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Catalog of rank-4 temperaments: Difference between revisions

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{{Mapping|legend=1| 1 0 0 0 -2 | 0 1 0 0 2 | 0 0 1 0 1 | 0 0 0 1 0 }}
{{Mapping|legend=1| 1 0 0 0 -2 | 0 1 0 0 2 | 0 0 1 0 1 | 0 0 0 1 0 }}
: Mapping generators: ~2, ~3, ~5, ~7
: Mapping generators: ~2, ~3, ~5, ~7


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1＼1, ~3/2 = 694.823, ~5/4 = 378.660, ~7/4 = 968.826
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 694.823{{c}}, ~5/4 = 378.660{{c}}, ~7/4 = 968.826{{c}}
* [[CWE]]: ~2 = 1＼1, ~3/2 = 693.197, ~5/4 = 376.082, ~7/4 = 965.060
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 693.197{{c}}, ~5/4 = 376.082{{c}}, ~7/4 = 965.060{{c}}


{{Optimal ET sequence|legend=1| 7d, 9, 10, 12, 19, 26, 45 }}
{{Optimal ET sequence|legend=1| 7d, 9, 10, 12, 19, 26, 45 }}


[[Badness]]: 0.0219 × 10<sup>-6</sup>
[[Badness]] (Smith): 0.0219 × 10<sup>-6</sup>


== Mothwellsmic (99/98) ==
== Mothwellsmic (99/98) ==
Line 25: Line 24:


{{Mapping|legend=1| 1 0 0 0 1 | 0 1 0 0 -2 | 0 0 1 0 0 | 0 0 0 1 2 }}
{{Mapping|legend=1| 1 0 0 0 1 | 0 1 0 0 -2 | 0 0 1 0 0 | 0 0 0 1 2 }}
: Mapping generators: ~2, ~3, ~5, ~7
: Mapping generators: ~2, ~3, ~5, ~7


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1＼1, ~3/2 = 700.306, ~5/4 = 386.314, ~7/4 = 974.000
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 700.306{{c}}, ~5/4 = 386.314{{c}}, ~7/4 = 974.000{{c}}
* [[CWE]]: ~2 = 1＼1, ~3/2 = 700.060, ~5/4 = 385.931, ~7/4 = 973.388
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 700.060{{c}}, ~5/4 = 385.931{{c}}, ~7/4 = 973.388{{c}}


{{Optimal ET sequence|legend=1| 5, 8d, 9, 12, 17c, 19e, 22, 31, 53, 84e, 96, 127 }}
{{Optimal ET sequence|legend=1| 5, 8d, 9, 12, 17c, 19e, 22, 31, 53, 84e, 96, 127 }}


[[Badness]]: 0.0299 × 10<sup>-6</sup>
[[Badness]] (Smith): 0.0299 × 10<sup>-6</sup>


== Ptolemismic (100/99) ==
== Ptolemismic (100/99) ==
Line 42: Line 40:


{{Mapping|legend=1| 1 0 0 0 2 | 0 1 0 0 -2 | 0 0 1 0 2 | 0 0 0 1 0 }}
{{Mapping|legend=1| 1 0 0 0 2 | 0 1 0 0 -2 | 0 0 1 0 2 | 0 0 0 1 0 }}
: Mapping generators: ~2, ~3, ~5, ~7
: Mapping generators: ~2, ~3, ~5, ~7


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1＼1, ~3/2 = 703.961, ~5/4 = 382.009, ~7/4 = 968.826
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 703.961{{c}}, ~5/4 = 382.009{{c}}, ~7/4 = 968.826{{c}}
* [[CWE]]: ~2 = 1＼1, ~3/2 = 704.475, ~5/4 = 383.076, ~7/4 = 969.890
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 704.475{{c}}, ~5/4 = 383.076{{c}}, ~7/4 = 969.890{{c}}


{{Optimal ET sequence|legend=1| 7d, 8d, 10e, 12, 15, 19, 22, 27e, 34d, 41, 90e, 131e }} <nowiki>*</nowiki>
{{Optimal ET sequence|legend=1| 7d, 8d, 10e, 12, 15, 19, 22, 27e, 34d, 41, 90e, 131e }} <nowiki>*</nowiki>
Line 53: Line 50:
<nowiki>*</nowiki> [[optimal patent val]]: [[104edo|104]]
<nowiki>*</nowiki> [[optimal patent val]]: [[104edo|104]]


[[Badness]]: 0.0225 × 10<sup>-6</sup>
[[Badness]] (Smith): 0.0225 × 10<sup>-6</sup>


== Biyatismic (121/120) ==
== Biyatismic (121/120) ==
Line 61: Line 58:


{{Mapping|legend=1| 1 0 1 0 2 | 0 1 1 0 1 | 0 0 -2 0 -1 | 0 0 0 1 0 }}
{{Mapping|legend=1| 1 0 1 0 2 | 0 1 1 0 1 | 0 0 -2 0 -1 | 0 0 0 1 0 }}
: Mapping generators: ~2, ~3, ~11/10, ~7
: Mapping generators: ~2, ~3, ~11/10, ~7


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1＼1, ~3/2 = 702.602, ~11/10 = 157.450, ~7/4 = 968.826
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.602{{c}}, ~11/10 = 157.450{{c}}, ~7/4 = 968.826{{c}}
* [[CWE]]: ~2 = 1＼1, ~3/2 = 701.985, ~11/10 = 157.610, ~7/4 = 967.819
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.985{{c}}, ~11/10 = 157.610{{c}}, ~7/4 = 967.819{{c}}


{{Optimal ET sequence|legend=1| 14c, 15, 22, 31, 46, 53, 60e, 68, 77, 91e, 99, 130e, 159ee, 190ee }}
{{Optimal ET sequence|legend=1| 14c, 15, 22, 31, 46, 53, 60e, 68, 77, 91e, 99, 130e, 159ee, 190ee }}


[[Badness]]: 0.0345 × 10<sup>-6</sup>
[[Badness]] (Smith): 0.0345 × 10<sup>-6</sup>


== Valinorsmic (176/175) ==
== Valinorsmic (176/175) ==
Line 78: Line 74:


{{Mapping|legend=1| 1 0 0 0 -4 | 0 1 0 0 0 | 0 0 1 0 2 | 0 0 0 1 1 }}
{{Mapping|legend=1| 1 0 0 0 -4 | 0 1 0 0 0 | 0 0 1 0 2 | 0 0 0 1 1 }}
: Mapping generators: ~2, ~3, ~5, ~7
: Mapping generators: ~2, ~3, ~5, ~7


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1＼1, ~3/2 = 701.955, ~5/4 = 388.882, ~7/4 = 970.703
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.955{{c}}, ~5/4 = 388.882{{c}}, ~7/4 = 970.703{{c}}
* [[CWE]]: ~2 = 1＼1, ~3/2 = 702.587, ~5/4 = 389.393, ~7/4 = 971.520
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.587{{c}}, ~5/4 = 389.393{{c}}, ~7/4 = 971.520{{c}}


{{Optimal ET sequence|legend=1| 22, 31, 46, 53, 58, 80, 111 }}
{{Optimal ET sequence|legend=1| 22, 31, 46, 53, 58, 80, 111 }}


[[Badness]]: 0.0186 × 10<sup>-6</sup>
[[Badness]] (Smith): 0.0186 × 10<sup>-6</sup>


=== Tridecimal valinorsmic ===
=== Tridecimal valinorsmic ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 96: Line 90:


Mapping: {{Mapping| 1 0 0 0 -4 1 | 0 1 0 0 0 -3 | 0 0 1 0 2 2 | 0 0 0 1 1 1 }}
Mapping: {{Mapping| 1 0 0 0 -4 1 | 0 1 0 0 0 -3 | 0 0 1 0 2 2 | 0 0 0 1 1 1 }}
: Mapping generators: ~2, ~3, ~5, ~7


