Miracle extensions: Difference between revisions
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→Tuning spectra: cleanup |
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<nowiki/>* In 11-limit [[CWE tuning]], octave reduced | <nowiki/>* In 11-limit [[CWE tuning]], octave reduced | ||
== Tuning spectra == | == Tunings == | ||
=== Miraculous === | * 5-limit POTE: ~15/14 = 116.673 | ||
* 7-limit POTE: ~15/14 = 116.675 | |||
* 11-limit POTE | |||
** Miracle: ~15/14 = 116.633 | |||
** Revelation: ~15/14 = 116.277 | |||
* 13-limit POTE | |||
** Miraculous: ~15/14 = 116.747 | |||
** Benediction: ~15/14 = 116.574 | |||
** Manna: ~15/14 = 116.739 | |||
** Revelation: ~15/14 = 116.268 | |||
=== Tuning spectra === | |||
==== Miraculous ==== | |||
{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
|- | |- | ||
| Line 335: | Line 347: | ||
|- | |- | ||
| | | | ||
| | | 15/8 | ||
| 111.731 | | 111.731 | ||
| | | | ||
| Line 345: | Line 357: | ||
|- | |- | ||
| | | | ||
| | | 7/4 | ||
| 115.587 | | 115.587 | ||
| | | | ||
| Line 387: | Line 399: | ||
| {{monzo| 0 -27 25 5 }} | | {{monzo| 0 -27 25 5 }} | ||
| 116.573 | | 116.573 | ||
| 7 limit least squares | | 7-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| {{monzo| 0 -19 20 }} | | {{monzo| 0 -19 20 }} | ||
| 116.578 | | 116.578 | ||
| 5 limit least squares | | 5-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| | | 5/3 | ||
| 116.588 | | 116.588 | ||
| 5 and 7 limit minimax | | 5- and 7-odd-limit minimax | ||
|- | |- | ||
| | | | ||
| Line 405: | Line 417: | ||
|- | |- | ||
| | | | ||
| | | 11/6 | ||
| 116.596 | | 116.596 | ||
| | | | ||
|- | |- | ||
| | | | ||
| | | 11/7 | ||
| 116.617 | | 116.617 | ||
| | | | ||
|- | |- | ||
| | | | ||
| Line 432: | Line 439: | ||
| {{monzo| 0 17 -11 -6 11 }} | | {{monzo| 0 17 -11 -6 11 }} | ||
| 116.672 | | 116.672 | ||
| 11 limit least squares | | 11-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| | | 9/5 | ||
| 116.716 | | 116.716 | ||
| 9, 11 and 13 limit minimax | | 9-, 11- and 13-odd-limit minimax | ||
|- | |- | ||
| | | | ||
| {{monzo| 0 117 -44 -19 }} | | {{monzo| 0 117 -44 -19 }} | ||
| 116.721 | | 116.721 | ||
| 9 limit least squares | | 9-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| Line 477: | Line 469: | ||
| {{monzo| 0 127 -84 -36 100 -44 }} | | {{monzo| 0 127 -84 -36 100 -44 }} | ||
| 116.820 | | 116.820 | ||
| 15 limit least squares | | 15-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| {{monzo| 0 141 -70 -35 84 -42 }} | | {{monzo| 0 141 -70 -35 84 -42 }} | ||
| 116.846 | | 116.846 | ||
| 13 limit least squares | | 13-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| | | 3/2 | ||
| 116.993 | | 116.993 | ||
| 15 limit minimax | | 15-odd-limit minimax | ||
|- | |- | ||
| 4\41 | | 4\41 | ||
| Line 500: | Line 492: | ||
|- | |- | ||
| | | | ||
| | | 13/9 | ||
| 117.559 | | 117.559 | ||
| | | | ||
| Line 515: | Line 507: | ||
|- | |- | ||
| | | | ||
| | | 13/8 | ||
| 119.824 | | 119.824 | ||
| | | | ||
| Line 525: | Line 517: | ||
|- | |- | ||
| | | | ||
| | | 13/7 | ||
| 128.298 | | 128.298 | ||
| | | | ||
|} | |} | ||
=== Benediction === | ==== Benediction ==== | ||
{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
|- | |- | ||
| Line 539: | Line 531: | ||
|- | |- | ||
| | | | ||
| | | 15/8 | ||
| 111.731 | | 111.731 | ||
| | | | ||
|- | |- | ||
| | | | ||
| | | 7/4 | ||
| 115.587 | | 115.587 | ||
| | | | ||
| Line 569: | Line 561: | ||
|- | |- | ||
| | | | ||
| | | 13/8 | ||
| 116.455 | | 116.455 | ||
| | | | ||
| Line 584: | Line 576: | ||
|- | |- | ||
| | | | ||
