24-tone Equal Temperament divides the intervals of Western-standard 12-tone Equal Temperament, so that there are 24 equal divisions to the octave instead of 12. The notes between the notes of the 12-tone Equal Temperament scale (aka "Chromatic Scale") are thus referred to as quarter-tones.
This excellent lecture by Sami Abu Shumays explains the problem of trying to shoehorn Arabic maqam into strict 24-tone Equal Temperament, as part of a general introduction into the use of microtones in Arabic Music.
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