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Miracle extensions: Difference between revisions

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→Tunings: 17-limit warts and tuning ranges
→Tunings: move target tunings out of the spectra
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== Tunings ==
== Tunings ==
* 5-limit POTE: ~15/14 = 116.673
=== Prime-optimized tunings ===
* 7-limit POTE: ~15/14 = 116.675
* 5-limit POTE: ~16/15 = 116.673{{c}}
* 7-limit POTE: ~15/14 = 116.675{{c}}
* 11-limit POTE
* 11-limit POTE
** Miracle: ~15/14 = 116.633
** Miracle: ~15/14 = 116.633{{c}}
** Revelation: ~15/14 = 116.277
** Revelation: ~15/14 = 116.277{{c}}
* 13-limit POTE
* 13-limit POTE
** Miraculous: ~15/14 = 116.747
** Miraculous: ~15/14 = 116.747{{c}}
** Benediction: ~15/14 = 116.574
** Benediction: ~15/14 = 116.574{{c}}
** Manna: ~15/14 = 116.739
** Manna: ~15/14 = 116.739{{c}}
** Revelation: ~15/14 = 116.268
** Revelation: ~15/14 = 116.268{{c}}
 
=== Target tunings ===
* 5-odd-limit least squares: ~16/15 = 116.578{{c}} (eigenmonzo: {{monzo| 0 -19 20 }})
* 7-odd-limit least squares: ~15/14 = 116.573{{c}} (eigenmonzo: {{monzo| 0 -27 25 5 }})
* 9-odd-limit least squares: ~15/14 = 116.721{{c}} (eigenmonzo: {{monzo| 0 117 -44 -19 }})
* 11-odd-limit least squares
** Miracle: ~15/14 = 116.672{{c}} (eigenmonzo: {{monzo| 0 17 -11 -6 11 }})
** Revelation: ~15/14 = 116.198{{c}} (eigenmonzo: {{monzo| 0 -195 35 5 89 }})
* 13-odd-limit least squares
** Miraculous: ~15/14 = 116.846{{c}} (eigenmonzo: {{monzo| 0 141 -70 -35 84 -42 }})
** Benediction: ~15/14 = 116.56309{{c}} (eigenmonzo: {{monzo| 0 -234 39 4 -115 228 }})
** Manna: ~15/14 = 116.780{{c}} (eigenmonzo: {{monzo| 0 18 -111 -76 43 204 }})
** Revelation: ~15/14 = 116.249{{c}} (eigenmonzo: {{monzo| 0 -234 39 4 102 11 }})
* 15-odd-limit least squares
** Miraculous: ~15/14 = 116.820{{c}} (eigenmonzo: {{monzo| 0 127 -84 -36 100 -44 }})
** Benediction: ~15/14 = 116.56348{{c}} (eigenmonzo: {{monzo| 0 -251 22 5 -131 261 }})
** Manna: ~15/14 = 116.764{{c}} (eigenmonzo: {{monzo| 0 -37 -166 -77 59 243 }})
** Revelation: ~15/14 = 116.229{{c}} (eigenmonzo: {{monzo| 0 -251 22 5 117 13 }})


