Posted by Dan Clouse on October 17, 2003 at 07:07:26:
In Reply to: ATT: Rick Denney posted by tim on October 16, 2003 at 03:57:29:
Just to clutter up some of the nice math you guys are throwing out there, there's another large factor not considered yet. It's a number called linear density (mass/length). In the case of stringed instruments, linear density is the reason a "fat" string will play lower than a "thin" string, even at the same tension. The sheer mass of vibrating material produces a lower pitch!
It stand to reason that this applies to tubas as well, so logically speaking, a small-bore tuba technically needs to be LONGER than a large-bore tuba to make up for the smaller linear density of it's air column. If one tuba is actually longer or shorter than another to produce the same pitch, no hard number can be applied to tubas in general to explain tuning tendancies.
This introduces another phenomenon of brass playing though: the bell. The bell of a brass instrument does something very pecular: it makes the nodal point of the instrument's standing wave OUTSIDE the instrument. This affectively lengthens the instrument by some hard-to-calculate number. In practical terms, some tuba players may notice a difficulty in playing under low ceilings. It's possibly due the low ceiling causing direct interference. Because of the differences in bell shapes, the nodal point will be a different point outside of each model of tuba. This again affects the "intonation math" discussion.
Sorry I didn't give any answers, just more questions. I'm interested to see where this goes though!
Dan "Just Listen" Clouse