marzan122 wrote:I must clarify. I am not interested in whether this is a 3/4, 4/4, 5/4, or a 6/4 tuba. I am interested in how to measure the taper of a tuba.
A tuba, being a conical instrument, gets bigger starting from the leadpipe all the way to the bell, with a cylindrical section for the valves.
The rate of change of the taper can itself be different (and I assume is) from one section of the tuba to another.
How does one measure these dimensions?
Thanks.
At defined intervals along the taper, measure the circumference of the tubing, divide by pi, and that's the diameter. Then, subtract the thickness of the brass (which has to be assumed or measured by disassembling the instrument and measuring the edges that insert into the ferrules) to get the inner diameter. Take half that, square it, and multiply it by pi to get the area. Use that area as a sample of a length of the taper, and multiply by that length. That gives you an approximation of the volume.
What that means, though, is anybody's guess.
Bell tapers are usually modeled using cardboard templates that are trimmed until they fit the shape perfectly. It usually takes several because the bells on old tubas are usually no longer symmetrical, and then a estimate is made.
When I wrote this article,
http://www.rickdenney.com/york_vs_miraphone.htm, that's how I made my measurements. Again, what does it mean? Nobody really knows for sure.
In the instruments I've seen, the taper is usually conical in sections. By conical, I mean that the taper is constant in that section. I usually see a constant taper from the main slide to the bottom bow, a bigger taper in the bells stack, and then a flare (which by definition does not have a constant taper). The leadpipe often has a constant taper, or at least it starts out that way. There may be a taper between the last valve and the main slide, maybe not. Some instruments increase the bore from one valve to the next.
It's the sum of all these tapers that determines the acoustic characteristics of the instrument, and the more one knows about the science of that, the more one will be surprised that any musical series of harmonics can be achieved.
I have two reasons for measuring something: I want to build a model of it in the hopes that the model will help me understand it, or I want to reproduce it. Many attempts at building such models have been attempted.
Rick "wondering what you hope to achieve with measurement" Denney