Quarter-tone
A quarter tone is an interval half as wide (aurally, or logarithmically) as a semitone, which is half a whole tone.
In equal temperament the quarter tone is 50 cents or 21/24 or 1.029302236643. In 24 tone equal temperament, or the quarter tone scale, it is the smallest step. In just intonation it is often 36:35 or 33:34.
Many composers are known for having written music including quarter tones or the quarter tone scale, including:
List of quarter tone pieces
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