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1＼1, ~3/2 = 702.304, ~5/4 = 388.738, ~7/4 = 970.598
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 702.304{{c}}, ~5/4 = 388.738{{c}}, ~7/4 = 970.598{{c}}
* CWE: ~2 = 1＼1, ~3/2 = 702.694, ~5/4 = 389.382, ~7/4 = 971.530
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 702.694{{c}}, ~5/4 = 389.382{{c}}, ~7/4 = 971.530{{c}}


{{Optimal ET sequence|legend=0}}
{{Optimal ET sequence|legend=0|  }}


Badness:
Badness (Smith):


{{Todo|complete temperament data|inline=1}}
{{Todo|complete temperament data|inline=1}}
Line 117: Line 109:


{{Mapping|legend=1| 1 1 0 0 2 | 0 2 0 0 5 | 0 0 1 0 0 | 0 0 0 1 0 }}
{{Mapping|legend=1| 1 1 0 0 2 | 0 2 0 0 5 | 0 0 1 0 0 | 0 0 0 1 0 }}
: Mapping generators: ~2, ~11/9, ~5, ~7
: Mapping generators: ~2, ~11/9, ~5, ~7


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1＼1, ~11/9 = 350.572, ~5/4 = 386.314, ~7/4 = 968.826
* [[CTE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.572{{c}}, ~5/4 = 386.314{{c}}, ~7/4 = 968.826{{c}}
* [[CWE]]: ~2 = 1＼1, ~11/9 = 350.549, ~5/4 = 386.239, ~7/4 = 968.735
* [[CWE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.549{{c}}, ~5/4 = 386.239{{c}}, ~7/4 = 968.735{{c}}


{{Optimal ET sequence|legend=1| 7d, 10, 14c, 17c, 24, 27e, 31, 41, 58, 72, 130, 202 }}
{{Optimal ET sequence|legend=1| 7d, 10, 14c, 17c, 24, 27e, 31, 41, 58, 72, 130, 202 }}


[[Badness]]: 0.0509 × 10<sup>-6</sup>
[[Badness]] (Smith): 0.0509 × 10<sup>-6</sup>


== Frostmic (245/242) ==
== Frostmic (245/242) ==
Line 134: Line 125:


{{Mapping|legend=1| 1 0 1 0 0 | 0 1 0 0 0 | 0 0 2 0 1 | 0 0 0 1 1 }}
{{Mapping|legend=1| 1 0 1 0 0 | 0 1 0 0 0 | 0 0 2 0 1 | 0 0 0 1 1 }}
: Mapping generators: ~2, ~3, ~11/7, ~7
: Mapping generators: ~2, ~3, ~11/7, ~7


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1＼1, ~3/2 = 701.955, ~11/7 = 792.479, ~7/4 = 964.861
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.955{{c}}, ~11/7 = 792.479{{c}}, ~7/4 = 964.861{{c}}
* [[CWE]]: ~2 = 1＼1, ~3/2 = 701.753, ~11/7 = 792.335, ~7/4 = 964.527
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.753{{c}}, ~11/7 = 792.335{{c}}, ~7/4 = 964.527{{c}}


{{Optimal ET sequence|legend=1| 9, 12, 15, 23de, 24, 26, 27e, 38d, 41, 91, 106d }}
{{Optimal ET sequence|legend=1| 9, 12, 15, 23de, 24, 26, 27e, 38d, 41, 91, 106d }}


[[Badness]]: 0.0897 × 10<sup>-6</sup>
[[Badness]] (Smith): 0.0897 × 10<sup>-6</sup>


== Akua (352/351, 847/845) ==
== Akua (352/351, 847/845) ==
Line 151: Line 141:


{{Mapping|legend=1| 1 0 0 10 0 5 | 0 1 0 -6 0 -3 | 0 0 1 1 0 0 | 0 0 0 0 1 1 }}
{{Mapping|legend=1| 1 0 0 10 0 5 | 0 1 0 -6 0 -3 | 0 0 1 1 0 0 | 0 0 0 0 1 1 }}
: Mapping generators: ~2, ~3, ~5, ~11
: Mapping generators: ~2, ~3, ~5, ~11


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1＼1, ~3/2 = 702.873, ~5/4 = 386.213, ~11/8 = 550.306
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.873{{c}}, ~5/4 = 386.213{{c}}, ~11/8 = 550.306{{c}}
* [[CWE]]: ~2 = 1＼1, ~3/2 = 702.896, ~5/4 = 386.784, ~11/8 = 551.068
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.896{{c}}, ~5/4 = 386.784{{c}}, ~11/8 = 551.068{{c}}


{{Optimal ET sequence|legend=1| 12f, 17c, 24d, 29, 41, 46, 53, 58, 87, 111, 140, 152f, 198, 350f, 437f, 490f }}
{{Optimal ET sequence|legend=1| 12f, 17c, 24d, 29, 41, 46, 53, 58, 87, 111, 140, 152f, 198, 350f, 437f, 490f }}


[[Badness]]: 2.550 × 10<sup>-6</sup>
[[Badness]] (Smith): 2.550 × 10<sup>-6</sup>


== Keenanismic (385/384) ==
== Keenanismic (385/384) ==
Line 170: Line 159:


{{Mapping|legend=1| 1 0 0 0 7 | 0 1 0 0 1 | 0 0 1 0 -1 | 0 0 0 1 -1 }}
{{Mapping|legend=1| 1 0 0 0 7 | 0 1 0 0 1 | 0 0 1 0 -1 | 0 0 0 1 -1 }}
: Mapping generators: ~2, ~3, ~5, ~7
: Mapping generators: ~2, ~3, ~5, ~7


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1＼1, ~3/2 = 702.363, ~5/4 = 385.439, ~7/4 = 967.547
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.363{{c}}, ~5/4 = 385.439{{c}}, ~7/4 = 967.547{{c}}
* [[CWE]]: ~2 = 1＼1, ~3/2 = 701.693, ~5/4 = 385.149, ~7/4 = 967.300
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.693{{c}}, ~5/4 = 385.149{{c}}, ~7/4 = 967.300{{c}}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 183: Line 171:
{{Optimal ET sequence|legend=1| 9, 10, 12e, 15, 19, 22, 31, 41, 53, 68, 72, 118, 159, 190, 212, 284, 330e, 402de }}
{{Optimal ET sequence|legend=1| 9, 10, 12e, 15, 19, 22, 31, 41, 53, 68, 72, 118, 159, 190, 212, 284, 330e, 402de }}


[[Badness]]: 15.2 × 10<sup>-9</sup>
[[Badness]] (Smith): 15.2 × 10<sup>-9</sup>


=== Martwin ===
=== Martwin ===
Line 195: Line 183:
: 4/3 length = 1.0820, 6/5 length = 1.3935, 10/9 length = 1.6247
: 4/3 length = 1.0820, 6/5 length = 1.3935, 10/9 length = 1.6247


[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 702.629, ~5/4 = 385.219, ~7/4 = 967.741
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 702.629{{c}}, ~5/4 = 385.219{{c}}, ~7/4 = 967.741{{c}}


[[Minimax tuning]]: {{confirm}} <!-- contradiction with the data in Keenanismic family -->
[[Minimax tuning]]: {{confirm}} <!-- contradiction with the data in Keenanismic family -->
Line 203: Line 191:
{{Optimal ET sequence|legend=1| 12e, 15, 19, 22f, 26, 31f, 41, 46, 53, 72, 87, 125f, 140, 159, 212, 299, 371df, 465cef, 677cdeeff, 764cdeeff }}
{{Optimal ET sequence|legend=1| 12e, 15, 19, 22f, 26, 31f, 41, 46, 53, 72, 87, 125f, 140, 159, 212, 299, 371df, 465cef, 677cdeeff, 764cdeeff }}


[[Badness]]: 2.21 × 10<sup>-6</sup>
[[Badness]] (Smith): 2.21 × 10<sup>-6</sup>


=== Ancient ===
=== Ancient ===
Line 212: Line 200:
{{Mapping|legend=1| 1 0 0 0 7 -4 | 0 1 0 0 1 -1 | 0 0 1 0 -1 4 | 0 0 0 1 -1 0 }}
{{Mapping|legend=1| 1 0 0 0 7 -4 | 0 1 0 0 1 -1 | 0 0 1 0 -1 4 | 0 0 0 1 -1 0 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 702.358, ~5/4 = 385.674, ~7/4 = 967.452
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 702.358{{c}}, ~5/4 = 385.674{{c}}, ~7/4 = 967.452{{c}}


