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add unchanged-intervals along with eigenmonzo, per prior agreement on Xenwiki Work Group
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,171 edits
"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Line 40: Line 40:
: [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.9/5.7
: [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.9/5.7


{{Val list|legend=1| 9, 10, 12, 19, 31, 41, 53, 72, 197, 269c }}
{{Optimal ET sequence|legend=1| 9, 10, 12, 19, 31, 41, 53, 72, 197, 269c }}


[[Badness]]: 0.0365 × 10<sup>-3</sup>
[[Badness]]: 0.0365 × 10<sup>-3</sup>
Line 98: Line 98:
: [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.9/5.11/9
: [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.9/5.11/9


{{Val list|legend=1| 9, 10, 12e, 19, 22, 31, 41, 53, 72, 166, 197e, 238c, 269ce, 341ce }}
{{Optimal ET sequence|legend=1| 9, 10, 12e, 19, 22, 31, 41, 53, 72, 166, 197e, 238c, 269ce, 341ce }}


[[Badness]]: 0.255 × 10<sup>-3</sup>
[[Badness]]: 0.255 × 10<sup>-3</sup>
Line 133: Line 133:
* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.15/11.15/13
* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.15/11.15/13


Optimal GPV sequence: {{Val list| 19, 22, 31, 50, 53, 72, 103, 175f, 300ceff, 403bceeff, 578bbccdeeefff }}
{{Optimal ET sequence|legend=1| 19, 22, 31, 50, 53, 72, 103, 175f, 300ceff, 403bceeff, 578bbccdeeefff }}


Badness: 0.690 × 10<sup>-3</sup>
Badness: 0.690 × 10<sup>-3</sup>
Line 152: Line 152:
* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.7.15/13
* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.7.15/13


Optimal GPV sequence: {{Val list| 19, 22f, 31f, 41, 53, 72, 125f, 166, 238cf }}
{{Optimal ET sequence|legend=1| 19, 22f, 31f, 41, 53, 72, 125f, 166, 238cf }}


Badness: 0.721 × 10<sup>-3</sup>
Badness: 0.721 × 10<sup>-3</sup>
Line 169: Line 169:
Optimal tuning (POTE): ~3/2 = 700.9619, ~5/4 = 383.0310
Optimal tuning (POTE): ~3/2 = 700.9619, ~5/4 = 383.0310


Optimal GPV sequence: {{Val list| 19, 22f, 31fg, 41, 53g, 72, 166g, 238cfg, 404ccefgg }}
{{Optimal ET sequence|legend=1| 19, 22f, 31fg, 41, 53g, 72, 166g, 238cfg, 404ccefgg }}


Badness: 0.869 × 10<sup>-3</sup>
Badness: 0.869 × 10<sup>-3</sup>
Line 182: Line 182:
Optimal tuning (POTE): ~3/2 = 700.9658, ~5/4 = 383.3063
Optimal tuning (POTE): ~3/2 = 700.9658, ~5/4 = 383.3063


Optimal GPV sequence: {{Val list| 19g, 22f, 31f, 41g, 53, 72, 166g, 238cfg, 404ccefgg }}
{{Optimal ET sequence|legend=1| 19g, 22f, 31f, 41g, 53, 72, 166g, 238cfg, 404ccefgg }}


Badness: 0.917 × 10<sup>-3</sup>
Badness: 0.917 × 10<sup>-3</sup>
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* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.7.15/13
* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.7.15/13


Optimal GPV sequence: {{Val list| 9, 22f, 31, 63, 72, 103, 166, 238cf, 269ce, 507bcceff, 610bcceeff }}
{{Optimal ET sequence|legend=1| 9, 22f, 31, 63, 72, 103, 166, 238cf, 269ce, 507bcceff, 610bcceeff }}


Badness: 0.862 × 10<sup>-3</sup>
Badness: 0.862 × 10<sup>-3</sup>
Line 212: Line 212:
Optimal tuning (POTE): ~3/2 = 701.9156, ~5/4 = 383.2445
Optimal tuning (POTE): ~3/2 = 701.9156, ~5/4 = 383.2445


