Key signatures with Quarter Tones

Question

I know how to write the key signatures for any note within the 12-note chromatic scale. I know this doesn't come up very often, but what are some ways to write out key signatures for passages of music in a key center based off of a quarter tone?

For example, I know A major has 3 sharps. What would a key signature look like for A half-sharp major?

• I considered simply notating something like "A=453hz" and writing in A, but shifting between tuning systems can get a bit unwieldy (especially if performing on a real instrument) and I'd rather avoid that.
• I considered having three "3/2 sharp" glyphs on F, C, and G, and placing a "1/2 sharp" glyph on D, A, E, and B. I noticed, though, that under this system, every microtonal key signature has seven accidentals in it, and a lot of them have "1/2 sharp" and "1/2 flat" signs in the same key signature (example: G 1/2 flat major).
• I also considered shorthanding them, writing "3/2 sharp" glyphs on F, C, and G, and leaving the other notes with nothing. One advantage of this is that the visual look of A major is preserved, with the three sharp-ish accidentals, and the performer would know that all the other notes logically must be 1/2 sharp. It would be like reading a normal key signature, then seeing the altered accidental and deducing that everything is a quarter tone flatter than A major.
• I'm open to other suggestions (as long as they use some form of microtonal key signatures) as well - there's probably a better system out there that I haven't discovered.

Answer 1

In this video, the semisharps are simply written out completely in the same order as the sharps would be. Later on he uses a combination of semiflats and semisharps while still sticking to the circle of fifths. Although it's in the context of 31 edo, it should still be applicable (and you probably won't need the key signatures with both sharps and flats because in 24edo, the two 12edo chains aren't linked). The description of the video has some resources as well, such as a list of 31edo key signatures and some of the sources that he used.

I don't think there's any existing convention, so you're free to make your own as long as you explain it.

Answer 2

In most cases, I'd use A=453.

There are a few reasons for this:
1. As you said, it is easier to notate and keeps it nice and clean
2. Any performer with enough skill to comfortably handle quarter tone notation won't be intimidated by an alternate tuning
3. Many instruments require frequent re-tuning back to A=440 anyway. Unless the musician has perfect pitch, you could just play A=453 as the tuning pitch and they probably wouldn't even notice!
4. If alternate tuning (and quarter tones themselves) are not possible, like on a piano, it is much easier for someone to quickly adapt and make playable (unless, of course, you make extensive use of quarter tone accidentals

Conversely, here are a few reasons you might consider another option:
1. Sheet music packed with lots of quarter tone accidentals can look freaking awesome! :)
2. If much of the song is in a standard key and tuning and you modulate to a half sharp key at some point

Answer 3

If you want normal intervals and notes but EVERYTHING out a quarter-tone, yes 'A=253' seems sensible.

Quarter-tones more often occur as accidentals within a normal chromatic A=440 framework. And there currently seems more interest in alternative tuning schemes producing 'pure' intervals than in quarter-tones as such.

Either way, they are outside the scope of standard key signatures. If you want to invent a custom notation, be sure to explain it!

Answer 4

If writing sheet music for A half sharp major, I would personally put a half sharp motif on all 7 notes at the beginning of the clef as well as the 3 sharps on F, C and G, as these 3 notes need to be sharpened by three quarters of a tone. I don't know if this is correct, but at least I would understand it?