Klarinet Archive - Posting 000513.txt from 2000/08

From: Roger Shilcock <roger.shilcock@-----.uk>
Subj: Re: [kl] inharmonic (anharmonic) vs. decay vs periodic vs recipe
Date: Fri, 18 Aug 2000 04:20:39 -0400

He will of course correct me if necessary, but it seemed to me that Tony
P. was equating "harmonic" with "susceptible to Fourier analysis". IS the
escapement-controlled motion of a pendulum analysable into sinusoidal
components? If not, why not?
(I really want to know...).
Roger S.

On Thu, 17 Aug 2000, William
Wright wrote:

> Date: Thu, 17 Aug 2000 12:56:52 -0700 (PDT)
> From: William Wright <Bilwright@-----.net>
> Reply-To: klarinet@-----.org
> To: klarinet@-----.org
> Subject: Re: [kl] inharmonic (anharmonic) vs. decay vs periodic vs recipe
>
> <><> Bill wrote:
> Thus sine waves are periodic, but not all periodic waves are harmonic.
>
> <><> and Tony replied:
> Yes, all periodic waves are harmonic.
>
>
>
> Well <friendly smile, I'm not a troll> my college physics text
> (Sears & Zemansky) doesn't agree. It says:
>
> "Any sort of motion which repeats itself in equal intervals of time is
> called periodic, and if the motion is back and forth over the same path,
> it is also called oscillatory. A complete vibration or oscillation
> means one round trip...."
>
> and my text goes on to say that harmonic refers to a special sort of
> oscillatory motion where the "elastic restoring force" [acting on the
> body in motion] is not constant but instead "varies during the motion"
> such that "the acceleration is directly proportional to the object's
> displacement [from the position where no force is active on the body]."
>
> The result of all this is our friend, the sinusoidal wave.
>
> But there are plenty of periodic motions, both discontinuous and
> continuous, that are caused by forces whose strength at any moment is
> *not* proportional to the displacement. Such periodic motions are not
> sinusoidal or harmonic; and without the sine and cosine functions, all
> of the remaining 'harmonic' analysis falls apart and leads to
> misunderstandings.
>
> A simple example would be the pendulum on a clock, where the pendulum
> swings harmonically if unhindered, but the periodic interference of the
> escapement inside the clock converts the second hand's periodic harmonic
> motion into a periodic but not harmonic motion -- repeated periodically
> once every second.
>
> More germane to our discussion, the inertia of air molecules -- which
> has a significant effect in a clarinet -- is not directy linked to the
> reed's displacement at any moment in time. Nor is the reed's own
> inertia, for that matter. Inertia may not relate to the 'equal
> temperament' topic that began this thread, but it is one example of how
> a periodic motion can (is) modified to produce motion that is still
> periodic but no longer harmonic.
>
>
>
> ....before I go any further with this, I'll stop talking and give you an
> opprtunity to respond to this most basic assertion, if you disagree with
> it.
>
>
> Thanks,
> Bill
>
>
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