Optimal GPV sequence: {{Val list| 10, 19f, 22, 31, 41, 53, 94 }}
{{Optimal ET sequence|legend=1| 10, 19f, 22, 31, 41, 53, 94 }}


Badness: 0.866 × 10<sup>-3</sup>
Badness: 0.866 × 10<sup>-3</sup>
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* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.3.13/5
* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.3.13/5


Optimal GPV sequence: {{Val list| 9, 19f, 22, 31f, 41, 63, 72, 185cf, 257cff }}
{{Optimal ET sequence|legend=1| 9, 19f, 22, 31f, 41, 63, 72, 185cf, 257cff }}


Badness: 0.920 × 10<sup>-3</sup>
Badness: 0.920 × 10<sup>-3</sup>
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* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.5/3.13/11
* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.5/3.13/11


Optimal GPV sequence: {{Val list| 9, 10, 19, 22f, 31, 41, 72f, 91, 122f, 163df }}
{{Optimal ET sequence|legend=1| 9, 10, 19, 22f, 31, 41, 72f, 91, 122f, 163df }}


Badness: 0.745 × 10<sup>-3</sup>
Badness: 0.745 × 10<sup>-3</sup>
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Optimal tuning (POTE): ~15/13 = 249.7138, ~5/4 = 383.5816
Optimal tuning (POTE): ~15/13 = 249.7138, ~5/4 = 383.5816


Optimal GPV sequence: {{Val list| 9, 10, 19, 44, 53, 72, 125f, 197ef, 269ceff }}
{{Optimal ET sequence|legend=1| 9, 10, 19, 44, 53, 72, 125f, 197ef, 269ceff }}


Badness: 0.9997 × 10<sup>-3</sup>
Badness: 0.9997 × 10<sup>-3</sup>
Line 288: Line 288:
[[Minimax tuning]]: [[11-odd-limit]] [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.7/5.11/9
[[Minimax tuning]]: [[11-odd-limit]] [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.7/5.11/9


{{Val list|legend=1| 9, 12, 19e, 22, 31, 53, 84e, 96, 127 }}
{{Optimal ET sequence|legend=1| 9, 12, 19e, 22, 31, 53, 84e, 96, 127 }}


[[Badness]]: 0.381 × 10<sup>-3</sup>
[[Badness]]: 0.381 × 10<sup>-3</sup>
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* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.11/9.13/7
* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.11/9.13/7


Optimal GPV sequence: {{Val list| 12f, 19e, 22, 31, 53, 84e, 118d, 171de, 202def }}
{{Optimal ET sequence|legend=1| 12f, 19e, 22, 31, 53, 84e, 118d, 171de, 202def }}


Badness: 0.818 × 10<sup>-3</sup>
Badness: 0.818 × 10<sup>-3</sup>
Line 328: Line 328:
[[Minimax tuning]]: [[11-odd-limit]] [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.7/5.11/9
[[Minimax tuning]]: [[11-odd-limit]] [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.7/5.11/9


{{Val list|legend=1| 12, 19, 22, 34d, 41, 104, 157ce, 198ce, 220ce, 261ce }}
{{Optimal ET sequence|legend=1| 12, 19, 22, 34d, 41, 104, 157ce, 198ce, 220ce, 261ce }}


[[Projection pair]]s: 7 225/32 11 100/9
[[Projection pair]]s: 7 225/32 11 100/9
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Minimax tuning: 13-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.11/9.13/9
Minimax tuning: 13-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.11/9.13/9


Optimal GPV sequence: {{Val list| 12f, 19f, 22, 29, 34d, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef }}
{{Optimal ET sequence|legend=1| 12f, 19f, 22, 29, 34d, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef }}


Projection pairs: 7 225/32 11 100/9 13 3200/243
Projection pairs: 7 225/32 11 100/9 13 3200/243
Line 360: Line 360:
[[Minimax tuning]]: [[11-odd-limit]] [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.9/7.11
[[Minimax tuning]]: [[11-odd-limit]] [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.9/7.11


{{Val list|legend=1| 7d, 9, 10, 12, 19, 31e, 50e }}
{{Optimal ET sequence|legend=1| 7d, 9, 10, 12, 19, 31e, 50e }}


