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Miracle extensions: Difference between revisions

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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:
|-
|-
|  
|  
| 16/15
| 15/8
| 111.731
| 111.731
|  
|  
Line 345: Line 357:
|-
|-
|  
|  
| 8/7
| 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
|-
|-
|  
|  
| 6/5
| 5/3
| 116.588
| 116.588
| 5 and 7 limit minimax
| 5- and 7-odd-limit minimax
|-
|-
|  
|  
Line 405: Line 417:
|-
|-
|  
|  
| 12/11
| 11/6
| 116.596
| 116.596
|  
|  
|-
|-
|  
|  
| 14/11
| 11/7
| 116.617
| 116.617
|  
|  
|-
|
|
| 116.633
| POTE11
|-
|-
|  
|  
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
| 116.673
| POTE5
|-
|
|
| 116.675
| POTE7
|-
|
| 10/9
| 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
|-
|
|
| 116.747
| POTE13
|-
|-
|  
|  
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
|-
|-
|  
|  
| 4/3
| 3/2
| 116.993
| 116.993
| 15 limit minimax
| 15-odd-limit minimax
|-
|-
| 4\41
| 4\41
Line 500: Line 492:
|-
|-
|  
|  
| 18/13
| 13/9
| 117.559
| 117.559
|  
|  
Line 515: Line 507:
|-
|-
|  
|  
| 16/13
| 13/8
| 119.824
| 119.824
|  
|  
Line 525: Line 517:
|-
|-
|  
|  
| 14/13
| 13/7
| 128.298
| 128.298
|  
|  
|}
|}


=== Benediction ===
==== Benediction ====
{| class="wikitable center-all left-4"
{| class="wikitable center-all left-4"
|-
|-
Line 539: Line 531:
|-
|-
|  
|  
| 16/15
| 15/8
| 111.731
| 111.731
|  
|  
|-
|-
|  
|  
| 8/7
| 7/4
| 115.587
| 115.587
|  
|  
Line 569: Line 561:
|-
|-
|  
|  
| 16/13
| 13/8
| 116.455
| 116.455
|  
|  
Line 584: Line 576:
|-
|-
|  
|  
| 14/13
| 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
|-
|
|
| 116.574
| POTE13
|-
|-
|  
|  
| {{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:
|-
|-
|  
|  
| 18/13
| 13/9
| 116.595
| 116.595
| 13 limit minimax
| 13-odd-limit minimax
|-
|-
|  
|  
| 12/11
| 11/6
| 116.596
| 116.596
|  
|  
Line 659: Line 646:
|-
|-
|  
|  
| 14/11
| 11/7
| 116.617
| 116.617
|  
|  
|-
|
|
| 116.633
| POTE11
|-
|-
|  
|  
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
|-
|
|
| 116.673
| POTE5
|-
|
|
| 116.675
| POTE7
|-
|-
|  
|  
| 10/9
| 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:
|-
|-
|  
|  
| 4/3
| 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:
|-
|-
|  
|  
| 16/15
| 15/8
| 111.731
| 111.731
|  
|  
|-
|-
|  
|  
| 8/7
| 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
|-
|-
|  
|  
| 6/5
| 5/3
| 116.588
| 116.588
| 5 and 7 limit minimax
| 5- and 7-odd-limit minimax
|-
|-
|  
|  
Line 808: Line 780:
|-
|-
|  
|  
| 12/11
| 11/6
| 116.596
| 116.596
|  
|  
|-
|-
|  
|  
| 14/11
| 11/7
| 116.617
| 116.617
|  
|  
|-
|
|
| 116.633
| POTE11
|-
|-
|  
|  
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
| 116.673
| POTE5
|-
|
|
| 116.675
| POTE7
|-
|
| 10/9
| 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
|-
|
|
| 116.739
| POTE13
|-
|-
|  
|  
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:
|-
|-
|  
|  
| 14/13
| 13/7
| 116.79254
| 116.79254
|  
|  
|-
|-
|  
|  
| 18/13
| 13/9
| 116.79299
| 116.79299
|  
|  
Line 913: Line 865:
|-
|-
|  
|  
| 16/13
| 13/8
| 116.856
| 116.856
|  
|  
Line 923: Line 875:
|-
|-
|  
|  
| 4/3
| 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:
|-
|-
|  
|  
| 16/15
| 15/8
| 111.731
| 111.731
|  
|  
Line 967: Line 919:
|-
|-
|  
|  
| 14/11
| 11/7
| 115.536
| 115.536
|  
|  
Line 977: Line 929:
|-
|-
|  
|  
| 8/7
| 7/4
| 115.587
| 115.587
|  
|  
Line 987: Line 939:
|-
|-
|  
|  
| 12/11
| 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
|-
|
|
| 116.268
| POTE13
|-
|
|
| 116.277
| POTE11
|-
|-
|  
|  
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
|-
|-
|  
|  
| 6/5
| 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
| 116.673
| POTE5
|-
|
|
| 116.675
| POTE7
|-
|
| 10/9
| 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:
|-
|-
|  
|  
| 4/3
| 3/2
| 116.993
| 116.993
|  
|  
Line 1,112: Line 1,044:
|-
|-
|  
|  
| 18/13
| 13/9
| 117.559
| 117.559
|  
|  
Line 1,127: Line 1,059:
|-
|-
|  
|  
| 16/13
| 13/8
| 119.824
| 119.824
|  
|  
Line 1,137: Line 1,069:
|-
|-
|  
|  
| 14/13
| 13/7
| 128.298
| 128.298
|  
|  
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