{{Optimal ET sequence|legend=1| 15, 19, 22, 31, 50, 53, 72, 87, 103, 140, 159, 190, 243e, 315ef, 330e, 402def }}
{{Optimal ET sequence|legend=1| 15, 19, 22, 31, 50, 53, 72, 87, 103, 140, 159, 190, 243e, 315ef, 330e, 402def }}


[[Badness]]: 2.57 × 10<sup>-6</sup>
[[Badness]] (Smith): 2.57 × 10<sup>-6</sup>


=== Commas 351/350, 385/384 ===
=== Commas 351/350, 385/384 ===
Line 225: Line 213:
{{Mapping|legend=1| 1 0 0 0 7 1 | 0 1 0 0 1 -3 | 0 0 1 0 -1 2 | 0 0 0 1 -1 1 }}
{{Mapping|legend=1| 1 0 0 0 7 1 | 0 1 0 0 1 -3 | 0 0 1 0 -1 2 | 0 0 0 1 -1 1 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 701.205, ~5/4 = 386.715, ~7/4 = 967.646
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 701.205{{c}}, ~5/4 = 386.715{{c}}, ~7/4 = 967.646{{c}}


{{Optimal ET sequence|legend=1| 19, 22, 26, 31, 46, 53, 72, 103, 149, 221ef, 324bdef, 473bdeeff, 495bdeefff, 545bddeefff, 598bcdeeefff }}
{{Optimal ET sequence|legend=1| 19, 22, 26, 31, 46, 53, 72, 103, 149, 221ef, 324bdef, 473bdeeff, 495bdeefff, 545bddeefff, 598bcdeeefff }}


[[Badness]]: 2.98 × 10<sup>-6</sup>
[[Badness]] (Smith): 2.98 × 10<sup>-6</sup>


=== Zaxa ===
=== Zaxa ===
Line 239: Line 227:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1＼1, ~3/2 = 702.657, ~5/4 = 385.632, ~7/4 = 967.829
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.657{{c}}, ~5/4 = 385.632{{c}}, ~7/4 = 967.829{{c}}
* [[CWE]]: ~2 = 1＼1, ~3/2 = 702.603, ~5/4 = 385.644, ~7/4 = 967.903
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.603{{c}}, ~5/4 = 385.644{{c}}, ~7/4 = 967.903{{c}}


{{Optimal ET sequence|legend=1| 22, 31, 41, 46, 53, 77, 87, 118, 140, 258e, 461e }}
{{Optimal ET sequence|legend=1| 22, 31, 41, 46, 53, 77, 87, 118, 140, 258e, 461e }}


[[Badness]]: 3.35 × 10<sup>-6</sup>
[[Badness]] (Smith): 3.35 × 10<sup>-6</sup>


=== Commas 364/363, 385/384 ===
=== Commas 364/363, 385/384 ===
Line 253: Line 241:
{{Mapping|legend=1| 1 0 0 0 7 12 | 0 1 0 0 1 3 | 0 0 1 0 -1 -2 | 0 0 0 1 -1 -3 }}
{{Mapping|legend=1| 1 0 0 0 7 12 | 0 1 0 0 1 3 | 0 0 1 0 -1 -2 | 0 0 0 1 -1 -3 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 702.761, ~5/4 = 385.159, ~7/4 = 966.298
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 702.761{{c}}, ~5/4 = 385.159{{c}}, ~7/4 = 966.298{{c}}


{{Optimal ET sequence|legend=1| 9, 15, 22, 26, 31f, 37, 41, 46, 63, 72, 87, 159 }}
{{Optimal ET sequence|legend=1| 9, 15, 22, 26, 31f, 37, 41, 46, 63, 72, 87, 159 }}


[[Badness]]: 3.32 × 10<sup>-6</sup>
[[Badness]] (Smith): 3.32 × 10<sup>-6</sup>


=== Commas 385/384, 847/845 ===
=== Commas 385/384, 847/845 ===
Line 265: Line 253:


{{Mapping|legend=1| 1 0 0 0 7 7 | 0 1 0 0 1 1 | 0 0 1 1 -2 -2 | 0 0 0 2 -2 -1 }}
{{Mapping|legend=1| 1 0 0 0 7 7 | 0 1 0 0 1 1 | 0 0 1 1 -2 -2 | 0 0 0 2 -2 -1 }}
: Mapping generators: ~2, ~3, ~5, ~13/11
: Mapping generators: ~2, ~3, ~5, ~13/11


[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 702.368, ~5/4 = 385.416, ~13/11 = 291.066
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 702.368{{c}}, ~5/4 = 385.416{{c}}, ~13/11 = 291.066{{c}}


{{Optimal ET sequence|legend=1| 34, 37, 41, 46, 53, 87, 103, 140, 190, 243e, 330e, 520de, 573dee }}
{{Optimal ET sequence|legend=1| 34, 37, 41, 46, 53, 87, 103, 140, 190, 243e, 330e, 520de, 573dee }}


[[Badness]]: 4.15 × 10<sup>-6</sup>
[[Badness]] (Smith): 4.15 × 10<sup>-6</sup>


== Werckismic (441/440) ==
== Werckismic (441/440) ==
Line 280: Line 267:


{{Mapping|legend=1| 1 0 0 0 -3 | 0 1 0 0 2 | 0 0 1 0 -1 | 0 0 0 1 2 }}
{{Mapping|legend=1| 1 0 0 0 -3 | 0 1 0 0 2 | 0 0 1 0 -1 | 0 0 0 1 2 }}
: Mapping generators: ~2, ~3, ~5, ~7
: Mapping generators: ~2, ~3, ~5, ~7


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1＼1, ~3/2 = 701.620, ~5/4 = 386.673, ~7/4 = 967.775
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.620{{c}}, ~5/4 = 386.673{{c}}, ~7/4 = 967.775{{c}}
* [[CWE]]: ~2 = 1＼1, ~3/2 = 701.496, ~5/4 = 386.432, ~7/4 = 967.588
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.496{{c}}, ~5/4 = 386.432{{c}}, ~7/4 = 967.588{{c}}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[11-odd-limit]]: ~2 = {{monzo| 1 0 0 0 0 }}, ~3 = {{monzo| 1/2 2/3 1/6 -1/3 1/6 }}, ~5 = {{monzo| 0 0 1 0 0 }}, ~7 = {{monzo| 1 -2/3 1/3 1/3 1/3 }}
* [[11-odd-limit]]: ~2 = {{monzo| 1 0 0 0 0 }}, ~3 = {{monzo| 1/2 2/3 1/6 -1/3 1/6 }}, ~5 = {{monzo| 0 0 1 0 0 }}, ~7 = {{monzo| 1 -2/3 1/3 1/3 1/3 }}
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.9/7.11
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.9/7.11


{{Optimal ET sequence|legend=1| 10, 12, 15, 19e, 26, 27e, 31, 41, 58, 72, 118, 130, 190, 248, 289, 320, 609d }}
{{Optimal ET sequence|legend=1| 10, 12, 15, 19e, 26, 27e, 31, 41, 58, 72, 118, 130, 190, 248, 289, 320, 609d }}
Line 305: Line 291:
: 3/2 length = 1.2263, 14/11 length = 1.4629, 21/16 length = 1.4657
: 3/2 length = 1.2263, 14/11 length = 1.4629, 21/16 length = 1.4657


[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 701.880, ~5/4 = 386.523, ~7/4 = 967.841
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 701.880{{c}}, ~5/4 = 386.523{{c}}, ~7/4 = 967.841{{c}}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 322: Line 308:
{{Mapping|legend=1| 1 0 0 0 -3 1 | 0 1 0 0 2 -3 | 0 0 1 0 -1 2 | 0 0 0 1 2 1 }}
{{Mapping|legend=1| 1 0 0 0 -3 1 | 0 1 0 0 2 -3 | 0 0 1 0 -1 2 | 0 0 0 1 2 1 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 701.175, ~5/4 = 387.330, ~7/4 = 968.480
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 701.175{{c}}, ~5/4 = 387.330{{c}}, ~7/4 = 968.480{{c}}


