Posted by Frederick J. Young on April 23, 2001 at 09:02:18:
In Reply to: Re: Re: Re: why compensating, really? posted by Matt G on April 22, 2001 at 11:51:36:
When physical scientists scale devices we try to keep all the dimensionless quantities constant in the various devices and their scale models. In the case of horns we would keep the ratio of bell diameter to total horn length constant. We would also keep the ratio of bore through the valves to total horn length constant. In addition we would keep the ratio of metal thickness to total horn length constant. This would imply that a tuba would have 16 times the area through the valves as a flugelhorn and would weigh at 8 times as much.
This is called the Buckingham Theory of dimensional analyses which you can find described in great detail in many books.
With this in mind it is clear that even the largest tubas used now are more closely related to the French horns than they are to the flugel horns or cornets.
The lack of large enough bore makes many tubas have about the same overtones as a harmonica!