Re: Music Glossary - 1.64 Concert Pitch (2.12.2)

[Hans Aberg]

On 4 Apr 2009, at 19:32, Henning Plumeyer wrote:

> > Therefore, by definition, all blown > musical instruments will have  
> > a fundamental frequency of 2L.
>
> Hi,
> not quite: clarinets sound an octave lower than you would expect  
> when you regard their length.
> They behave like stopped organ pipes. I don't know exactly why -- it  
> comes from their cylindrical bore.
> (Saxophones have a conical bore and allthough they have mouthpieces  
> very similar to clarinets they are as long as other wind instruments.)

It is confusing, because flutes, oboes and bassoons are cylindrical  
bore and blow over on the octave, the sax blows over on the octave but  
is conical bore, the clarinet is cylindrical bore but blows over on  
the pure fifth (interval ratio 3).

> I think the _wavelength_ (not the frequency) of non-clarinet wind  
> instruments is 2 times the length of the instrument.

You get a standing wave with a maximum at the open end(s) and a  
minimum at the closed end(s). If both ends are open, the lowest  
frequency has minimum in the middle. This then a half wavelength.  
However, if you take a flute and measure its length, and compute the  
frequency from this, taking the speed of air at the temperature of the  
air in the flute, then it does not match exactly. There are some  
"convection" phenomena going on.

Now, if the pipe is open at one end and closed at the other, this is a  
quarter of the length. So the frequency goes down one octave  
(roughly). You can check this by taking a flute and play the lowest  
note, or the mouthpiece part alone, and cover the lower end with the  
hand.

When checking the partials, the open pipe can play all overtones, but  
the open-closed pipe can only play the odd ones. This gives the  
clarinet it distinct sound. In a real measured spectrum, there may be  
a lot of "sporadic" (weak in amplitude) frequencies - this is just the  
main behavior.

  Hans