{{Optimal ET sequence|legend=1| 12f, 14cf, 19e, 26, 27e, 31, 45ef, 46, 58, 72, 103, 130, 233, 279, 409, 512bf, 642bf }}
{{Optimal ET sequence|legend=1| 12f, 14cf, 19e, 26, 27e, 31, 45ef, 46, 58, 72, 103, 130, 233, 279, 409, 512bf, 642bf }}
Line 333: Line 319:
{{Mapping|legend=1| 1 0 0 0 -3 2 | 0 1 0 0 2 -1 | 0 0 1 0 -1 -1 | 0 0 0 1 2 2 }}
{{Mapping|legend=1| 1 0 0 0 -3 2 | 0 1 0 0 2 -1 | 0 0 1 0 -1 -1 | 0 0 0 1 2 2 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 702.601, ~5/4 = 387.137, ~7/4 = 966.418
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 702.601{{c}}, ~5/4 = 387.137{{c}}, ~7/4 = 966.418{{c}}


{{Optimal ET sequence|legend=1| 10, 12f, 17c, 19e, 27e, 29, 31, 41, 46, 58, 87, 118, 145, 232 }}
{{Optimal ET sequence|legend=1| 10, 12f, 17c, 19e, 27e, 29, 31, 41, 46, 58, 87, 118, 145, 232 }}
Line 344: Line 330:
{{Mapping|legend=1| 1 0 0 0 -3 11 | 0 1 0 0 2 -4 | 0 0 1 0 -1 2 | 0 0 0 1 2 -2 }}
{{Mapping|legend=1| 1 0 0 0 -3 11 | 0 1 0 0 2 -4 | 0 0 1 0 -1 2 | 0 0 0 1 2 -2 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 700.555, ~5/4 = 387.816, ~7/4 = 967.984
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 700.555{{c}}, ~5/4 = 387.816{{c}}, ~7/4 = 967.984{{c}}


{{Optimal ET sequence|legend=1| 17c, 26, 29, 31, 43, 46, 60e, 72, 103, 149, 221ef, 324bdef, 473bdeeff, 545bddeefff }}
{{Optimal ET sequence|legend=1| 17c, 26, 29, 31, 43, 46, 60e, 72, 103, 149, 221ef, 324bdef, 473bdeeff, 545bddeefff }}
Line 355: Line 341:
{{Mapping|legend=1| 1 0 0 0 -3 11 7 | 0 1 0 0 2 -4 -3 | 0 0 1 0 -1 2 2 | 0 0 0 1 2 -2 -1 }}
{{Mapping|legend=1| 1 0 0 0 -3 11 7 | 0 1 0 0 2 -4 -3 | 0 0 1 0 -1 2 2 | 0 0 0 1 2 -2 -1 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 700.606, ~5/4 = 387.655, ~7/4 = 967.876
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 700.606{{c}}, ~5/4 = 387.655{{c}}, ~7/4 = 967.876{{c}}


{{Optimal ET sequence|legend=1| 17cg, 26, 29g, 31, 43, 46, 60e, 72, 103, 149, 221ef }}
{{Optimal ET sequence|legend=1| 17cg, 26, 29g, 31, 43, 46, 60e, 72, 103, 149, 221ef }}
Line 365: Line 351:


{{Mapping|legend=1| 1 0 0 0 -3 -3 | 0 1 0 0 2 2 | 0 0 1 1 1 1 | 0 0 0 2 4 5 }}
{{Mapping|legend=1| 1 0 0 0 -3 -3 | 0 1 0 0 2 2 | 0 0 1 1 1 1 | 0 0 0 2 4 5 }}
: Mapping generators: ~2, ~3, ~5, ~13/11
: Mapping generators: ~2, ~3, ~5, ~13/11


[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 701.611, ~5/4 = 386.882, ~13/11 = 290.287
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 701.611{{c}}, ~5/4 = 386.882{{c}}, ~13/11 = 290.287{{c}}


{{Optimal ET sequence|legend=1| 12f, 16, 17c, 25e, 29, 41, 46, 58, 87, 103, 145, 149, 161, 190, 248, 438d }}
{{Optimal ET sequence|legend=1| 12f, 16, 17c, 25e, 29, 41, 46, 58, 87, 103, 145, 149, 161, 190, 248, 438d }}
Line 378: Line 363:


{{Mapping|legend=1| 1 0 0 0 2 | 0 1 0 0 3 | 0 0 1 0 1 | 0 0 0 1 -2 }}
{{Mapping|legend=1| 1 0 0 0 2 | 0 1 0 0 3 | 0 0 1 0 1 | 0 0 0 1 -2 }}
: Mapping generators: ~2, ~3, ~5, ~7
: Mapping generators: ~2, ~3, ~5, ~7


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1＼1, ~3/2 = 701.6167, ~5/4 = 386.0717, ~7/4 = 969.5334
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.6167{{c}}, ~5/4 = 386.0717{{c}}, ~7/4 = 969.5334{{c}}
* [[CWE]]: ~2 = 1＼1, ~3/2 = 701.6950, ~5/4 = 386.1796, ~7/4 = 969.6366
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.6950{{c}}, ~5/4 = 386.1796{{c}}, ~7/4 = 969.6366{{c}}


{{Optimal ET sequence|legend=1| 8d, 9, 10, 12e, 14c, 17c, 19, 22, 27e, 31, 41, 53, 58, 72, 130, 152, 224, 354, 506e, 578, 730de, 761d, 985d, 1115de, 1267dde }}
{{Optimal ET sequence|legend=1| 8d, 9, 10, 12e, 14c, 17c, 19, 22, 27e, 31, 41, 53, 58, 72, 130, 152, 224, 354, 506e, 578, 730de, 761d, 985d, 1115de, 1267dde }}


[[Badness]]: 0.0105 × 10<sup>-6</sup>
[[Badness]] (Smith): 0.0105 × 10<sup>-6</sup>


=== Commas 540/539, 729/728 ===
=== Commas 540/539, 729/728 ===
Line 395: Line 379:


{{Mapping|legend=1| 1 0 0 0 2 -3 | 0 1 0 0 3 6 | 0 0 1 0 1 0 | 0 0 0 1 -2 -1 }}
{{Mapping|legend=1| 1 0 0 0 2 -3 | 0 1 0 0 3 6 | 0 0 1 0 1 0 | 0 0 0 1 -2 -1 }}
: Mapping generators: ~2, ~3, ~5, ~7
: Mapping generators: ~2, ~3, ~5, ~7


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1＼1, ~3/2 = 701.6687, ~5/4 = 386.0441, ~7/4 = 969.5668
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.6687{{c}}, ~5/4 = 386.0441{{c}}, ~7/4 = 969.5668{{c}}
* [[CWE]]: ~2 = 1＼1, ~3/2 = 701.7230, ~5/4 = 386.1818, ~7/4 = 969.6607
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.7230{{c}}, ~5/4 = 386.1818{{c}}, ~7/4 = 969.6607{{c}}


{{Optimal ET sequence|legend=1| 12e, 14cf, 17c, 19, 22f, 31f, 39df, 41, 53, 58, 72, 111, 130, 183, 224, 354, 578, 985d, 1267ddef }}
{{Optimal ET sequence|legend=1| 12e, 14cf, 17c, 19, 22f, 31f, 39df, 41, 53, 58, 72, 111, 130, 183, 224, 354, 578, 985d, 1267ddef }}


[[Badness]]: 1.73 × 10<sup>-6</sup>
[[Badness]] (Smith): 1.73 × 10<sup>-6</sup>


=== Commas 540/539, 847/845 ===
=== Commas 540/539, 847/845 ===
Line 412: Line 395:


