Degenerate Key Signatures

Debate: Is Bb-Eb-F# a valid key signature?
An informal poll says “No”, though one respondent said anything should be possible in jazz. I have seen it used for the key of G harmonic minor, though certainly not on music from any major publishing house. It may be unfamiliar, but if I can trust that the piece strictly adheres to the scale, I can find it comfortable. There’s something to be said for a clean page, and frankly seeing an accidental that I already know is defined just distracts me.
Mark Levine’s approach to jazz theory uses melodic minor scales frequently. As a kid, I was taught that melodic minor is raised six and seven on the way up, lowered on the way down. This is an oversimplification, since melodies can move up or down in any interval. Levine defines the melodic minor as lowered third, raised six, and raised seven – in other words, a major scale with a minor third.
This leads to an odd set of key signatures. D melodic minor has one sharp—C#. The key of A melodic minor has F# and G# but no C#. G melodic minor has Bb-F#. So far I’ve seen those only in his textbooks.
I have seen illogical mixes such as Bb-C#-G# and, more absurdly, C#-D#-Fx. These were in a 20th-century piece, and they were in place for only a few measures. In the second case, with the double sharp, the music was transitioning to a sharp key; for consistency with the following measures, it was written with sharps instead of flats. Also, I play a transposing instrument, and the score had fewer accidentals. Even accepting those justifications, the key signature for G# Major would have been a lie since it reflected neither the melody scale nor the chords; in any case, since my part happened to use only a few notes of the scale during that period, the publisher simply saved ink and confusion by leaving the rest out.
I spoke with someone who ran a sheet music business on Broadway decades ago. He had a pretty low opinion of a copyist who would use such tactics. Nowadays sheet music software usually makes such things impossible. Still, I think it’s an object lesson that the sheet music is a representation and not the music itself.

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