Porcupine: Difference between revisions
→Tuning spectra: +diamond monotone and tradeoffs |
→Tuning spectra: +prime-optimized tunings |
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* [[porcupinewoo22]] | * [[porcupinewoo22]] | ||
== | == Tunings == | ||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+style=white-space:nowrap | 5-limit Prime-Optimized Tunings | |||
|- | |||
! Weight-skew\Order !! Euclidean | |||
|- | |||
| Tenney || CTE<br>~10/9 = 164.1659¢ | |||
|- | |||
| Tenney-Weil || CTWE<br>~10/9 = 164.0621¢ | |||
|- | |||
| Equilateral || CEE<br>~10/9 = 163.6049¢<br>Eigenmonzo basis: 2.84375 | |||
|- | |||
| Equilateral-Weil || CEWE<br>~10/9 = 163.2835¢<br>Eigenmonzo basis: 2.375 | |||
|- | |||
| Benedetti || CBE<br>~10/9 = 164.3761¢<br>Eigenmonzo basis: 2.30375 | |||
|- | |||
| Benedetti-Weil || CBWE<br>~10/9 = 164.3761¢<br>Eigenmonzo basis: 2.30375 | |||
|} | |||
=== | {| class="wikitable mw-collapsible mw-collapsed" | ||
|+style=white-space:nowrap | 2.3.5.11 Subgroup Prime-Optimized Tunings | |||
|- | |||
! Weight-skew\Order !! Euclidean | |||
|- | |||
| Tenney || CTE<br>~11/10 = 163.8867¢ | |||
|- | |||
| Tenney-Weil || CTWE<br>~11/10 = 163.9951¢ | |||
|- | |||
| Equilateral || CEE<br>~11/10 = 163.1459¢<br>Eigenmonzo basis: 2.{{monzo| 0 3 5 4 }} | |||
|- | |||
| Equilateral-Weil || CEWE<br>~11/10 = 162.8445¢<br>Eigenmonzo basis: 2.{{monzo| 0 3 13 8 }} | |||
|- | |||
| Benedetti || CBE<br>~11/10 = 164.2393¢<br>Eigenmonzo basis: 2.{{monzo| 0 605 363 60 }} | |||
|- | |||
| Benedetti-Weil || CBWE<br>~11/10 = 164.4623¢<br>Eigenmonzo basis: 2.{{monzo| 0 -1595 -957 90 }} | |||
|} | |||
=== Tuning spectra === | |||
{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
|+ Tuning spectrum of 13-limit porcupine | |||
! Edo<br>Generator | ! Edo<br>Generator | ||
! [[Eigenmonzo|Eigenmonzo<br>(Unchanged Interval)]] | ! [[Eigenmonzo|Eigenmonzo<br>(Unchanged Interval)]] | ||
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| 6/5 | | 6/5 | ||
| 157.821 | | 157.821 | ||
| Lower bound of 5, 7-, and 9-odd-limit diamond tradeoff | | Lower bound of 5-, 7-, and 9-odd-limit diamond tradeoff | ||
|- | |- | ||
| | | | ||
| Line 224: | Line 259: | ||
| | | | ||
| 160.000 | | 160.000 | ||
| Lower bound of 7, 9, and 11-odd-limit diamond monotone | | Lower bound of 7-, 9-, and 11-odd-limit diamond monotone | ||
|- | |- | ||
| | | | ||
| Line 274: | Line 309: | ||
| | | | ||
| 163.636 | | 163.636 | ||
| Upper bound of 7, 9, and 11-odd-limit diamond monotone | | Upper bound of 7-, 9-, and 11-odd-limit diamond monotone | ||
|- | |- | ||
| | | | ||
| Line 336: | Line 371: | ||
| Upper bound of 9- and 11-odd-limit diamond tradeoff | | Upper bound of 9- and 11-odd-limit diamond tradeoff | ||
|} | |} | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
! Edo Generator | |+ Tuning spectrum of porcupinefish | ||
! Edo<br>Generator | |||
! Eigenmonzo<br>(Unchanged Interval) | ! Eigenmonzo<br>(Unchanged Interval) | ||
! Generator (¢) | ! Generator (¢) | ||