{{Mapping|legend=1| 1 0 0 0 2 2 | 0 1 0 0 3 3 | 0 0 1 1 -1 -1 | 0 0 0 2 -4 -3 }}
{{Mapping|legend=1| 1 0 0 0 2 2 | 0 1 0 0 3 3 | 0 0 1 1 -1 -1 | 0 0 0 2 -4 -3 }}
: Mapping generators: ~2, ~3, ~5, ~13/11
: Mapping generators: ~2, ~3, ~5, ~13/11


[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 701.284, ~5/4 = 386.211, ~13/11 = 291.733
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 701.284{{c}}, ~5/4 = 386.211{{c}}, ~13/11 = 291.733{{c}}


{{Optimal ET sequence|legend=1| 8d, 9, 12e, 17c, 32f, 33cd, 36ce, 41, 53, 58, 94, 103, 111, 152f, 255, 407f }}
{{Optimal ET sequence|legend=1| 8d, 9, 12e, 17c, 32f, 33cd, 36ce, 41, 53, 58, 94, 103, 111, 152f, 255, 407f }}


[[Badness]]: 3.97 × 10<sup>-6</sup>
[[Badness]] (Smith): 3.97 × 10<sup>-6</sup>


=== Commas 540/539, 625/624 ===
=== Commas 540/539, 625/624 ===
Line 428: Line 410:
{{Mapping|legend=1| 1 0 0 0 2 -4 | 0 1 0 0 3 -1 | 0 0 1 0 1 4 | 0 0 0 1 -2 0 }}
{{Mapping|legend=1| 1 0 0 0 2 -4 | 0 1 0 0 3 -1 | 0 0 1 0 1 4 | 0 0 0 1 -2 0 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 701.702, ~5/4 = 385.631, ~7/4 = 969.467
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 701.702{{c}}, ~5/4 = 385.631{{c}}, ~7/4 = 969.467{{c}}


{{Optimal ET sequence|legend=1| 19, 22, 31, 49f, 50, 53, 72, 103, 121, 152f, 193, 224 }}
{{Optimal ET sequence|legend=1| 19, 22, 31, 49f, 50, 53, 72, 103, 121, 152f, 193, 224 }}


[[Badness]]: 3.59 × 10<sup>-6</sup>
[[Badness]] (Smith): 3.59 × 10<sup>-6</sup>


=== Commas 540/539, 676/675 ===
=== Commas 540/539, 676/675 ===
Line 440: Line 422:


{{Mapping|legend=1| 1 0 0 0 2 -1 | 0 2 0 0 6 3 | 0 0 1 0 1 1 | 0 0 0 1 -2 0 }}
{{Mapping|legend=1| 1 0 0 0 2 -1 | 0 2 0 0 6 3 | 0 0 1 0 1 1 | 0 0 0 1 -2 0 }}
: Mapping generators: ~2, ~26/15, ~5, ~7
: Mapping generators: ~2, ~26/15, ~5, ~7


[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~26/15 = 950.906, ~5/4 = 386.474, ~7/4 = 969.892
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~26/15 = 950.906{{c}}, ~5/4 = 386.474{{c}}, ~7/4 = 969.892{{c}}


{{Optimal ET sequence|legend=1| 9, 10, 14cf, 19, 33cdff, 39df, 48c, 49, 53, 58, 72, 111, 121, 130, 183, 251e, 304d, 376, 434de }}
{{Optimal ET sequence|legend=1| 9, 10, 14cf, 19, 33cdff, 39df, 48c, 49, 53, 58, 72, 111, 121, 130, 183, 251e, 304d, 376, 434de }}


[[Badness]]: 3.06 × 10<sup>-6</sup>
[[Badness]] (Smith): 3.06 × 10<sup>-6</sup>


== Pentacircle (896/891) ==
== Pentacircle (896/891) ==
Line 455: Line 436:


{{Mapping|legend=1| 1 0 0 0 7 | 0 1 0 0 -4 | 0 0 1 0 0 | 0 0 0 1 1 }}
{{Mapping|legend=1| 1 0 0 0 7 | 0 1 0 0 -4 | 0 0 1 0 0 | 0 0 0 1 1 }}
: Mapping generators: ~2, ~3, ~5, ~7
: Mapping generators: ~2, ~3, ~5, ~7


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1＼1, ~3/2 = 703.576, ~5/4 = 386.314, ~7/4 = 968.126
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 703.576{{c}}, ~5/4 = 386.314{{c}}, ~7/4 = 968.126{{c}}
* [[CWE]]: ~2 = 1＼1, ~3/2 = 703.743, ~5/4 = 387.245, ~7/4 = 969.048
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 703.743{{c}}, ~5/4 = 387.245{{c}}, ~7/4 = 969.048{{c}}


{{Optimal ET sequence|legend=1| 12, 17c, 19e, 22, 34d, 39d, 41, 58, 80, 87, 99e, 121, 145, 167, 208, 266e, 699bbcdeee }}
{{Optimal ET sequence|legend=1| 12, 17c, 19e, 22, 34d, 39d, 41, 58, 80, 87, 99e, 121, 145, 167, 208, 266e, 699bbcdeee }}


[[Badness]]: 0.0658 × 10<sup>-6</sup>
[[Badness]] (Smith): 0.0658 × 10<sup>-6</sup>


=== Tridecimal pentacircle a.k.a. gentle ===
=== Tridecimal pentacircle a.k.a. gentle ===
Line 473: Line 453:
{{Mapping|legend=1| 1 0 0 0 7 12 | 0 1 0 0 -4 -7 | 0 0 1 0 0 0 | 0 0 0 1 1 1 }}
{{Mapping|legend=1| 1 0 0 0 7 12 | 0 1 0 0 -4 -7 | 0 0 1 0 0 0 | 0 0 0 1 1 1 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 703.786, ~5/4 = 386.314, ~7/4 = 967.665
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 703.786{{c}}, ~5/4 = 386.314{{c}}, ~7/4 = 967.665{{c}}


{{Optimal ET sequence|legend=1| 12f, 17c, 22, 29, 34d, 41, 46, 58, 80, 87, 121, 167, 179ef, 208, 266ef, 433bceef, 641bbceeeff, 699bbcdeeeff }}
{{Optimal ET sequence|legend=1| 12f, 17c, 22, 29, 34d, 41, 46, 58, 80, 87, 121, 167, 179ef, 208, 266ef, 433bceef, 641bbceeeff, 699bbcdeeeff }}


[[Badness]]: 3.375 × 10<sup>-6</sup>
[[Badness]] (Smith): 3.375 × 10<sup>-6</sup>


== Topsy (847/845, 1001/1000) ==
== Topsy (847/845, 1001/1000) ==
Line 485: Line 465:


{{Mapping|legend=1| 1 0 0 2 0 1 | 0 1 0 0 0 0 | 0 0 1 1 1 1 | 0 0 0 4 -3 1 }}
{{Mapping|legend=1| 1 0 0 2 0 1 | 0 1 0 0 0 0 | 0 0 1 1 1 1 | 0 0 0 4 -3 1 }}
: Mapping generators: ~2, ~3, ~5, ~13/10
: Mapping generators: ~2, ~3, ~5, ~13/10


[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 701.955, ~5/4 = 386.699, ~13/10 = 454.558
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 701.955{{c}}, ~5/4 = 386.699{{c}}, ~13/10 = 454.558{{c}}


{{Optimal ET sequence|legend=1| 16, 21, 24d, 29, 37, 45ef, 50, 53, 58, 87, 103, 111, 140, 190, 198, 301, 388, 689e }}
{{Optimal ET sequence|legend=1| 16, 21, 24d, 29, 37, 45ef, 50, 53, 58, 87, 103, 111, 140, 190, 198, 301, 388, 689e }}
Line 498: Line 477:


{{Mapping|legend=1| 1 0 0 0 2 | 0 1 0 1 2 | 0 0 1 0 -1 | 0 0 0 2 1 }}
{{Mapping|legend=1| 1 0 0 0 2 | 0 1 0 1 2 | 0 0 1 0 -1 | 0 0 0 2 1 }}
: Mapping generators: ~2, ~3, ~5, ~55/36
: Mapping generators: ~2, ~3, ~5, ~55/36