=== Tuning spectra ===
=== Tuning spectra ===
Line 397: Line 416:
| 116.571
| 116.571
| 175ffggg val
| 175ffggg val
|-
|
| {{monzo| 0 -27 25 5 }}
| 116.573
| 7-odd-limit least squares
|-
|
| {{monzo| 0 -19 20 }}
| 116.578
| 5-odd-limit least squares
|-
|-
|  
|  
Line 437: Line 446:
| 116.667
| 116.667
| 72fg val
| 72fg val
|-
|
| {{monzo| 0 17 -11 -6 11 }}
| 116.672
| 11-odd-limit least squares
|-
|-
|  
|  
Line 447: Line 451:
| 116.716
| 116.716
| 9-, 11- and 13-odd-limit minimax
| 9-, 11- and 13-odd-limit minimax
|-
|
| {{monzo| 0 117 -44 -19 }}
| 116.721
| 9-odd-limit least squares
|-
|-
|  
|  
Line 472: Line 471:
| 116.814
| 116.814
| 113fgg val
| 113fgg val
|-
|
| {{monzo| 0 127 -84 -36 100 -44 }}
| 116.820
| 15-odd-limit least squares
|-
|
| {{monzo| 0 141 -70 -35 84 -42 }}
| 116.846
| 13-odd-limit least squares
|-
|-
|  
|  
Line 601: Line 590:
| 116.547
| 116.547
|  
|  
|-
|
| {{monzo| 0 -234 39 4 -115 228 }}
| 116.56309
| 13-odd-limit least squares
|-
|
| {{monzo| 0 -251 22 5 -131 261 }}
| 116.56348
| 15-odd-limit least squares
|-
|-
| 17\175
| 17\175
Line 616: Line 595:
| 116.571
| 116.571
| 175f val
| 175f val
|-
|
| {{monzo| 0 -27 25 5 }}
| 116.573
| 7-odd-limit least squares
|-
|
| {{monzo| 0 -19 20 }}
| 116.578
| 5-odd-limit least squares
|-
|-
|  
|  
Line 666: Line 635:
| 116.667
| 116.667
| Upper bound of 13- to 17-odd-limit, <br>and 17-limit 21-odd-limit diamond monotone
| Upper bound of 13- to 17-odd-limit, <br>and 17-limit 21-odd-limit diamond monotone
|-
|
| {{monzo| 0 17 -11 -6 11 }}
| 116.672
| 11-odd-limit least squares
|-
|-
|  
|  
Line 676: Line 640:
| 116.716
| 116.716
| 9- and 11-odd-limit minimax
| 9- and 11-odd-limit minimax
|-
|
| {{monzo| 0 117 -44 -19 }}
| 116.721
| 9-odd-limit least squares
|-
|-
|  
|  
Line 770: Line 729:
| 116.571
| 116.571
| 175fffgg val
| 175fffgg val
|-
|
| {{monzo| 0 -27 25 5 }}
| 116.573
| 7-odd-limit least squares
|-
|
| {{monzo| 0 -19 20 }}
| 116.578
| 5-odd-limit least squares
|-
|-
|  
|  
Line 810: Line 759:
| 116.667
| 116.667
| Lower bound of 13- to 17-odd-limit, <br>and 17-limit 21-odd-limit diamond monotone
| Lower bound of 13- to 17-odd-limit, <br>and 17-limit 21-odd-limit diamond monotone
|-
|
| {{monzo| 0 17 -11 -6 11 }}
| 116.672
| 11-odd-limit least squares
|-
|-
|  
|  
Line 820: Line 764:
| 116.716
| 116.716
| 9- and 11-odd-limit minimax
| 9- and 11-odd-limit minimax
|-
|
| {{monzo| 0 117 -44 -19 }}
| 116.721
| 9-odd-limit least squares
|-
|-
|  
|  
Line 845: Line 784:
| 116.760
| 116.760
| 13-odd-limit minimax
| 13-odd-limit minimax
|-
|
| {{monzo| 0 -37 -166 -77 59 243 }}
| 116.764
| 15-odd-limit least squares
|-
|
| {{monzo| 0 18 -111 -76 43 204 }}
| 116.780
| 13-odd-limit least squares
|-
|-
|  
|  
Line 979: Line 908:
| 116.164
| 116.164
| 11-, 13- and 15-odd-limit minimax
| 11-, 13- and 15-odd-limit minimax
|-
|
| {{monzo| 0 -195 35 5 89 }}
| 116.198
| 11-odd-limit least squares
|-
|
| {{monzo| 0 -251 22 5 117 13 }}
| 116.229
| 15-odd-limit least squares
|-
|-
|  
|  
Line 994: Line 913:
| 116.241
| 116.241
|  
|  
|-
|
| {{monzo| 0 -234 39 4 102 11 }}
| 116.249
| 13-odd-limit least squares
|-
|-
|  
|  
Line 1,004: Line 918:
| 116.502
| 116.502
|  
|  
|-
|
| {{monzo| 0 -27 25 5 }}
| 116.573
| 7-odd-limit least squares
|-
|
| {{monzo| 0 -19 20 }}
| 116.578
| 5-odd-limit least squares
|-
|-
|  
|  
Line 1,034: Line 938:
| 116.716
| 116.716
| 9-odd-limit minimax
| 9-odd-limit minimax
|-
|
| {{monzo| 0 117 -44 -19 }}
| 116.721
| 9-odd-limit least squares
|-
|-
|  
|  
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