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For example, in 31-TET, all tones are accessible via (double) sharps or (double) flats on CDEFGAB. So there exists key signatures, for example, D double-flat major. (That's same as C half-sharp major.) Wikipedia has a comprehensive list of the keys.

But what for 24-TET? The in-between tones are not accessible via sharps nor flats on CDEFGAB. I can't think of the key signature, for example, C half-sharp major. How should they be denoted?

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  • Most musicians interpret "D Double Flat" tro be enharmonically equivalent to C, whereas you seem to be using the term to describe what others call "D three-halves flat", sometimes represented by a backwards flat next to a regular flat.
    – user45266
    Oct 17, 2019 at 23:55
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    @user45266 That applies to 24-TET, but not in 31-TET. In 31-TET, D double flat is C half-sharp, and D three-halves flat is C sharp.
    – Dannyu NDos
    Oct 18, 2019 at 1:59

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A quartertone key signature sounds extremely complicated and painful to read.

If for some reason you need to notate a piece in a quartertone key I'd say add staff text at the beginning of the piece telling the performer to re-tune their instrument a quartertone up or down and use the nearest normal key signature.

Alternatively, use no key signature and go wild with the half-accidentals.

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A quick DuckDuckGo search for ‘24-TET notation’ leads to the wikipedia article on quarter tones which shows one possible notation system ,and to Introduction to quarter tones which details another.

As a player who only ever produces quarter tones accidentally or as part of a slide, I cannot advise on which is ‘better’ ...

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