Date: Thu Apr 19 13:32:59 2007

Author: Richard Berg

Subject: Re: music pipes

Post:

The data in the slides from (I think) Brian Holmes' talk show the source
of the brass instruments acting as though they were open tubes.

The simple tube blown by the lips at one end produces the overtone series
of that tube acting as a closed resonance tube, the lips being the closed
end, with an overtone series based on f1 = 61 Hz (except for the
fundamental, which is very difficult to sound).

Adding the bell and the mouthpiece "rearranges" the harmonices so that
(with the exception of the fundamental) they are now the harmonics of an
OPEN tube of the same length (well, almost, 61 Hz going to 116 Hz). The
real exception is the fundamental, called the pedal tone, which for the
trumpet (cornet) is very weak and therefore (mostly) unusable in musical
performance. It is weak BECAUSE the harmonics of the actual fundamental
note do not line up with the (experimental) harmonics of the tube.

The fundamental frequency of the original closed tube is calculated (on
his slide) as frequency = speed of sound / 4 x tube length.

The fundamental frequency of the tube with mouthpiece plus bell is ABOUT
double, so its basic operation is like an open tube of that length. This
appears to be strictly fortuitous.

The stability of notes (including the pedal tone) on the trumpet are
discussed in an article by Benade: The Physics of Brasses, by Arthur H.
Benade, Scientific American, July 1973.

If you do the same set of operations for the trombone, you will find that
the fundamental resonance is very close to the correct frequency in the
harmonic series, so it IS usable and trombone players use theie pedal
notes. Even I can easily sound the pedal tones on the trombone.

I don't have enough to do this week.

Dick


On Wed, 18 Apr 2007 cbettis@unlserve.unl.edu wrote:

> Dick,
>
> I understand your point about the mouthpiece and bell giving you the even
> harmonics in a cylindrical brass instrument, but isn't it true, that to
> calculate the pedal tone, you use the length of the pipe and assume it's
> closed at one end?
>
> Cliff
>

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Dr. Richard E. Berg, Professor of the Practice
Director, Physics Lecture-Demonstration Facility
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