Klarinet Archive - Posting 000446.txt from 1997/11

From: Dee Hays <deerich@-----.net>
Subj: Re: Recording the clarinet
Date: Tue, 11 Nov 1997 22:27:45 -0500

No instrument is mathematically "pure". NOR DID I SAY THAT IT WAS. The
uneven molar shape that you refer to puts it in the rough class of a square wave as
opposed to sine, sawtooth, or triangular. The clarinet wave shape certainly can not
be classifed as one of the latter three types.

Actually I believe the book did discuss the presence and strength of the various
harmonics (or I saw the information somewhere else). Even though we speak as if
only the odd harmonics are present, you are indeed right that this is not quite
true. The evens are present in varying degrees. Note that this is in relation to
the fundamental (chalumeau note). They will contribute to the characteristic sound
of the instrument to some degree. It is simply that the odd partials are the ones
that can be controlled or "triggered" to produce the various clarinet registers.

My question was: Is it the wave form that causes the recording problems? One
respondent stated that it was the rise time. Therefore is the wave square enough to
actually support this statment? Or to put it another way, what are the respective
rise times of the various instruments?

Dee Hays
deerich@-----.net
Canton, SD

Martin Pergler wrote:

> I'm not an acoustician, but my sense is that your book simplified it a bit
> too much to make your argument go through. As I'm typing this, I'm playing
> a clarinet into the mike on my computer and running a scope and Fourier
> Transform program. In the chalumeau register, the relative amplitudes of
> the harmonics are very roughly 1, 0, 1.2, 0.5, 0.9, 0.6, and then slowly
> going down. Indeed, very little of even harmonics, but quite a bit more of
> the odd harmonics than a pure square wave, whose decomposition would be
> 1,0,1/3,0,1/5,0,1/7, etc. (Hey, I get to use math in Klarinet!). The
> high amplitude of the higher harmonics in general makes the wave have a
> complex shape, going several times across the axis in one period.
>
> In the clarion register, we just kill the fundamental and overblow on the
> twelth. But the second harmonic of the overblown note is the sixth of the
> original note, and this was present. Actually playing it into the computer
> and renumbering the harmonics to start on the new note gives me a
> decomposition of about 1, 0.5, 0.4, 0.4, 0.2. The new even harmonics are
> just as prominent as the old ones (and conventional wisdom is that this is
> what makes the clarinet have two distinct "registers", chalumeau and
> clarion). The waveform is much simpler and does have sort of an uneven
> molar shape, but not square.
>
> [In all this, by nth harmonic *I* mean "n times fundamental frequency".
> Terminology confuses me slightly. You can say nth harmonic and nth
> partial, and one means "n times fundamental" and the other "n-1
> times fundamental" and I always forget which is which. Apologies
> if I have it the wrong way around.]
>
> Comparing with a good baroque recorder (my substitute for flute), I get
> that its decomposition is about 1, 0, 0.2, 0, 0, ..., ie an almost perfect
> sine wave. I don't play oboe, but I recall reading somewhere that it has a
> lot more of twice base frequency than fundamental.
>
> A pure "sawtooth" wave would have decomposition 1, 1/2, 1/3, 1/4, 1/5,
> ... and rises very quickly at the beginning of the period and then falls
> away slowly. I forget the decomposition for a triangle wave; I'll
> figure it out at later when I run Maple (a math program).
>
> Incidentally, playing into your computer and watching the scope is fun (in
> moderation) and can be enlightening. You can watch for evenness of the
> decomposition, and you can really see differences between certain thoat
> tone fingerings. I'll have to play around and see if there are differences
> between "focussed" and "unfocussed" sound, whatever those words mean, etc.
>
> Does anybody use scopes as teaching tools for clarinet? I've used it
> as a learning tool for singing, since for instance it is easy to
> see the "singers formant" (what makes male solo voices sound the
> way they do and carry), and those infamous voce di strega exercises
> just make all the higher partials zoom up and it's left to
> "experience" to then tone down the undesirable ones.