Bunya: Difference between revisions
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Complete tuning spectrum |
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Additionally, the generator can be taken to represent [[21/19]], which gives us an extension for prime 19 at +29 generator steps. | Additionally, the generator can be taken to represent [[21/19]], which gives us an extension for prime 19 at +29 generator steps. | ||
See [[Tetracot family #Bunya]] for technical data. | |||
== Interval chain == | == Interval chain == | ||
Latest revision as of 10:38, 30 May 2026
| Bunya |
100/99, 225/224, 243/242 (11-limit)
100/99, 144/143, 225/224, 243/242
(13-limit)
13-odd-limit: 10.9 ¢
13-odd-limit: 34 notes
The bunya temperament is one of the 7-limit extensions of tetracot, the 5-limit temperament tempering out the tetracot comma (20000/19683), and is naturally a full 13-limit temperament.
In addition to the tetracot comma, bunya tempers out 225/224, making it a marvel temperament. This means the ~15/8, at 13 generator steps, is equated with ~28/15, and ~7/4 is found as twice of that interval.
Additionally, the generator can be taken to represent 21/19, which gives us an extension for prime 19 at +29 generator steps.
See Tetracot family #Bunya 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 | 175.9 | 10/9, 11/10 |
| 2 | 351.7 | 11/9, 16/13 |
| 3 | 527.6 | 15/11 |
| 4 | 703.4 | 3/2 |
| 5 | 879.3 | 5/3 |
| 6 | 1055.1 | 11/6, 24/13 |
| 7 | 31.0 | 40/39, 45/44, 55/54, 56/55 |
| 8 | 206.8 | 9/8 |
| 9 | 382.7 | 5/4 |
| 10 | 558.5 | 11/8, 18/13 |
| 11 | 734.4 | 20/13 |
| 12 | 910.2 | 22/13 |
| 13 | 1086.1 | 15/8, 28/15 |
| 14 | 61.9 | 25/24, 27/26, 28/27, 33/32 |
| 15 | 237.8 | 15/13 |
| 16 | 413.6 | 14/11 |
| 17 | 589.5 | 7/5 |
| 18 | 765.3 | 14/9 |
| 19 | 941.2 | 45/26 |
| 20 | 1117.1 | 21/11 |
| 21 | 92.9 | 21/20 |
| 22 | 268.8 | 7/6 |
| 23 | 444.6 | 35/27 |
| 24 | 620.5 | 56/39, 63/44 |
| 25 | 796.3 | 63/40 |
| 26 | 972.2 | 7/4 |
| 27 | 1148.0 | 35/18 |
* In 13-limit CWE tuning, octave reduced
Tunings
Tuning spectrum
| Edo generator |
Eigenmonzo (unchanged-interval) |
Generator (¢) | Comments |
|---|---|---|---|
| 11/10 | 165.004 | ||
| 1\7 | 171.429 | 7d val | |
| 11/9 | 173.704 | ||
| 12/11 | 174.894 | ||
| 7\48 | 175.000 | 48d val, lower bound of 7- to 13-odd-limit diamond monotone | |
| 11/8 | 175.132 | ||
| 15/14 | 175.427 | ||
| 7/5 | 175.442 | 11-odd-limit minimax | |
| 3/2 | 175.489 | ||
| 6\41 | 175.610 | Lower bound of 15-odd-limit diamond monotone | |
| 7/4 | 175.724 | ||
| 7/6 | 175.767 | 7-odd-limit minimax | |
| 9/7 | 175.829 | 9-odd-limit minimax | |
| 13/11 | 175.899 | 13- and 15-odd-limit minimax | |
| 11\75 | 176.000 | ||
| 13/7 | 176.011 | ||
| 15/8 | 176.021 | ||
| 11/7 | 176.094 | ||
| 5/4 | 176.257 | 5-odd-limit minimax | |
| 13/9 | 176.338 | ||
| 5\34 | 176.471 | 34d val, upper bound of 7- to 15-odd-limit diamond monotone | |
| 15/13 | 176.516 | ||
| 5/3 | 176.872 | ||
| 13/10 | 176.890 | ||
| 13/12 | 176.905 | ||
| 4\27 | 177.778 | 27dde val | |
| 15/11 | 178.984 | ||
| 13/8 | 179.736 | ||
| 3\20 | 180.000 | 20cddde val | |
| 9/5 | 182.404 |