[[Badness]]: 0.464 × 10<sup>-3</sup>
[[Badness]]: 0.464 × 10<sup>-3</sup>
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* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.9/7.13/9
* 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.9/7.13/9


Optimal GPV sequence: {{Val list| 9, 10, 12f, 19, 31e, 50e }}
{{Optimal ET sequence|legend=1| 9, 10, 12f, 19, 31e, 50e }}


Badness: 0.733 × 10<sup>-3</sup>
Badness: 0.733 × 10<sup>-3</sup>
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[[Optimal tuning]] ([[POTE]]): ~3/2 = 701.8913, ~5/4 = 382.4083
[[Optimal tuning]] ([[POTE]]): ~3/2 = 701.8913, ~5/4 = 382.4083


{{Val list|legend=1| 12e, 19e, 34d, 41, 53, 60e, 94, 229c, 248ce, 289cce, 342ccee, 383cce }}
{{Optimal ET sequence|legend=1| 12e, 19e, 34d, 41, 53, 60e, 94, 229c, 248ce, 289cce, 342ccee, 383cce }}


[[Badness]]: 1.250 × 10<sup>-3</sup>
[[Badness]]: 1.250 × 10<sup>-3</sup>
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Optimal tuning (POTE): ~3/2 = 701.8913, ~5/4 = 382.4083
Optimal tuning (POTE): ~3/2 = 701.8913, ~5/4 = 382.4083


Optimal GPV sequence: {{Val list| 12e, 19e, 34d, 41, 53, 94, 429ccdeef, 523ccdeef }}
{{Optimal ET sequence|legend=1| 12e, 19e, 34d, 41, 53, 94, 429ccdeef, 523ccdeef }}


Badness: 1.075 × 10<sup>-3</sup>
Badness: 1.075 × 10<sup>-3</sup>
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: [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.9/5.11
: [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.9/5.11


{{Val list|legend=1| 10, 12, 19e, 29, 31, 41, 60e, 72, 247c, 319bcde, 391bcde, 463bccde }}
{{Optimal ET sequence|legend=1| 10, 12, 19e, 29, 31, 41, 60e, 72, 247c, 319bcde, 391bcde, 463bccde }}


[[Badness]]: 0.344 × 10<sup>-3</sup>
[[Badness]]: 0.344 × 10<sup>-3</sup>
Line 458: Line 458:
Optimal tuning (POTE): ~3/2 = 700.4006, ~5/4 = 381.4025
Optimal tuning (POTE): ~3/2 = 700.4006, ~5/4 = 381.4025


Optimal GPV sequence: {{Val list| 10, 12f, 19e, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233ccddeef, 274ccddeff, 305ccddeeff }}
{{Optimal ET sequence|legend=1| 10, 12f, 19e, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233ccddeef, 274ccddeff, 305ccddeeff }}


Badness: 0.736 × 10<sup>-3</sup>
Badness: 0.736 × 10<sup>-3</sup>
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Optimal tuning (POTE): ~3/2 = 700.3407, ~5/4 = 383.2592
Optimal tuning (POTE): ~3/2 = 700.3407, ~5/4 = 383.2592


Optimal GPV sequence: {{Val list| 12f, 29, 31f, 41, 72, 185cf, 341cf, 413bcff, 526bccdff }}
{{Optimal ET sequence|legend=1| 12f, 29, 31f, 41, 72, 185cf, 341cf, 413bcff, 526bccdff }}


Badness: 0.900 × 10<sup>-3</sup>
Badness: 0.900 × 10<sup>-3</sup>
Line 484: Line 484:
Optimal tuning (POTE): ~3/2 = 699.4864, ~5/4 = 384.0998
Optimal tuning (POTE): ~3/2 = 699.4864, ~5/4 = 384.0998


Optimal GPV sequence: {{Val list| 12f, 19e, 31, 53e, 60eff, 72, 103, 175f }}
{{Optimal ET sequence|legend=1| 12f, 19e, 31, 53e, 60eff, 72, 103, 175f }}


