I wasn't going to get into this because experience in threads about transposing/non-transposing always get more complex than necessary. But this observation MAY help:
In most (MOST) woodwind families, the instruments are all played and scored as transposing instruments: think of clarinets and saxophones. This means that the Eb alto sax player can sit down and immediately read and play the Eb baritone sax part, but can also sit down and immediately play the soprano, tenor, C melody (Ha! If you have one!), bass, and contrabass saxophone parts -- all WITH THE SAME FINGERINGS. Hold down your first three fingers on the keys and you're playing a G. Except it's not a CONCERT G (except on the C Melody sax) and it's actually a different pitch when played on an alto or bari vs. a tenor or soprano. And if you compare the written parts you'll see that they're quite different in terms of the notes that represent the same pitch (when the parts are in unison). If you're a woodwind player, you should be well familiar with these facts.
Tubas and euphoniums are the other way around (so to speak). There's only ONE tuba part (generally speaking). It's THE TUBA PART. You have to know how to play it (proper fingerings) with YOUR TUBA (BBb, Eb, F, CC). In woodwind families, the fingerings remain the same but the parts change. In low brass families the part remains the same but the fingerings change.
The exception is the British Brass Band where the ONLY non-transposing part is the bass trombone. In the BBB, the tuba (and euph) parts are all transposing -- so there are DIFFERENT parts (and differently pitched/notated parts) for the BBb and the EEb tubas, and they're all in treble clef!! Why? For basically the same reason that saxophones and clarinets are scored in this way: so that a player can switch among members of the family and not have to learn new/different fingerings. In fact, so a trumpet player can quickly pick up a baritone, euphonium, or tuba and just sit down and at least play with the "right" (SAME) fingerings.
This is, of course, a bit of an over-simplification and largely devoid of any "theory". But I think it may provide some insight into how and why (in a practical sense) things are the way they are with tubas and their different "keys". (The "key" of a tuba really refers to the fundamental pitch of the open instrument -- basically, how long the tube is.)
Sometimes even composers will be confused by this. A few years ago the community band I was in played a nice piece by a contemporary composer (then either at or visiting Duke University), and the tuba part had on it "Tuba in F". Complete nonsense. It was just (non-transposing) tuba. It wasn't even particularly appropriate to use an F tuba in playing it (which will definitely have a different tonal quality than a BBb or a CC). So I just played it on my compensating Eb and my section mate played it on her BBb -- same pitches but different fingerings.
Last edited by ghmerrill; 02-27-2019 at 09:29 AM.
Gary Merrill
Wessex EEb Bass tuba (DW 3XL or 2XL)
Mack Brass Compensating Euph (DE N106, Euph J, J9 euph)
Amati Oval Euph (DE 104, Euph J, J6 euph)
1924 Buescher 3-valve Eb tuba (with std US receiver), Kelly 25
Schiller American Heritage 7B clone bass trombone (DE LB K/K10/112/14 Lexan, Brass Ark MV50R)
1947 Olds "Standard" trombone (Olds #3)