Opossum: Difference between revisions
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m Text replacement - "Eigenmonzo<br>(unchanged-interval)" to "Unchanged interval<br>(eigenmonzo)" |
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== Tunings == | == Tunings == | ||
{| class="wikitable center-1 mw-collapsible mw-collapsed" | |||
{| class="wikitable center-1" | |+ style="font-size: 105%; white-space: nowrap;" | Least-squares tunings | ||
|- | |- | ||
! Target | ! Target | ||
| Line 91: | Line 91: | ||
|- | |- | ||
! Edo<br>generator | ! Edo<br>generator | ||
! [[Eigenmonzo| | ! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]] | ||
! Generator (¢) | ! Generator (¢) | ||
! Comments | ! Comments | ||
| Line 118: | Line 118: | ||
| | | | ||
| 150.000 | | 150.000 | ||
| | | 8d val, lower bound of 7-odd-limit diamond monotone | ||
|- | |- | ||
| | | | ||
| Line 153: | Line 153: | ||
| | | | ||
| 156.522 | | 156.522 | ||
| | | 23bcf val | ||
|- | |- | ||
| | | | ||
| Line 163: | Line 163: | ||
| | | | ||
| 157.895 | | 157.895 | ||
| | | 38bceff val | ||
|- | |- | ||
| 7\53 | | 7\53 | ||
| | | | ||
| 158.491 | | 158.491 | ||
| | | 53bcefff val | ||
|- | |- | ||
| | | | ||
Latest revision as of 06:56, 21 June 2025
Opossum is an alternative extension to porcupine. It is defined by tempering out 28/27 and 126/125.
See Porcupine family #Opossum for technical data.
Interval chain
In the following table, odd harmonics 1–11 and their inverses are in bold.
| # | Cents* | Approximate ratios* |
|---|---|---|
| 0 | 0.0 | 1/1 |
| 1 | 160.0 | 10/9, 11/10, 12/11, 15/14 |
| 2 | 320.0 | 6/5, 11/9 |
| 3 | 480.0 | 4/3, 9/7 |
| 4 | 640.0 | 10/7, 16/11, 22/15 |
| 5 | 800.0 | 8/5, 11/7 |
| 6 | 960.0 | 12/7, 16/9 |
| 7 | 1120.0 | 40/21, 48/25, 64/33 |
| 8 | 80.0 | 16/15, 36/35 |
| 9 | 240.0 | 8/7 |
* In 15edo tuning, octave reduced
Tunings
| Target | Generator | Eigenmonzo |
|---|---|---|
| 5-odd-limit | ~10/9 = 162.996 ¢ | 262144/234375 |
| 7-odd-limit | ~10/9 = 158.732 ¢ | [0 -5 3 19⟩ |
| 9-odd-limit | ~12/11 = 159.481 ¢ | [0 3 2 22⟩ |
| 11-odd-limit | ~12/11 = 159.564 ¢ | [-27 2 1 9 -1⟩ |
| 13-odd-limit | ~12/11 = 158.421 ¢ | [0 15 6 34 -1 -15⟩ |
| 15-odd-limit | ~12/11 = 159.377 ¢ | [0 32 23 35 -5 -21⟩ |
Tuning spectrum
| Edo generator |
Unchanged interval (eigenmonzo) |
Generator (¢) | Comments |
|---|---|---|---|
| 15/14 | 119.443 | ||
| 13/12 | 138.573 | ||
| 13/11 | 144.605 | ||
| 9/7 | 145.028 | ||
| 1\8 | 150.000 | 8d val, lower bound of 7-odd-limit diamond monotone | |
| 11/6 | 150.637 | ||
| 13/10 | 151.405 | ||
| 13/7 | 153.100 | ||
| 7/5 | 154.372 | ||
| 7/6 | 155.522 | ||
| 11/7 | 156.498 | ||
| 3\23 | 156.522 | 23bcf val | |
| 5/3 | 157.821 | ||
| 5\38 | 157.895 | 38bceff val | |
| 7\53 | 158.491 | 53bcefff val | |
| 15/13 | 158.710 | ||
| 7/4 | 159.019 | 7-, 9-, 11-, 13- and 15-odd-limit minimax | |
| 13/9 | 159.154 | ||
| 2\15 | 160.000 | Upper bound of 7-odd-limit diamond monotone 9- and 11-odd-limit diamond monotone (singleton) | |
| 11/8 | 162.171 | ||
| 5/4 | 162.737 | 5-odd-limit minimax | |
| 15/8 | 163.966 | ||
| 11/10 | 165.004 | ||
| 15/11 | 165.762 | ||
| 3/2 | 166.015 | ||
| 11/9 | 173.704 | ||
| 13/8 | 179.736 | ||
| 9/5 | 182.404 |