by themselves, their waveforms
*aren't* completely periodic. (See
http://www.sneezy.org/Databases/Logs/1999/01/000080.txt) Therefore they
aren't susceptible to the analysis above. Their sounds aren't harmonic,
and so they are said to be 'anharmonic', or to 'exhibit anharmonicity'.

If the amplitude of all the sine wave components in a wave happened
to decay without changing their FREQUENCY relationships, then the
decaying wave _would_ be harmonic.
Notice that my statement does not require that the AMPLITUDES decay
uniformly. Once again, 'harmonicity' requires only that the FREQUENCIES
have unchanging relationships.

<><> (in another message, someone used the word "recipe" fairly
often)

Changes in the relative amplitudes affect our perceptions -- as we
have discussed many times -- and therefore changes in the relative
amplitudes of the various components of a wave during decay are
important.
Therefore the word "recipe" usually **does** include amplitude as
well as frequency.
This is important for the clarinet because there is a "change of
feel" as amplitude increases. When the amplitude is low (as in a 'pp'
note) and you begin a gentle crescendo, the amplitudes of the various
sine wave components are *not* increasing at the same rate. If your
note begins 'harmonic', it will remain harmonic but the 'tone color'
will change because the 'recipe' is changing slightly.
It turns out that at this point in the crescendo, the reed is not
closing completely or shutting off the air flow completely.
At the "change of feel" point, the reed does begin to close
completely. And now, as you continue the crescendo, the amplitudes of
the various sine wave components *do* increase in approximately equal
proportion. At this point, the recipe is remaining much closer to
constant.
During the crescendo, of course, the relationship of the component
frequencies may change as well. But once again, amplitude and frequency
are two different issues, and trying to describe both of them with the
single adjective 'harmonic' will confuse two separate issues, each of
which has its own effects.

At least, that's how I understand it.

Cheers,
Bill

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