| | | 13/7 | ||
| 116.509 | | 116.509 | ||
| | | | ||
| Line 606: | Line 598: | ||
| {{monzo| 0 -234 39 4 -115 228 }} | | {{monzo| 0 -234 39 4 -115 228 }} | ||
| 116.56309 | | 116.56309 | ||
| 13 limit least squares | | 13-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| {{monzo| 0 -251 22 5 -131 261 }} | | {{monzo| 0 -251 22 5 -131 261 }} | ||
| 116.56348 | | 116.56348 | ||
| 15 limit least squares | | 15-odd-limit least squares | ||
|- | |- | ||
| 17\175 | | 17\175 | ||
| Line 621: | Line 613: | ||
| {{monzo| 0 -27 25 5 }} | | {{monzo| 0 -27 25 5 }} | ||
| 116.573 | | 116.573 | ||
| 7 limit least squares | | 7-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| {{monzo| 0 -19 20 }} | | {{monzo| 0 -19 20 }} | ||
| 116.578 | | 116.578 | ||
| 5 limit least squares | | 5-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| 6/5 | | 6/5 | ||
| 116.588 | | 116.588 | ||
| 5, 7 and 15 limit minimax | | 5-, 7- and 15-odd-limit minimax | ||
|- | |- | ||
| | | | ||
| Line 644: | Line 631: | ||
|- | |- | ||
| | | | ||
| | | 13/9 | ||
| 116.595 | | 116.595 | ||
| 13 limit minimax | | 13-odd-limit minimax | ||
|- | |- | ||
| | | | ||
| | | 11/6 | ||
| 116.596 | | 116.596 | ||
| | | | ||
| Line 659: | Line 646: | ||
|- | |- | ||
| | | | ||
| | | 11/7 | ||
| 116.617 | | 116.617 | ||
| | | | ||
|- | |- | ||
| | | | ||
| Line 681: | Line 663: | ||
| {{monzo| 0 17 -11 -6 11 }} | | {{monzo| 0 17 -11 -6 11 }} | ||
| 116.672 | | 116.672 | ||
| 11 limit least squares | | 11-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| | | 9/5 | ||
| 116.716 | | 116.716 | ||
| 9 and 11 limit minimax | | 9- and 11-odd-limit minimax | ||
|- | |- | ||
| | | | ||
| {{monzo| 0 117 -44 -19 }} | | {{monzo| 0 117 -44 -19 }} | ||
| 116.721 | | 116.721 | ||
| 9 limit least squares | | 9-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| Line 719: | Line 691: | ||
|- | |- | ||
| | | | ||
| | | 3/2 | ||
| 116.993 | | 116.993 | ||
| | | | ||
| Line 734: | Line 706: | ||
|} | |} | ||
=== Manna === | ==== Manna ==== | ||
{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
|- | |- | ||
| Line 743: | Line 715: | ||
|- | |- | ||
| | | | ||
| | | 15/8 | ||
| 111.731 | | 111.731 | ||
| | | | ||
|- | |- | ||
| | | | ||
| | | 7/4 | ||
| 115.587 | | 115.587 | ||
| | | | ||
| Line 790: | Line 762: | ||
| {{monzo| 0 -27 25 5 }} | | {{monzo| 0 -27 25 5 }} | ||
| 116.573 | | 116.573 | ||
| 7 limit least squares | | 7-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| {{monzo| 0 -19 20 }} | | {{monzo| 0 -19 20 }} | ||
| 116.578 | | 116.578 | ||
| 5 limit least squares | | 5-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| | | 5/3 | ||
| 116.588 | | 116.588 | ||
| 5 and 7 limit minimax | | 5- and 7-odd-limit minimax | ||
|- | |- | ||
| | | | ||
| Line 808: | Line 780: | ||
|- | |- | ||
| | | | ||
| | | 11/6 | ||
| 116.596 | | 116.596 | ||
| | | | ||
|- | |- | ||
| | | | ||
| | | 11/7 | ||
| 116.617 | | 116.617 | ||
| | | | ||
|- | |- | ||
| | | | ||
| Line 835: | Line 802: | ||
| {{monzo| 0 17 -11 -6 11 }} | | {{monzo| 0 17 -11 -6 11 }} | ||
| 116.672 | | 116.672 | ||
| 11 limit least squares | | 11-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| | | 9/5 | ||
| 116.716 | | 116.716 | ||
| 9 and 11 limit minimax | | 9- and 11-odd-limit minimax | ||
|- | |- | ||
| | | | ||
| {{monzo| 0 117 -44 -19 }} | | {{monzo| 0 117 -44 -19 }} | ||
| 116.721 | | 116.721 | ||
| 9 limit least squares | | 9-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| 15/13 | | 15/13 | ||
| 116.725 | | 116.725 | ||
| 15 limit minimax | | 15-odd-limit minimax | ||
