Monkey
The monkey temperament is one of the 7-limit extensions of tetracot, the 5-limit temperament tempering out the tetracot comma (15625/15552), and is naturally a full 13-limit temperament.
| Monkey |
100/99, 243/242, 385/384 (11-limit)
100/99, 144/143, 243/242, 385/384
(13-limit)
13-limit 21-odd-limit: 12.8 ¢
13-limit 21-odd-limit: 34 notes
In addition to the tetracot comma, monkey tempers out 875/864, making it a keemic temperament. It also tempers out 5120/5103, making it a hemifamity temperament, so the septimal comma is equated with the syntonic comma. At 7 generator steps, this diesis-sized interval also represents 40/39, 45/44, 55/54, 65/64, 66/65, and 121/120 in the 2.3.5.7.13-subgroup version of tetracot, and divides the chromatic semitone in four. The same interval is now used to bridge septimal intervals with Pythagorean intervals alike.
Additionally, the generator can be taken to represent 21/19, which gives us an extension for prime 19 at -12 generator steps.
See Tetracot family #Monkey for technical data.
Interval chain
In the following tables, odd harmonics 1–13 and their inverses are in bold.
| # | Cents* | Approximate ratios |
|---|---|---|
| 0 | 0.0 | 1/1 |
| 1 | 175.6 | 11/10, 10/9 |
| 2 | 351.2 | 11/9, 16/13 |
| 3 | 526.9 | 15/11 |
| 4 | 702.5 | 3/2 |
| 5 | 878.1 | 5/3 |
| 6 | 1053.7 | 11/6, 24/13 |
| 7 | 29.4 | 40/39, 45/44, 55/54, 64/63 |
| 8 | 205.0 | 9/8 |
| 9 | 380.6 | 5/4 |
| 10 | 556.2 | 11/8, 18/13 |
| 11 | 731.8 | 20/13, 32/21 |
| 12 | 907.5 | 22/13 |
| 13 | 1083.1 | 13/7, 15/8 |
| 14 | 58.7 | 25/24, 27/26, 33/32, 36/35 |
| 15 | 234.3 | 8/7, 15/13 |
| 16 | 409.9 | 33/26 |
| 17 | 585.6 | 45/32, 88/63 |
| 18 | 761.2 | 25/16, 54/35 |
| 19 | 936.8 | 12/7 |
| 20 | 1112.4 | 40/21 |
| 21 | 88.1 | 22/21 |
| 22 | 263.7 | 75/64, 81/70 |
| 23 | 439.3 | 9/7 |
| 24 | 614.9 | 10/7 |
| 25 | 790.5 | 11/7 |
| 26 | 966.2 | 225/128, 243/140, 256/147 |
| 27 | 1141.8 | 27/14 |
* In 13-limit CWE tuning, octave reduced
Tunings
Tuning spectrum
| Eigenmonzo (unchanged-interval) |
Generator (¢) | Comments |
|---|---|---|
| 11/10 | 165.004 | |
| 11/9 | 173.704 | |
| 14/13 | 174.746 | |
| 12/11 | 174.894 | |
| 11/8 | 175.132 | |
| 14/11 | 175.300 | 11-odd-limit minimax |
| 8/7 | 175.412 | |
| 7/6 | 175.428 | |
| 9/7 | 175.438 | |
| 4/3 | 175.489 | |
| 15/14 | 175.694 | |
| 7/5 | 175.729 | 7, 9, 13 and 15-odd-limit minimax |
| 13/11 | 175.899 | |
| 16/15 | 176.021 | |
| 5/4 | 176.257 | 5-odd-limit minimax |
| 18/13 | 176.338 | |
| 15/13 | 176.516 | |
| 6/5 | 176.872 | |
| 13/10 | 176.890 | |
| 13/12 | 176.905 | |
| 15/11 | 178.984 | |
| 16/13 | 179.736 | |
| 10/9 | 182.404 |