[[Optimal tuning]]:  
[[Optimal tuning]]:  
* [[CTE]]: ~2 = 1＼1, ~3/2 = 701.998, ~5/4 = 386.252, ~55/36 = 733.436
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.998{{c}}, ~5/4 = 386.252{{c}}, ~55/36 = 733.436{{c}}
* [[CWE]]: ~2 = 1＼1, ~3/2 = 701.978, ~5/4 = 386.232, ~55/36 = 733.430
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.978{{c}}, ~5/4 = 386.232{{c}}, ~55/36 = 733.430{{c}}


{{Optimal ET sequence|legend=1| 7d, 8d, 10, 15, 23de, 24d, 26, 31, 41, 65d, 72, 118, 152, 224, 270, 342, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }}
{{Optimal ET sequence|legend=1| 7d, 8d, 10, 15, 23de, 24d, 26, 31, 41, 65d, 72, 118, 152, 224, 270, 342, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }}
Line 515: Line 493:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1＼1, ~3/2 = 702.076, ~5/4 = 386.208, ~55/36 = 733.438
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.076{{c}}, ~5/4 = 386.208{{c}}, ~55/36 = 733.438{{c}}
* [[CWE]]: ~2 = 1＼1, ~3/2 = 702.099, ~5/4 = 386.248, ~55/36 = 733.449
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.099{{c}}, ~5/4 = 386.248{{c}}, ~55/36 = 733.449{{c}}


{{Optimal ET sequence|legend=1| 15, 26, 41, 46, 72, 87, 111, 183, 224, 270, 311, 494 }}
{{Optimal ET sequence|legend=1| 15, 26, 41, 46, 72, 87, 111, 183, 224, 270, 311, 494 }}
Line 526: Line 504:


{{Mapping|legend=1| 1 0 0 0 6 | 0 1 0 0 -6 | 0 0 1 0 3 | 0 0 0 1 0 }}
{{Mapping|legend=1| 1 0 0 0 6 | 0 1 0 0 -6 | 0 0 1 0 3 | 0 0 0 1 0 }}
: Mapping generators: ~2, ~3, ~5, ~7
: Mapping generators: ~2, ~3, ~5, ~7


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1＼1, ~3/2 = 701.5449, ~5/4 = 386.7538, ~7/4 = 968.8259
* [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.5449{{c}}, ~5/4 = 386.7538{{c}}, ~7/4 = 968.8259{{c}}
* [[CWE]]: ~2 = 1＼1, ~3/2 = 701.4729, ~5/4 = 386.5374, ~7/4 = 968.6210
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.4729{{c}}, ~5/4 = 386.5374{{c}}, ~7/4 = 968.6210{{c}}


{{Optimal ET sequence|legend=1| 12, 19, 26, 39d, 46, 53, 58, 72, 118, 130, 183, 190, 248, 255, 301, 373, 804, 876, 1177be }}
{{Optimal ET sequence|legend=1| 12, 19, 26, 39d, 46, 53, 58, 72, 118, 130, 183, 190, 248, 255, 301, 373, 804, 876, 1177be }}


[[Badness]]: 0.0820 × 10<sup>-6</sup>
[[Badness]] (Smith): 0.0820 × 10<sup>-6</sup>


=== Commas 729/728, 1001/1000 ===
=== Commas 729/728, 1001/1000 ===
Line 543: Line 520:


{{Mapping|legend=1| 1 0 0 0 6 -3 | 0 1 0 0 -6 6 | 0 0 1 0 3 0 | 0 0 0 1 0 -1 }}
{{Mapping|legend=1| 1 0 0 0 6 -3 | 0 1 0 0 -6 6 | 0 0 1 0 3 0 | 0 0 0 1 0 -1 }}
: Mapping generators: ~2, ~3, ~5, ~7
: Mapping generators: ~2, ~3, ~5, ~7


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1＼1, ~3/2 = 701.5537, ~5/4 = 386.7680, ~7/4 = 968.8144
* [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.5537{{c}}, ~5/4 = 386.7680{{c}}, ~7/4 = 968.8144{{c}}
* [[CWE]]: ~2 = 1＼1, ~3/2 = 701.4770, ~5/4 = 386.5437, ~7/4 = 968.6150
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.4770{{c}}, ~5/4 = 386.5437{{c}}, ~7/4 = 968.6150{{c}}


{{Optimal ET sequence|legend=1| 53, 58, 72, 111, 130, 183, 190, 243e, 248, 301, 373, 804, 1177be }}
{{Optimal ET sequence|legend=1| 53, 58, 72, 111, 130, 183, 190, 243e, 248, 301, 373, 804, 1177be }}


[[Badness]]: 3.33 × 10<sup>-6</sup>
[[Badness]] (Smith): 3.33 × 10<sup>-6</sup>


== Kalismic (9801/9800) ==
== Kalismic (9801/9800) ==
Line 560: Line 536:


{{Mapping|legend=1| 2 0 0 0 3 | 0 1 0 0 -2 | 0 0 1 0 1 | 0 0 0 1 1 }}
{{Mapping|legend=1| 2 0 0 0 3 | 0 1 0 0 -2 | 0 0 1 0 1 | 0 0 0 1 1 }}
: Mapping generators: ~99/70, ~3, ~5, ~7
: Mapping generators: ~99/70, ~3, ~5, ~7


[[Optimal tuning]]:  
[[Optimal tuning]]:  
* [[CTE]]: ~99/70 = 1＼2, ~3/2 = 701.942, ~5/4 = 386.327, ~7/4 = 968.846
* [[CTE]]: ~99/70 = 600.000{{c}}, ~3/2 = 701.942{{c}}, ~5/4 = 386.327{{c}}, ~7/4 = 968.846{{c}}
* [[CWE]]: ~99/70 = 1＼2, ~3/2 = 701.940, ~5/4 = 386.323, ~7/4 = 968.840
* [[CWE]]: ~99/70 = 600.000{{c}}, ~3/2 = 701.940{{c}}, ~5/4 = 386.323{{c}}, ~7/4 = 968.840{{c}}


{{Optimal ET sequence|legend=1| 8d, 10, 12, 22, 34d, 46, 58, 72, 118, 130, 152, 224, 270, 342, 612, 836, 1084, 1106, 1236, 1506, 1578, 1848, 2684, 4038, 4190, 4532, 11254, 15786e, 21896e }}
{{Optimal ET sequence|legend=1| 8d, 10, 12, 22, 34d, 46, 58, 72, 118, 130, 152, 224, 270, 342, 612, 836, 1084, 1106, 1236, 1506, 1578, 1848, 2684, 4038, 4190, 4532, 11254, 15786e, 21896e }}
Line 579: Line 554:
: 3/2 length = 1.1956, 7/4 length = 1.4506, 14/13 length = 1.8299
: 3/2 length = 1.1956, 7/4 length = 1.4506, 14/13 length = 1.8299


[[Optimal tuning]] ([[CTE]]): ~99/70 = 1＼1, ~3/2 = 702.024, ~5/4 = 386.294, ~7/4 = 969.114
[[Optimal tuning]] ([[CTE]]): ~99/70 = 600.000{{c}}, ~3/2 = 702.024{{c}}, ~5/4 = 386.294{{c}}, ~7/4 = 969.114{{c}}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 593: Line 568:


{{Mapping|legend=1| 1 0 0 0 0 | 0 1 0 2 2 | 0 0 1 -1 -1 | 0 0 0 3 4 }}
{{Mapping|legend=1| 1 0 0 0 0 | 0 1 0 2 2 | 0 0 1 -1 -1 | 0 0 0 3 4 }}
: Mapping generators: ~2, ~3, ~5, ~11/7
: Mapping generators: ~2, ~3, ~5, ~11/7


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]] and [[CWE]]: ~2 = 1＼1, ~3/2 = 702.031, ~5/4 = 386.233, ~11/7 = 783.508
* [[CTE]] and [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.031{{c}}, ~5/4 = 386.233{{c}}, ~11/7 = 783.508{{c}}