Badness: 0.889 × 10<sup>-3</sup>
Badness: 0.889 × 10<sup>-3</sup>
Line 497: Line 497:
Optimal tuning (POTE): ~3/2 = 699.5536, ~5/4 = 383.5696
Optimal tuning (POTE): ~3/2 = 699.5536, ~5/4 = 383.5696


Optimal GPV sequence: {{val list| 29, 31, 43, 60e, 72, 103, 175f, 482bccddeefff, 554bbccddeeeffff }}
{{Optimal ET sequence|legend=1| 29, 31, 43, 60e, 72, 103, 175f, 482bccddeefff, 554bbccddeeeffff }}


Badness: 0.953 × 10<sup>-3</sup>
Badness: 0.953 × 10<sup>-3</sup>
Line 510: Line 510:
Optimal tuning (POTE): ~3/2 = 699.6262, ~5/4 = 383.4458
Optimal tuning (POTE): ~3/2 = 699.6262, ~5/4 = 383.4458


Optimal GPV sequence: {{val list| 29g, 31, 43, 60e, 72, 103, 175f, 307bcdeeffg, 379bccdeeffgg, 482bccddeefffgg, 554bbccddeeeffffgg }}
{{Optimal ET sequence|legend=1| 29g, 31, 43, 60e, 72, 103, 175f, 307bcdeeffg, 379bccdeeffgg, 482bccddeefffgg, 554bbccddeeeffffgg }}


Badness: 0.772 × 10<sup>-3</sup>
Badness: 0.772 × 10<sup>-3</sup>
Line 525: Line 525:
[[Optimal tuning]] ([[POTE]]): ~3/2 = 700.6242, ~5/4 = 383.2978
[[Optimal tuning]] ([[POTE]]): ~3/2 = 700.6242, ~5/4 = 383.2978


{{Val list|legend=1| 12, 22, 34d, 50, 60e, 72, 166, 238c, 310c }}
{{Optimal ET sequence|legend=1| 12, 22, 34d, 50, 60e, 72, 166, 238c, 310c }}


[[Badness]]: 0.743 × 10<sup>-3</sup>
[[Badness]]: 0.743 × 10<sup>-3</sup>
Line 545: Line 545:
: [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.9/5.11
: [[Eigenmonzo subgroup]] ([[unchanged-interval basis]]): 2.9/5.11


{{Val list|legend=1| 31, 41, 72, 247c, 281, 353c, 425bc, 497bc }}
{{Optimal ET sequence|legend=1| 31, 41, 72, 247c, 281, 353c, 425bc, 497bc }}


[[Badness]]: 0.499 × 10<sup>-3</sup>
[[Badness]]: 0.499 × 10<sup>-3</sup>
Line 566: Line 566:
Optimal tuning (POTE): ~11/9 = 349.9247, ~5/4 = 384.3505
Optimal tuning (POTE): ~11/9 = 349.9247, ~5/4 = 384.3505


Optimal GPV sequence: {{Val list| 31, 72, 103, 175f }} <nowiki>*</nowiki>
{{Optimal ET sequence|legend=1| 31, 72, 103, 175f }} <nowiki>*</nowiki>


<nowiki>*</nowiki> optimal patent val: [[240edo|240]]
<nowiki>*</nowiki> optimal patent val: [[240edo|240]]
Line 583: Line 583:
[[Optimal tuning]] ([[POTE]]): ~400/231 = 950.1474, ~5/4 = 383.6467
[[Optimal tuning]] ([[POTE]]): ~400/231 = 950.1474, ~5/4 = 383.6467


{{Val list|legend=1| 19, 29, 43, 53, 72, 197e, 269ce, 341ce, 610bce }}
{{Optimal ET sequence|legend=1| 19, 29, 43, 53, 72, 197e, 269ce, 341ce, 610bce }}


[[Badness]]: 1.54 × 10<sup>-3</sup>
[[Badness]]: 1.54 × 10<sup>-3</sup>
Line 596: Line 596:
Optimal tuning (POTE): ~26/15 = 950.2349, ~5/4 = 383.5558
Optimal tuning (POTE): ~26/15 = 950.2349, ~5/4 = 383.5558


