Wollemia: Difference between revisions
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m Separate the comma groups with ";", as elsewhere in the field and on other regtemp pages |
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| Title = Wollemia | | Title = Wollemia | ||
| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13 | | Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13 | ||
| Comma basis = [[126/125]], [[2240/2187]] (7-limit);<br>[[56/55]], [[100/99]], [[243/242]] (11-limit)<br>[[56/55]], [[91/90]], [[100/99]], [[243/242]]<br>(13-limit) | | Comma basis = [[126/125]], [[2240/2187]] (7-limit);<br>[[56/55]], [[100/99]], [[243/242]] (11-limit);<br>[[56/55]], [[91/90]], [[100/99]], [[243/242]]<br>(13-limit) | ||
| Edo join 1 = 27e | Edo join 2 = 34 | | Edo join 1 = 27e | Edo join 2 = 34 | ||
| Mapping = 1; 4 9 19 10 -2 | | Mapping = 1; 4 9 19 10 -2 | ||
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The '''wollemia''' [[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 '''wollemia''' [[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, wollemia tempers out [[126/125]], making it a [[ | In addition to the tetracot comma, wollemia tempers out [[126/125]], making it a [[starling temperaments|starling temperament]]. | ||
See [[Tetracot family #Wollemia]] for technical data. | |||
{{Todo|inline=1|expand}} | {{Todo|inline=1|expand}} | ||
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| | | | ||
| 171.429 | | 171.429 | ||
| | | 7d val | ||
|- | |- | ||
| | | | ||
Latest revision as of 15:19, 8 September 2026
| Wollemia |
56/55, 100/99, 243/242 (11-limit);
56/55, 91/90, 100/99, 243/242
(13-limit)
13-odd-limit: 21.7 ¢
13-odd-limit: 27 notes
The wollemia 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, wollemia tempers out 126/125, making it a starling temperament.
See Tetracot family #Wollemia for technical data.
|
Todo: expand |
Interval chain
| # | Cents* | Approximate ratios |
|---|---|---|
| 0 | 0.0 | 1/1 |
| 1 | 177.1 | 10/9, 11/10 |
| 2 | 354.2 | 11/9, 16/13 |
| 3 | 531.3 | 15/11 |
| 4 | 708.4 | 3/2 |
| 5 | 885.5 | 5/3 |
| 6 | 1062.6 | 11/6, 24/13, 28/15 |
| 7 | 39.7 | 40/39, 45/44, 55/54 |
| 8 | 216.8 | 9/8 |
| 9 | 393.9 | 5/4, 14/11 |
| 10 | 570.9 | 7/5, 11/8, 18/13 |
| 11 | 748.0 | 14/9, 20/13 |
| 12 | 925.1 | 22/13 |
| 13 | 1102.2 | 15/8, 21/11 |
| 14 | 79.3 | 21/20, 25/24, 27/26 |
| 15 | 256.4 | 7/6, 15/13 |
| 16 | 433.5 | 33/26, 35/27 |
| 17 | 610.6 | 45/32, 63/44 |
| 18 | 787.7 | 25/16 |
| 19 | 964.8 | 7/4 |
| 20 | 1141.9 | 35/18, 49/25 |
* 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 | ||
| 11/6 | 174.894 | ||
| 11/8 | 175.132 | ||
| 3/2 | 175.489 | ||
| 13/11 | 175.899 | ||
| 15/8 | 176.021 | ||
| 5/4 | 176.257 | 5-odd-limit minimax | |
| 13/9 | 176.338 | ||
| 5\34 | 176.471 | Lower bound of 7- to 13-odd-limit diamond monotone | |
| 15/13 | 176.516 | ||
| 5/3 | 176.872 | ||
| 13/10 | 176.890 | ||
| 13/12 | 176.905 | ||
| 7/4 | 177.307 | 7-, 9-, 11-, 13- and 15-odd-limit minimax | |
| 13/7 | 177.538 | ||
| 4\27 | 177.777 | 27e val, upper bound of 9- to 13-odd-limit diamond monotone 15-odd-limit diamond monotone (singleton) | |
| 7/6 | 177.791 | ||
| 7/5 | 178.251 | ||
| 9/7 | 178.629 | ||
| 15/11 | 178.984 | ||
| 11/7 | 179.723 | ||
| 13/8 | 179.736 | ||
| 3\20 | 180.000 | 20cde val, upper bound of 7-odd-limit diamond monotone | |
| 15/14 | 180.093 | ||
| 9/5 | 182.404 |