Why are band instruments built in flat keys?

Question

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.)

For example:

• 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).}

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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?

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_{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?}

Answer 1

One reason is probably that trombones used to be pitched in A and D, with A at roughly 466 Hz, and the pitch standard changed around them. The same would apply to other wind instruments as well.

See https://en.wikipedia.org/wiki/Sackbut#Pitch:

Until some time in the 18th century, the trombone was in A and the pitch of that A was about a half-step higher than it is today—460–480 Hz. There was a transition around the 18th century when trombones started to be thought of in B♭ at around 440 Hz. This change did not require a change in the instrument, merely a new set of slide positions for each note. But it does mean that the baroque and renaissance repertoire was intended to be played at the higher pitch. There are many examples of evidence for this:

• Fellow church instruments that are fixed pitch—cornetts and organs—were pitched at approximately A=460–480 Hz ("Chorton") across Europe in the Renaissance and baroque eras. High pitch is also seen in Renaissance wind bands.
• Virgiliano's treatise Il Dolcimeo (c. 1600). Aurelio Virgiliano's Il dolcimelo (c. 1600) teaches trombonists that first position gives A, E, A, C, E and G.[20]
• In 1687, Daniel Speer's Grund-richtiger concurs with these notes for the slide all the way in (while describing pushing the slide out a bit to get the C).
• Praetorius describes an alto in D, tenor in A, and bass in D.

The tenor trombones that survive are pitched closest to B♭ at A=440 Hz, which is the same as A at A=466 Hz. So what we now think of as a tenor trombone with B♭ in first position, pitched at A=440 was actually thought of as a trombone in A (in first position), pitched at A=466. Surviving basses in D at A=466 (E♭ at 440)—for example: Ehe, 1612 (Leipzig) and Hainlein, c.1630 (Nuremberg) confirm Praetorius' description. It is also worth noting that Rognoni's "Suzanne ung jour" setting descends repeatedly to BB♭, which is a tone lower than the lowest note playable on a bass in F; on a bass in D, it falls in (modern) fifth position.

Many groups now perform at A=466 Hz for the sake of greater historical accuracy.

Orchestras are based on strings, while bands are based on winds, so as the pitch standards changed, strings could adapt more easily by tightening or loosening their strings, while existing wind instruments had to be redefined relative to the new standard or replaced with slightly smaller or larger versions.