|- | |- | ||
| | | | ||
| Line 875: | Line 827: | ||
| 13/10 | | 13/10 | ||
| 116.760 | | 116.760 | ||
| 13 limit minimax | | 13-odd-limit minimax | ||
|- | |- | ||
| | | | ||
| {{monzo| 0 -37 -166 -77 59 243 }} | | {{monzo| 0 -37 -166 -77 59 243 }} | ||
| 116.764 | | 116.764 | ||
| 15 limit least squares | | 15-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| {{monzo| 0 18 -111 -76 43 204 }} | | {{monzo| 0 18 -111 -76 43 204 }} | ||
| 116.780 | | 116.780 | ||
| 13 limit least squares | | 13-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| Line 893: | Line 845: | ||
|- | |- | ||
| | | | ||
| | | 13/7 | ||
| 116.79254 | | 116.79254 | ||
| | | | ||
|- | |- | ||
| | | | ||
| | | 13/9 | ||
| 116.79299 | | 116.79299 | ||
| | | | ||
| Line 913: | Line 865: | ||
|- | |- | ||
| | | | ||
| | | 13/8 | ||
| 116.856 | | 116.856 | ||
| | | | ||
| Line 923: | Line 875: | ||
|- | |- | ||
| | | | ||
| | | 3/2 | ||
| 116.993 | | 116.993 | ||
| | | | ||
| Line 938: | Line 890: | ||
|} | |} | ||
=== Revelation === | ==== Revelation ==== | ||
{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
|- | |- | ||
| Line 947: | Line 899: | ||
|- | |- | ||
| | | | ||
| | | 15/8 | ||
| 111.731 | | 111.731 | ||
| | | | ||
| Line 967: | Line 919: | ||
|- | |- | ||
| | | | ||
| | | 11/7 | ||
| 115.536 | | 115.536 | ||
| | | | ||
| Line 977: | Line 929: | ||
|- | |- | ||
| | | | ||
| | | 7/4 | ||
| 115.587 | | 115.587 | ||
| | | | ||
| Line 987: | Line 939: | ||
|- | |- | ||
| | | | ||
| | | 11/6 | ||
| 115.938 | | 115.938 | ||
| | | | ||
| Line 999: | Line 951: | ||
| 11/9 | | 11/9 | ||
| 116.164 | | 116.164 | ||
| 11, 13 and 15 limit minimax | | 11-, 13- and 15-odd-limit minimax | ||
|- | |- | ||
| | | | ||
| {{monzo| 0 -195 35 5 89 }} | | {{monzo| 0 -195 35 5 89 }} | ||
| 116.198 | | 116.198 | ||
| 11 limit least squares | | 11-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| {{monzo| 0 -251 22 5 117 13 }} | | {{monzo| 0 -251 22 5 117 13 }} | ||
| 116.229 | | 116.229 | ||
| 15 limit least squares | | 15-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| Line 1,019: | Line 971: | ||
| {{monzo| 0 -234 39 4 102 11 }} | | {{monzo| 0 -234 39 4 102 11 }} | ||
| 116.249 | | 116.249 | ||
| 13 limit least squares | | 13-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| Line 1,049: | Line 991: | ||
| {{monzo| 0 -27 25 5 }} | | {{monzo| 0 -27 25 5 }} | ||
| 116.573 | | 116.573 | ||
| 7 limit least squares | | 7-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| {{monzo| 0 -19 20 }} | | {{monzo| 0 -19 20 }} | ||
| 116.578 | | 116.578 | ||
| 5 limit least squares | | 5-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| | | 5/3 | ||
| 116.588 | | 116.588 | ||
| 5 and 7 limit minimax | | 5- and 7-odd-limit minimax | ||
|- | |- | ||
| | | | ||
| Line 1,072: | Line 1,014: | ||
|- | |- | ||
| | | | ||
| | | 9/5 | ||
| 116.716 | | 116.716 | ||
| 9 limit minimax | | 9-odd-limit minimax | ||
|- | |- | ||
| | | | ||
| {{monzo| 0 117 -44 -19 }} | | {{monzo| 0 117 -44 -19 }} | ||
| 116.721 | | 116.721 | ||
| 9 limit least squares | | 9-odd-limit least squares | ||
|- | |- | ||
| | | | ||
| Line 1,102: | Line 1,034: | ||
|- | |- | ||
| | | | ||
| | | 3/2 | ||
| 116.993 | | 116.993 | ||
| | | | ||
| Line 1,112: | Line 1,044: | ||
|- | |- | ||
| | | | ||
| | | 13/9 | ||
| 117.559 | | 117.559 | ||
| | | | ||
| Line 1,127: | Line 1,059: | ||
|- | |- | ||
| | | | ||
| | | 13/8 | ||
| 119.824 | | 119.824 | ||
| | | | ||
| Line 1,137: | Line 1,069: | ||
|- | |- | ||
| | | | ||
| | | 13/7 | ||
| 128.298 | | 128.298 | ||
| | | | ||