Tritone: Difference between revisions
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Added commas separating the tritone pairs |
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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". | 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: | The following table compares selected JI tritone pairs and the commas separating them: | ||
{| class="wikitable sortable center-all right-3" | {| class="wikitable sortable center-all right-3" | ||
| Line 9: | Line 9: | ||
! | prime limit | ! | prime limit | ||
! | distance from 600{{cent}} | ! | distance from 600{{cent}} | ||
!comma | |||
|- | |- | ||
| [[729/512]], [[1024/729]] | | [[729/512]], [[1024/729]] | ||
| 3 | | 3 | ||
| 11.730 | | 11.730 | ||
|[[Pythagorean comma|531441/524288]] | |||
|- | |- | ||
| [[45/32]], [[64/45]] | | [[45/32]], [[64/45]] | ||
| 5 | | 5 | ||
| 9.776 | | 9.776 | ||
|[[Diaschisma|2048/2025]] | |||
|- | |- | ||
| [[7/5]], [[10/7]] | | [[7/5]], [[10/7]] | ||
| 7 | | 7 | ||
| 17.488 | | 17.488 | ||
|[[50/49]] | |||
|- | |- | ||
| [[99/70]], [[140/99]] | | [[99/70]], [[140/99]] | ||
| 11 | | 11 | ||
| 0.088 | | 0.088 | ||
|[[9801/9800]] | |||
|- | |- | ||
| [[13/9]], [[18/13]] | | [[13/9]], [[18/13]] | ||
| 13 | | 13 | ||
| 36.618 | | 36.618 | ||
|[[169/162]] | |||
|- | |- | ||
| [[24/17]], [[17/12]] | | [[24/17]], [[17/12]] | ||
| 17 | | 17 | ||
| 3.000 | | 3.000 | ||
|[[289/288]] | |||
|- | |- | ||
| [[27/19]], [[38/27]] | | [[27/19]], [[38/27]] | ||
| 19 | | 19 | ||
| 8.352 | | 8.352 | ||
|[[729/722]] | |||
|- | |- | ||
| [[23/16]], [[32/23]] | | [[23/16]], [[32/23]] | ||
| 23 | | 23 | ||
| 28.274 | | 28.274 | ||
|[[544/529]] | |||
|- | |- | ||
| 41/29, 58/41 | | 41/29, 58/41 | ||
| 41 | | 41 | ||
| 0.515 | | 0.515 | ||
|[[1682/1681]] | |||
|} | |} | ||
[[Category:Tritone]] <!-- main article --> | [[Category:Tritone]] <!-- main article --> | ||
Revision as of 05:39, 23 December 2024
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 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 |