Klarinet Archive - Posting 000479.txt from 2000/08

From: Tony@-----.uk (Tony Pay)
Subj: Re: [kl] inharmonic (anharmonic) vs. decay vs periodic vs recipe
Date: Thu, 17 Aug 2000 13:06:27 -0400

On Thu, 17 Aug 2000 09:30:05 -0700 (PDT), Bilwright@-----.net said:

> 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:

No, I'm not:-)

> > 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.

Yes, 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.

Yes, it need, if it is in a steady state.

> > 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.

Only if they were harmonic to begin with. They aren't harmonic to begin
with because of things like funny shapes (bells) and stiffness of the
strings (pianos).

> Notice that my statement does not require that the AMPLITUDES decay
> uniformly. Once again, 'harmonicity' requires only that the
> FREQUENCIES have unchanging relationships.

Yes, but irrelevant in this case.

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

Me, I suspect.

> 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.

All of this is true, and from Benade. Indeed, I reproduced the argument
myself in:

http://www.sneezy.org/Databases/Logs/2000/03/001021.txt

But it's nothing to do with this issue.

> 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.

I don't think I confused the issue, or referred to amplitude and
frequency with the same word 'harmonic'. Read it again.

To sum up:

Periodic oscillations are harmonic (Fourier).

Sustained sounds at a given dynamic, like woodwinds and organ, are
periodic. (Perhaps you didn't realise that.) The normal modes of a
clarinet tube are not in whole number ratios, but that doesn't matter,
because the system settles down to a steady state in which "the
fundamental frequency locks into position in such a way as to maximise
the weighted average height of all resonance values R1, R2,
R3,...corresponding to the harmonics f, 2f, 3f,.." (Benade, Physics of
wind instrument tone and response, 1971). Thus the anharmonicity of the
normal modes doesn't affect the harmonicity of the sustained sound.

Percussive sounds, that decay after initial input of energy, are in
general not periodic. This is not because they are decaying, though
indeed they are. It is because the normal modes of most physical
systems are not in whole number ratios, and therefore each of these
normal modes sounds independently -- they aren't driven to cooperate, as
they are in a sustained system. In the case of a bell, this is just
obvious. In the case of a piano, an attempt is made to design the
system so that the normal modes *are* as accurately as possible in whole
number ratios, but the attempt falls foul of physical parameters like
string stiffness and approximate geometry.

Tony
--
_________ Tony Pay
|ony:-) 79 Southmoor Rd Tony@-----.uk
| |ay Oxford OX2 6RE GMN family artist: www.gmn.com
tel/fax 01865 553339

... I almost had a psychic girlfriend but she left me before we met

---------------------------------------------------------------------
Unsubscribe from Klarinet, e-mail: klarinet-unsubscribe@-----.org
Subscribe to the Digest: klarinet-digest-subscribe@-----.org
Additional commands: klarinet-help@-----.org
Other problems: klarinet-owner@-----.org