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I tried to answer this question with some analysis long ago, with only limited success (limited by my samples and my own chops as much as anything). And I was looking at spectral differences when I think directivity may be more important.

https://www.rickdenney.com/the_tuba_sound.htm

But I think the main feature has been identified already: a large bell diameter-to-height ratio. Curves in the several feet of branches leading to the bell seem to matter. But there are so many interacting effects that really knowing what does what isn’t easy.

It’s a continuum. Some tubas are obviously Sousa-like and make it easy to get a Sousa-like sound. Others are profoundly German and get a focused, narrow sound with a lot of punch. Most are somewhere in between, no matter their design heritage, as designers of each try to attain the best features of the other.

Rick “it ain’t about the valves” Denney

The mechanical style of the valves probably only affects the demanded precision with which one must move them.

Due to their size, tubas require tremendous amount of precision in order to execute legato playing. Part of this precision involves timing of valve movement. Levers connected to rotors offer mechanical advantage which takes away some of the control involving timing of valve movement.
That having been pointed out, past a certain bore size, pistons are impractical for a couple of reasons.

Rick Denney wrote: ↑Fri May 27, 2022 5:36 am But I think the main feature has been identified already: a large bell diameter-to-height ratio. Curves in the several feet of branches leading to the bell seem to matter. But there are so many interacting effects that really knowing what does what isn’t easy.

I think this is a key factor. A sousaphone (or Helicon) is basically round; a "classic" german-style horn is straight, hangs a 180, then repeats until done. But bell flare is also a key factor - Wessex has shown than with their Chicago York and Chicago Presence 6/4 CC's (which are identical instruments aside from the bell flare). Less bell flare definitely creates a more direct sound that is more reminiscent of german-style instruments (this is as close to quantifiable and measurable as we can get here I think).

But to get back to the larger point (which has been made more than once), it's a combination of many factors most of which have not been isolated and systematically evaluated in testing (at least as far as published data goes).

As a Hack who collects tubas for no good reason, I believe that the type of music you play dictates the sound you want. I can play the blues on a nylon string classical guitar, but Bluegrass just does not sound good. Thus, the need for a steel string guitar for that twang. When I bought my Marzan Solo Piston tuba I started playing Sousa marches that I had not played in years. It had the brightness (Twang) that you hear when you listen to those marches. But the Marzan slant rotor that I got would fit into any European Orchestra doing "Finlandia". Two different beasts from the same mind.

Buy your wife's toys so she can't complain about you buying Yours,

CCC

The compact Holton B-flat (which I "built") is "fun" to play in a wind-band, but - at a genuine fortissimo and beyond - offers a bit too much "nose" (as the tubas in a wind-band - generally - are supposed to substitute for string basses).
It's wonderful for playing quite a few compositions written by eastern European orchestral music composers (it's maiden voyage involved playing Bartok). Though it's only 14 notes, I used it on "New World" later (yup: another composer from that same neck-o'-the-woods), and it was the easiest time I'd ever had entering at pianissimo and laying out those chord tones for the 'bones...Of course, having a world-class 'bone section sitting to my right made it even easier.
It's also great for when a B-flat tuba offers the best advantage, when playing with a quintet.

Again, as long as various tubas are BOTH "really good" and "really easy to play" (with no steep learning curves, nor excessive wonkiness about which one must constantly remind themselves) it's great to be able to grab a "just-right-for-the-job" tuba...rather than excessively going over scheduled pieces, to overcome some particular tuba's shortcomings - regarding various applications.

So now I’ve lost track: does my old silver Conn sousaphone have the American sound? I just got it back from the shop where the crushed bottom bow was resurrected, and the big pillowy sound is completely different from the 4/4 German rotary tubas that I’ve been playing.

jtm wrote: ↑Fri May 27, 2022 4:11 pm So now I’ve lost track: does my old silver Conn sousaphone have the American sound? I just got it back from the shop where the crushed bottom bow was resurrected, and the big pillowy sound is completely different from the 4/4 German rotary tubas that I’ve been playing.

In my opinion, you can’t get any more “American Sound” than a good Sousaphone.

Those made in India might (??) be examples of the D’Souza sound…(??)

bloke wrote: ↑Fri May 27, 2022 8:13 pm Those made in India might (??) be examples of the D’Souza sound…(??)

i especially like the ones with the two bells...