Bunya: Difference between revisions
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Complete intro and interval table |
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The '''bunya''' [[regular temperament|temperament]] is one of the [[7-limit]] [[extension]]s of [[tetracot]], the [[5-limit]] temperament [[tempering out]] the [[tetracot comma]] (20000/19683), and is naturally a full [[13-limit]] temperament. | The '''bunya''' [[regular temperament|temperament]] is one of the [[7-limit]] [[extension]]s 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 temperaments|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. | |||
== Interval chain == | == Interval chain == | ||
| Line 26: | Line 28: | ||
|- | |- | ||
| 0 | | 0 | ||
| 0. | | 0.0 | ||
| '''1/1''' | | '''1/1''' | ||
|- | |- | ||
| 1 | | 1 | ||
| 175. | | 175.9 | ||
| 10/9, 11/10 | | 10/9, 11/10 | ||
|- | |- | ||
| 2 | | 2 | ||
| 351. | | 351.7 | ||
| 11/9, '''16/13''' | | 11/9, '''16/13''' | ||
|- | |- | ||
| 3 | | 3 | ||
| 527. | | 527.6 | ||
| 15/11 | | 15/11 | ||
|- | |- | ||
| 4 | | 4 | ||
| 703. | | 703.4 | ||
| '''3/2''' | | '''3/2''' | ||
|- | |- | ||
| 5 | | 5 | ||
| 879. | | 879.3 | ||
| 5/3 | | 5/3 | ||
|- | |- | ||
| 6 | | 6 | ||
| 1055. | | 1055.1 | ||
| 11/6, 24/13 | | 11/6, 24/13 | ||
|- | |- | ||
| 7 | | 7 | ||
| 31. | | 31.0 | ||
| 40/39, 45/44, 55/54, 56/55 | | 40/39, 45/44, 55/54, 56/55 | ||
|- | |- | ||
| 8 | | 8 | ||
| | | 206.8 | ||
| '''9/8''' | | '''9/8''' | ||
|- | |- | ||
| 9 | | 9 | ||
| 382. | | 382.7 | ||
| '''5/4''' | | '''5/4''' | ||
|- | |- | ||
| 10 | | 10 | ||
| 558. | | 558.5 | ||
| '''11/8''', 18/13 | | '''11/8''', 18/13 | ||
|- | |- | ||
| 11 | | 11 | ||
| 734. | | 734.4 | ||
| 20/13 | | 20/13 | ||
|- | |- | ||
| 12 | | 12 | ||
| 910. | | 910.2 | ||
| 22/13 | | 22/13 | ||
|- | |- | ||
| 13 | | 13 | ||
| 1086. | | 1086.1 | ||
| 15/8, 28/15 | | 15/8, 28/15 | ||
|- | |- | ||
| 14 | | 14 | ||
| | | 61.9 | ||
| 25/24, 27/26, 28/27, 33/32 | | 25/24, 27/26, 28/27, 33/32 | ||
|- | |- | ||
| 15 | | 15 | ||
| | | 237.8 | ||
| 15/13 | | 15/13 | ||
|- | |- | ||
| 16 | | 16 | ||
| | | 413.6 | ||
| 14/11 | | 14/11 | ||
|- | |- | ||
| 17 | | 17 | ||
| | | 589.5 | ||
| 7/5 | | 7/5 | ||
|- | |- | ||
| 18 | | 18 | ||
| 765. | | 765.3 | ||
| 14/9 | | 14/9 | ||
|- | |- | ||
| 19 | | 19 | ||
| 941. | | 941.2 | ||
| | | 45/26 | ||
|- | |- | ||
| 20 | | 20 | ||
| 1117. | | 1117.1 | ||
| 21/11 | | 21/11 | ||
|- | |- | ||
| 21 | | 21 | ||
| | | 92.9 | ||
| 21/20 | | 21/20 | ||
|- | |- | ||
| 22 | | 22 | ||
| | | 268.8 | ||
| 7/6 | | 7/6 | ||
|- | |- | ||
| 23 | | 23 | ||
| | | 444.6 | ||
| | | 35/27 | ||
|- | |- | ||
| 24 | | 24 | ||
| | | 620.5 | ||
| | | 56/39, 63/44 | ||
|- | |- | ||
| 25 | | 25 | ||
| | | 796.3 | ||
| | | 63/40 | ||
|- | |- | ||
| 26 | | 26 | ||
| | | 972.2 | ||
| '''7/4''' | | '''7/4''' | ||
|- | |- | ||
| 27 | | 27 | ||
| 1148. | | 1148.0 | ||
| 35/18 | | 35/18 | ||
|} | |} | ||
<nowiki/>* In 13-limit | <nowiki/>* In 13-limit CWE tuning, octave reduced | ||
== Tunings == | == Tunings == | ||
Revision as of 09:50, 30 April 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.
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
| Eigenmonzo (unchanged-interval) |
Generator (¢) | Comments |
|---|---|---|
| 11/10 | 165.004 | |
| 11/9 | 173.704 | |
| 12/11 | 174.894 | |
| 11/8 | 175.132 | |
| 15/14 | 175.427 | |
| 7/5 | 175.442 | 11-odd-limit minimax |
| 4/3 | 175.489 | |
| 8/7 | 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 |
| 14/13 | 176.011 | |
| 16/15 | 176.021 | |
| 14/11 | 176.094 | |
| 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 |