Posted by Jim Tyler on October 30, 2000 at 22:45:37:
In Reply to: A theoretical question posted by Mario on October 30, 2000 at 09:05:50:
And to add to the confusion!!! The reason the partials, or overtones get closer as you get higher is: At the fundamental pitch of any brass instrument (the lowest note you can get with no valves depressed) there is only one standing wave in the horn. Each octave you go up, the frequency of the note doubles, so up one octave equals two standing waves. Up another octave equals four standing waves. Up another octave equals eight standing waves in the horn. Guess what happened to three, five, six, and seven standing waves? There are your partials that get closer together as you play higher. The next octave (if playable) would have nine, ten, eleven, twelve, thirteen, fourteen, and fifteen. With this many partials in this octave you could play most of the notes open. Gee! You can. To help demonstrate standing waves, pluck a guitar string and it will make an oval blur with the widest part in the middle. If you pluck it near one end, you can sometimes have a blur that looks like a figure eight with the middle of the string not moving at all. With a very long string at just the right tension you can see three and four "nodes" on the string. These are standing waves on a string. In a horn you can't see them but they are there.
I hope this helps someone understand why partials come closer together with the higher frequencies for a given length of tubing.
Jim Tyler