13/12

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Interval information
Ratio 13/12
Monzo |-2 -1 0 0 0 1>
Size in cents 138.57266
Name(s) tredecimal neutral second
Color name 3o2, tho 2nd

[sound info]

In 13-limit Just Intonation, 13/12 is a neutral second of about 138.6¢. It is a superparticular interval, as it is found in the harmonic series between the 13th and the 12th overtone (between 13/8 and 3/2 in the octave). It is flat of the 11-limit lesser neutral second of 12/11 by 144/143 (about 12.1¢), and sharp of the 13-limit large semitone of 14/13 by 169/168 (about 10.3¢).

The neutral second in 17edo is about 141.2¢, about 2.6¢ sharp of 13/12. Thus, if 10\17 (ten degrees of 17edo) is taken to approximate 3/2 and 12\17 taken to approximate 13/8, you can generate a 13-limit harmonic triad that approximates an 8:12:13 chord with a good 13/12.

See also Gallery of Just Intervals