Microtonality

Physics: 12-TET errors vs just intonation: M3=+13.7¢, m7=−31.2¢, P5=−2¢. 19-TET: better M3 (−7.4¢). 31-TET: near-perfect 5-limit JI (M3=−5.1¢, P5=−0.2¢). 53-TET: extremely accurate (M3=+1.4¢). 72-TET: standard in microtonality communities. Harry Partch: 43-tone 11-limit just scale. Quarter-tone (24-TET): Arabic maqam, Hába. Spectral music (Murail, Grisey): tune chords to overtone series. Bohlen-Pierce: tritave (3:1) divided into 13 steps. 1200 cents = 1 octave.