Klarinet Archive - Posting 000442.txt from 1995/03

From: Jonathan Cohler <cohler@-----.NET>
Subj: Re: Tone quality; Tone color
Date: Wed, 15 Mar 1995 17:46:05 -0500

>Maybe I'm all wet here and somewhat out of my league (not being an
>acoustician) but upon reading - and I'll paraphrase a little - it has
>been shown that instruments that instruments we musicians say have a
>"bright" timbre are those with high cutoff frequencies. The cutoff
>frequency of an instrument can be raised by increasing the diameter of
>the toneholes so...instruments with larger toneholes have a "brighter"
>timbre. (Benade 1976 from Campbell and Greated 1987).
>
>Steve Prescott
>Instrument Rep. Tech/Clarinetist
>Indiana State University
>mipresc@-----.edu

The cutoff is determined by the size, number and spacing of the toneholes.
(The number is pretty much fixed for clarinet, so basically the size and
spacing are what determine it.) The reason that cutoff is, as you point
out, so critical in determining the overall timbre of the instrument is
that the radiation of sound out of the toneholes changes dramatically at
the cutoff frequency.

Below the cutoff, the vast majority of radiation occurs out of the first
one or two open tone holes. Above the cutoff, radiation occurs from all
toneholes. Because the radiation losses are much greater above the cutoff,
a higher cutoff frequency means more energy retained in the high
frequencies, and conversely a lower cutoff means relatively less energy
retained in the high frequencies. (Greater radiation losses in a system
tend to lower the amplitude of the resonance and increase its width.)

I believe, however--and I may be confused on this point--that making the
tone holes larger =lowers= the cutoff thereby making the instrument
"darker". (Here I am defining darker to mean containing less energy in the
higher part of the spectrum.)

Here's my reasoning. The cutoff frequency occurs essentially when the
wavelength is on the order of the size of the tone holes. Therefore, with
bigger tone holes, this would occur at a longer wavelength, or a lower
frequency. Correct me if I'm wrong on this.

-------------------

Jonathan Cohler
cohler@-----.net