Date: 2010-06-21 17:00
Epic! Man, I would have thought that a narrow bore would have sharpened things... shows me what I know. Anyone able to explain the physics of this?
Actually, it depends on where you do the narrowing/widening. Stephen Fox has some interesting materials on his website where he discusses this.
I'm not an acoustics expert, but basically, as I understand it, if you narrow the bore, the effect it has is related to where the narrowing is in relation to the length of the standing wave in the bore. At a high pressure region of the wave, narrowing the bore sharpens the note, while at a low pressure region narrowing the bore flattens the note.
In the lowest register, the upper half of the instrument is high pressure, while the lower half is low pressure. Things get more complicated as you jump to higher registers, because you have more "nodes" in your standing wave and consequently, you have multiple high pressure regions and multiple low pressure regions.
There's also another effect that has to do with the diameters of tone holes, called the "end correction." Basically speaking, narrower tone holes act like longer lengths of tubing. You can read about all this in Arthur Benade's "Fundamentals of Musical Acoustics."