Tritone

The tritone is the name of a musical interval that is made up of three whole tones. In 12edo, the tritone is exactly 600 ¢, or sqrt(2), and due to the predominance of this tuning, the term is also used generally to refer to any pitch in the neighborhood of 600 ¢, or roughly halfway between 4/3 and 3/2. In Medieval music theory, "tritone" referred more specifically to 729/512, this being the interval found by combining three (whole) tones: (9/8)3.

In tunings other than 12edo, and particularly in just intonation, there are a number of different tritones which have subtly different flavors, such as 7/5 and 10/7. The temperament eliminating 50/49 is of particular interest in that it equates these two tritones, and provides a JI basis for the 12edo concept of the "tritone substitution".

The following table compares selected JI tritone pairs:

Ratios	prime limit	distance from 600 ¢
729/512, 1024/729	3	11.730
45/32, 64/45	5	9.776
7/5, 10/7	7	17.488
99/70, 140/99	11	0.088
13/9, 18/13	13	36.618
24/17, 17/12	17	3.000
27/19, 38/27	19	8.352
23/16, 32/23	23	28.274
41/29, 58/41	41	0.515