{{Optimal ET sequence|legend=1| 12, 21, 23de, 26, 37, 46, 58, 72, 118, 130, 190, 239, 311, 441, 559, 752e, 870 }}
{{Optimal ET sequence|legend=1| 12, 21, 23de, 26, 37, 46, 58, 72, 118, 130, 190, 239, 311, 441, 559, 752e, 870 }}
Line 607: Line 581:


{{Mapping|legend=1| 1 0 0 0 0 -2 | 0 1 0 2 2 3 | 0 0 1 -1 -1 -1 | 0 0 0 3 4 5 }}
{{Mapping|legend=1| 1 0 0 0 0 -2 | 0 1 0 2 2 3 | 0 0 1 -1 -1 -1 | 0 0 0 3 4 5 }}
: Mapping generators: ~2, ~3, ~5, ~11/7
: Mapping generators: ~2, ~3, ~5, ~11/7


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1＼1, ~3/2 = 702.072, ~5/4 = 386.528, ~11/7 = 783.823
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.072{{c}}, ~5/4 = 386.528{{c}}, ~11/7 = 783.823{{c}}
* [[CWE]]: ~2 = 1＼1, ~3/2 = 702.253, ~5/4 = 386.776, ~11/7 = 783.875
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.253{{c}}, ~5/4 = 386.776{{c}}, ~11/7 = 783.875{{c}}


{{Optimal ET sequence|legend=1| 26, 37, 46, 58, 72, 121, 130, 193, 239, 251e, 323e, 369 }}
{{Optimal ET sequence|legend=1| 26, 37, 46, 58, 72, 121, 130, 193, 239, 251e, 323e, 369 }}
Line 622: Line 595:


{{Mapping|legend=1| 1 0 0 0 0 0 | 0 1 0 2 2 0 | 0 0 1 -1 -1 3 | 0 0 0 3 4 -5 }}
{{Mapping|legend=1| 1 0 0 0 0 0 | 0 1 0 2 2 0 | 0 0 1 -1 -1 3 | 0 0 0 3 4 -5 }}
: Mapping generators: ~2, ~3, ~5, ~11/7
: Mapping generators: ~2, ~3, ~5, ~11/7


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]] and [[CWE]]: ~2 = 1＼1, ~3/2 = 701.952, ~5/4 = 386.139, ~11/7 = 783.548
* [[CTE]] and [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.952{{c}}, ~5/4 = 386.139{{c}}, ~11/7 = 783.548{{c}}


{{Optimal ET sequence|legend=1| 46f, 49f, 58, 72, 118, 121, 130, 190, 193, 248, 311, 441, 752e, 1072 }}
{{Optimal ET sequence|legend=1| 46f, 49f, 58, 72, 118, 121, 130, 190, 193, 248, 311, 441, 752e, 1072 }}
Line 636: Line 608:


{{Mapping|legend=1| 1 0 2 0 1 | 0 1 2 0 2 | 0 0 -4 0 -1 | 0 0 0 1 0 }}
{{Mapping|legend=1| 1 0 2 0 1 | 0 1 2 0 2 | 0 0 -4 0 -1 | 0 0 0 1 0 }}
: Mapping generators: ~2, ~3, ~18/11, ~7
: Mapping generators: ~2, ~3, ~18/11, ~7


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1＼1, ~3/2 = 702.334, ~18/11 = 854.555, ~7/4 = 968.826
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.334{{c}}, ~18/11 = 854.555{{c}}, ~7/4 = 968.826{{c}}
* [[CWE]]: ~2 = 1＼1, ~3/2 = 702.292, ~18/11 = 854.548, ~7/4 = 968.756
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.292{{c}}, ~18/11 = 854.548{{c}}, ~7/4 = 968.756{{c}}


{{Optimal ET sequence|legend=1| 14c, 17c, 24, 31, 63, 80, 87, 111, 118, 198, 212, 292, 323, 410, 851e }}
{{Optimal ET sequence|legend=1| 14c, 17c, 24, 31, 63, 80, 87, 111, 118, 198, 212, 292, 323, 410, 851e }}


[[Badness]]: 0.351 × 10<sup>-6</sup>
[[Badness]] (Smith): 0.351 × 10<sup>-6</sup>


=== Tridecimal semicanousmic ===
=== Tridecimal semicanousmic ===
Line 655: Line 626:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1＼1, ~3/2 = 702.469, ~18/11 = 854.644, ~7/4 = 968.959
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 702.469{{c}}, ~18/11 = 854.644{{c}}, ~7/4 = 968.959{{c}}
* CWE: ~2 = 1＼1, ~3/2 = 702.483, ~18/11 = 854.642, ~7/4 = 968.989
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 702.483{{c}}, ~18/11 = 854.642{{c}}, ~7/4 = 968.989{{c}}


{{Optimal ET sequence|legend=0| 87, 111, 181, 198, 323, 410 }}
{{Optimal ET sequence|legend=0| 87, 111, 181, 198, 323, 410 }}


Badness: 17.1 × 10<sup>-6</sup>
Badness (Smith): 17.1 × 10<sup>-6</sup>


==== 17-limit ====
==== 17-limit ====
Line 670: Line 641:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1＼1, ~3/2 = 702.413, ~18/11 = 854.633, ~7/4 = 969.032
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 702.413{{c}}, ~18/11 = 854.633{{c}}, ~7/4 = 969.032{{c}}
* CWE: ~2 = 1＼1, ~3/2 = 702.411, ~18/11 = 854.634, ~7/4 = 969.026
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 702.411{{c}}, ~18/11 = 854.634{{c}}, ~7/4 = 969.026{{c}}


{{Optimal ET sequence|legend=0| 87, 94, 111, 181, 198g, 212g, 292, 323, 410 }}
{{Optimal ET sequence|legend=0| 87, 94, 111, 181, 198g, 212g, 292, 323, 410 }}


Badness: 34.0 × 10<sup>-6</sup>
Badness (Smith): 34.0 × 10<sup>-6</sup>


==== 19-limit ====
==== 19-limit ====
Line 685: Line 656:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1＼1, ~3/2 = 702.368, ~18/11 = 854.639, ~7/4 = 969.075
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 702.368{{c}}, ~18/11 = 854.639{{c}}, ~7/4 = 969.075{{c}}
* CWE: ~2 = 1＼1, ~3/2 = 702.351, ~18/11 = 854.644, ~7/4 = 969.010
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 702.351{{c}}, ~18/11 = 854.644{{c}}, ~7/4 = 969.010{{c}}


{{Optimal ET sequence|legend=0| 87, 94, 111, 181, 205, 212gh, 292h, 299, 323, 410, 622ef }}
{{Optimal ET sequence|legend=0| 87, 94, 111, 181, 205, 212gh, 292h, 299, 323, 410, 622ef }}


Badness: 41.9 × 10<sup>-6</sup>
Badness (Smith): 41.9 × 10<sup>-6</sup>


== Semiporwellismic (16384/16335) ==
== Semiporwellismic (16384/16335) ==
Line 698: Line 669:


{{Mapping|legend=1| 1 0 0 0 7 | 0 1 1 0 -2 | 0 0 2 0 -1 | 0 0 0 1 0 }}
{{Mapping|legend=1| 1 0 0 0 7 | 0 1 1 0 -2 | 0 0 2 0 -1 | 0 0 0 1 0 }}
: Mapping generators: ~2, ~3, ~128/99, ~7
: Mapping generators: ~2, ~3, ~128/99, ~7


[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 702.470, ~128/99 = 442.106, ~7/4 = 968.826
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 702.470{{c}}, ~128/99 = 442.106{{c}}, ~7/4 = 968.826{{c}}


{{Optimal ET sequence|legend=1| 19, 22, 41, 65d, 68, 84, 87, 111, 130, 152, 239, 282, 328, 369, 521e, 1370bcdeee, 1411bcdeee, 1609bccdeee }}
{{Optimal ET sequence|legend=1| 19, 22, 41, 65d, 68, 84, 87, 111, 130, 152, 239, 282, 328, 369, 521e, 1370bcdeee, 1411bcdeee, 1609bccdeee }}


[[Badness]]: 0.219 × 10<sup>-6</sup>
[[Badness]] (Smith): 0.219 × 10<sup>-6</sup>


