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". More specifically, an interval can be classified as a tritone if it is reasonably mapped to 12\24. The use of 24edo's 12\24 rather than 12edo's 6\12 better captures the characteristics of many intervals in the 11- and 13-limit.
The following table compares selected JI tritone pairs and the commas separating them:
| Ratios | Prime limit |
Distance from 600 ¢ |
Comma |
|---|---|---|---|
| 729/512, 1024/729 | 3 | 11.730 | 531441/524288 |
| 45/32, 64/45 | 5 | 9.776 | 2048/2025 |
| 7/5, 10/7 | 7 | 17.488 | 50/49 |
| 99/70, 140/99 | 11 | 0.088 | 9801/9800 |
| 13/9, 18/13 | 13 | 36.618 | 169/162 |
| 24/17, 17/12 | 17 | 3.000 | 289/288 |
| 27/19, 38/27 | 19 | 8.352 | 729/722 |
| 23/16, 32/23 | 23 | 28.274 | 544/529 |
| 41/29, 58/41 | 41 | 0.515 | 1682/1681 |