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How are sharps and flats written in the Nashville Number System? 5♯ or 5♭?

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Sharps and flats should be written as you guessed, after the number and using ♯/♭ notation. However, in common usage, some musicians use the flat symbol before the note rather than after it while still using the sharp symbol afterwards, e.g. ♭5 and 4♯.

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According to Wikipedia:

Accidentals modifying a scale degree are usually written to the left of the number. ♭7 ("flat 7") represents a B♭ major chord in the key of C, or an A♭ major chord in the key of B♭, or an F major chord in the key of G.

Music Theory for Musicians also indicates the accidental comes before the number, though giving only the example of b7.

All other sources consulted, if they addressed accidentals at all, only addressed b7.

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