Optimal GPV sequence: {{Val list| 19, 29, 43, 53, 72, 125f, 197ef, 269cef }}
{{Optimal ET sequence|legend=1| 19, 29, 43, 53, 72, 125f, 197ef, 269cef }}


Badness: 1.062 × 10<sup>-3</sup>
Badness: 1.062 × 10<sup>-3</sup>
Line 611: Line 611:
[[Optimal tuning]] ([[POTE]]): ~3/2 = 699.8719, ~11/10 = 158.3232
[[Optimal tuning]] ([[POTE]]): ~3/2 = 699.8719, ~11/10 = 158.3232


{{Val list|legend=1| 9, 15d, 16d, 20, 22, 31, 53, 82e, 84e, 113e, 144ee }}
{{Optimal ET sequence|legend=1| 9, 15d, 16d, 20, 22, 31, 53, 82e, 84e, 113e, 144ee }}


=== 13-limit ===
=== 13-limit ===
Line 624: Line 624:
Optimal tuning (POTE): ~3/2 = 698.7090, ~11/10 = 158.7117
Optimal tuning (POTE): ~3/2 = 698.7090, ~11/10 = 158.7117


Optimal GPV sequence: {{Val list| 9, 20, 22f, 29, 31 }}
{{Optimal ET sequence|legend=1| 9, 20, 22f, 29, 31 }}


=== Diana ===
=== Diana ===
Line 637: Line 637:
Optimal tuning (POTE): ~3/2 = 700.9789, ~11/10 = 159.0048
Optimal tuning (POTE): ~3/2 = 700.9789, ~11/10 = 159.0048


Optimal GPV sequence: {{Val list| 22, 29, 31, 53, 82e, 84e, 113e, 166ee }}
{{Optimal ET sequence|legend=1| 22, 29, 31, 53, 82e, 84e, 113e, 166ee }}


== Morfil ==
== Morfil ==
Line 650: Line 650:
[[Optimal tuning]] ([[POTE]]): ~3/2 = 700.8983, ~84/55 = 739.3812
[[Optimal tuning]] ([[POTE]]): ~3/2 = 700.8983, ~84/55 = 739.3812


{{Val list|legend=1| 29, 31, 60e, 91e, 94, 125 }}
{{Optimal ET sequence|legend=1| 29, 31, 60e, 91e, 94, 125 }}


[[Badness]]: 1.152 × 10<sup>-3</sup>
[[Badness]]: 1.152 × 10<sup>-3</sup>
Line 665: Line 665:
[[Optimal tuning]] ([[POTE]]): ~6/5 = 316.7318, ~11/8 = 549.2528
[[Optimal tuning]] ([[POTE]]): ~6/5 = 316.7318, ~11/8 = 549.2528


{{Val list|legend=1| 19, 34d, 53, 72, 197e, 269ce }}
{{Optimal ET sequence|legend=1| 19, 34d, 53, 72, 197e, 269ce }}


[[Badness]]: 1.275 × 10<sup>-3</sup>
[[Badness]]: 1.275 × 10<sup>-3</sup>
Line 680: Line 680:
Optimal tuning (POTE): ~6/5 = 316.7410, ~11/8 = 548.6028
Optimal tuning (POTE): ~6/5 = 316.7410, ~11/8 = 548.6028


Optimal GPV sequence: {{Val list| 19, 34d, 53, 72, 125f, 197ef, 269cef }}
{{Optimal ET sequence|legend=1| 19, 34d, 53, 72, 125f, 197ef, 269cef }}


Badness: 0.916 × 10<sup>-3</sup>
Badness: 0.916 × 10<sup>-3</sup>
Line 695: Line 695:
Optimal tuning (POTE): ~15/14 = 116.6327, ~13/8 = 837.7040
Optimal tuning (POTE): ~15/14 = 116.6327, ~13/8 = 837.7040


Optimal GPV sequence: {{Val list| 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef }}
{{Optimal ET sequence|legend=1| 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef }}


Badness: 0.738 × 10<sup>-3</sup>
Badness: 0.738 × 10<sup>-3</sup>
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