Posted by Klaus on June 23, 2001 at 18:44:08:
In Reply to: Re: Re: Sharp vs. Flat posted by Tubist on June 23, 2001 at 17:55:17:
To understand acoustics one must understand the monochord, from which Pythagoras deduced his rules of partials.
That simple instrument is close to perfect from a theoretical acoustical point of view. But only close. Mass and stiffness of the string material has it influences.
In string instruments the partial system is applied in form of the flageolets. Generally rumoured to be flat. To a degree, that one world class conductor prohibited the orchestral string basses to tune in by means of the flageolets. As their open strings would come out sharp related to the orchestra.
In wind instruments the Pythagorean rules only work on tubes cylindrical all the way or conical all the way. Valved brasses could be built cylindrical all the way. But like the bugles with a constant increase in bore, that is cone shaped, they would be of small musical interest.
All modern brass are compromising the Pythagorean rules. Some instruments more than others. The French horn is the least ideal brass from an acoustical point of view. The straight trombone is closest to the ideal.
Some makers are better in doing optimal compromises. None mentioned here! Just for the sake of the principle.
Let us take a look at your tuba. The maker might have done a great job on designing the main bugle. Then the valves are added. Necessarily adding cylindrical tubing to a conical body. Necessarily ruining the fine principles behind the design of the main bugle.
Playing through the partials will have the placements and the number of the nodes change. Creating varying problems. The addition of a relatively long cylindrical tubing like the 4th valve (+33.3333%) will create the worst problems.
Aside from a strongly developed embouchure, I should not suggest specific solutions to your problem. Only one could point to general arithmetics, where 1+3 sometimes is considered a valid substitution for 4. (If that would work for you, that would of course only be accidental. Almost!)
Klaus