Instruments in a military bands (and similar) are usually built in the keys of B-flat or E-flat.
(Whether these instruments are treated as transposing instruments or not is irrelevant. The key that they are built in sets the sound of the lowest open note.)
- Cornets: standard (Bb), soprano (Eb)
- Saxhorns: flugelhorn (Bb), alto/tenor (Eb), baritone (Bb)
- Trombones: tenor (Bb), alto (Eb)
- Tubas: euphonium/tenor (Bb), bass (Eb)1, contrabass (Bb)1
- Saxophones2: soprano (Bb), alto (Eb), tenor (Bb), baritone (Eb), etc.
1 The "military band" tubas come in Eb bass and Bb contrabass, whereas "orchestral" tubas come in F bass and C contrabass.
2 Saxophones originally came in two sets of seven instruments: a "military band" set alternating between Bb and Eb, and an "orchestral" set in C and F (this second set has not really survived).
I understand that it makes a lot of sense to have a family of instruments built in alternating keys that are a perfect 4th/5th apart, but I don't understand why Bb and Eb are chosen for band instruments.
Why are band instruments built in B-flat and E-flat, while orchestral instruments are in C and F?
These related posts do not answer my question:
Why are brass instruments more comfortable with flat keys?
Could B♭ instruments be built in C? Why are they in B♭ in the first place?