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Do frequencies between each note (A, A#, B...) have a specific name?

E.g.:

A5 has a frequency of 880.00 Hz. and A#5 has a frequency of 932.33 Hz., how do we identify frequencies that are inbetween these notes?

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I am going to refer you to another post on the StackExchange where this question is answered in substantial depth. Other musical notation systems have more than 12 notes per octave, and have names for the notes in their systems which you could use to describe the so-called "microtones" between the notes of the chromatic scale. Interestingly enough, the 12-tone "Western" chromatic scale you site is itself a set of names for tones in-between the 6-note octave or the 8-note octave.

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