== Symbiotic (19712/19683) ==
== Symbiotic (19712/19683) ==
Line 713: Line 683:


{{Mapping|legend=1| 1 0 0 0 -8 | 0 1 0 0 9 | 0 0 1 0 0 | 0 0 0 1 -1 }}
{{Mapping|legend=1| 1 0 0 0 -8 | 0 1 0 0 9 | 0 0 1 0 0 | 0 0 0 1 -1 }}
: Mapping generators: ~2, ~3, ~5, ~7
: Mapping generators: ~2, ~3, ~5, ~7


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1＼1, ~3/2 = 702.213, ~5/4 = 386.314, ~7/4 = 968.736
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.213{{c}}, ~5/4 = 386.314{{c}}, ~7/4 = 968.736{{c}}
* [[CWE]]: ~2 = 1＼1, ~3/2 = 702.244, ~5/4 = 386.406, ~7/4 = 968.859
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.244{{c}}, ~5/4 = 386.406{{c}}, ~7/4 = 968.859{{c}}


{{Optimal ET sequence|legend=1| 17c, 19e, 24, 34d, 41, 53, 58, 94, 99e, 118, 152, 270, 581, 733, 851, 1003, 1273, 1854, 2124b }}
{{Optimal ET sequence|legend=1| 17c, 19e, 24, 34d, 41, 53, 58, 94, 99e, 118, 152, 270, 581, 733, 851, 1003, 1273, 1854, 2124b }}


[[Badness]]: 0.120 × 10<sup>-6</sup>
[[Badness]] (Smith): 0.120 × 10<sup>-6</sup>


=== Tridecimal symbiotic ===
=== Tridecimal symbiotic ===
Line 732: Line 701:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1＼1, ~3/2 = 702.228, ~5/4 = 386.284, ~7/4 = 968.789
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.228{{c}}, ~5/4 = 386.284{{c}}, ~7/4 = 968.789{{c}}
* [[CWE]]: ~2 = 1＼1, ~3/2 = 702.254, ~5/4 = 386.401, ~7/4 = 968.898
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.254{{c}}, ~5/4 = 386.401{{c}}, ~7/4 = 968.898{{c}}


{{Optimal ET sequence|legend=1| 17c, 34dff, 36ce, 41, 53, 58, 94, 111, 152f, 212, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 3127bf }}
{{Optimal ET sequence|legend=1| 17c, 34dff, 36ce, 41, 53, 58, 94, 111, 152f, 212, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 3127bf }}


[[Badness]]: 3.31 × 10<sup>-6</sup>
[[Badness]] (Smith): 3.31 × 10<sup>-6</sup>


=== 2.3.5.7.11.13.19 subgroup ===
=== 2.3.5.7.11.13.19 subgroup ===
Line 747: Line 716:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1＼1, ~3/2 = 702.230, ~5/4 = 386.304, ~7/4 = 968.797
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 702.230{{c}}, ~5/4 = 386.304{{c}}, ~7/4 = 968.797{{c}}
* CWE: ~2 = 1＼1, ~3/2 = 702.255, ~5/4 = 386.408, ~7/4 = 968.902
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 702.255{{c}}, ~5/4 = 386.408{{c}}, ~7/4 = 968.902{{c}}


{{Optimal ET sequence|legend=0| 17ch, 24f, 34dffh, 36ceh, 41, 53, 58h, 94, 111, 152f, 212h, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 3127bfh }}
{{Optimal ET sequence|legend=0| 17ch, 24f, 34dffh, 36ceh, 41, 53, 58h, 94, 111, 152f, 212h, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 3127bfh }}


Badness: 4.37 × 10<sup>-6</sup>
Badness (Smith): 4.37 × 10<sup>-6</sup>


== Olympic (131072/130977) ==
== Olympic (131072/130977) ==
Line 760: Line 729:


{{Mapping|legend=1| 1 0 0 0 17 | 0 1 0 0 -5 | 0 0 1 0 0 | 0 0 0 1 -2 }}
{{Mapping|legend=1| 1 0 0 0 17 | 0 1 0 0 -5 | 0 0 1 0 0 | 0 0 0 1 -2 }}
: Mapping generators: ~2, ~3, ~5, ~7
: Mapping generators: ~2, ~3, ~5, ~7


[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 702.103, ~5/4 = 386.314, ~7/4 = 969.012
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 702.103{{c}}, ~5/4 = 386.314{{c}}, ~7/4 = 969.012{{c}}


{{Optimal ET sequence|legend=1| 41, 53, 84, 87, 130, 183, 224, 270, 494, 764, 1164, 1205, 1475, 1969, 2239, 3133de, 4608cde, 5102bcde, 10474bbccdddeee }}
{{Optimal ET sequence|legend=1| 41, 53, 84, 87, 130, 183, 224, 270, 494, 764, 1164, 1205, 1475, 1969, 2239, 3133de, 4608cde, 5102bcde, 10474bbccdddeee }}
Line 774: Line 742:
{{Mapping|legend=1| 1 0 0 0 17 12 | 0 1 0 0 -5 -2 | 0 0 1 0 0 -1 | 0 0 0 1 -2 -1 }}
{{Mapping|legend=1| 1 0 0 0 17 12 | 0 1 0 0 -5 -2 | 0 0 1 0 0 -1 | 0 0 0 1 -2 -1 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 702.103, ~5/4 = 386.298, ~7/4 = 969.007
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 702.103{{c}}, ~5/4 = 386.298{{c}}, ~7/4 = 969.007{{c}}


{{Optimal ET sequence|legend=1| 41, 46, 53, 84, 87, 130, 183, 217, 224, 270, 494, 764, 935, 1075, 1205, 1699, 2280, 2774e }} *
{{Optimal ET sequence|legend=1| 41, 46, 53, 84, 87, 130, 183, 217, 224, 270, 494, 764, 935, 1075, 1205, 1699, 2280, 2774e }} *
Line 786: Line 754:


{{Mapping|legend=1| 1 0 0 0 4 | 0 2 0 0 -3 | 0 0 1 0 2 | 0 0 0 1 -1 }}
{{Mapping|legend=1| 1 0 0 0 4 | 0 2 0 0 -3 | 0 0 1 0 2 | 0 0 0 1 -1 }}
: Mapping generators: ~2, ~400/231, ~5, ~7
: Mapping generators: ~2, ~400/231, ~5, ~7


[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~400/231 = 950.960, ~5/4 = 386.417, ~7/4 = 968.751
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~400/231 = 950.960{{c}}, ~5/4 = 386.417{{c}}, ~7/4 = 968.751{{c}}


{{Optimal ET sequence|legend=1| 15, 19, 29, 43, 53, 58, 68, 72 }}
{{Optimal ET sequence|legend=1| 15, 19, 29, 43, 53, 58, 68, 72 }}
Line 799: Line 766:


{{Mapping|legend=1| 1 0 4 0 -1 | 0 1 3 0 2 | 0 0 -5 0 1 | 0 0 0 1 0 }}
{{Mapping|legend=1| 1 0 4 0 -1 | 0 1 3 0 2 | 0 0 -5 0 1 | 0 0 0 1 0 }}
: Mapping generators: ~2, ~3, ~22/9, ~7
: Mapping generators: ~2, ~3, ~22/9, ~7


[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 702.738, ~11/9 = 344.406, ~7/4 = 968.826
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 702.738{{c}}, ~11/9 = 344.406{{c}}, ~7/4 = 968.826{{c}}


{{Optimal ET sequence|legend=1| 77, 80, 87, 94, 167 }}
{{Optimal ET sequence|legend=1| 77, 80, 87, 94, 167 }}
Line 815: Line 781:
{{Mapping|legend=1| 1 0 4 0 -1 4 | 0 1 3 0 2 -1 | 0 0 -5 0 1 1 | 0 0 0 1 0 0 }}
{{Mapping|legend=1| 1 0 4 0 -1 4 | 0 1 3 0 2 -1 | 0 0 -5 0 1 1 | 0 0 0 1 0 0 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1＼1, ~3/2 = 702.776, ~11/9 = 344.410, ~7/4 = 968.826
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 702.776{{c}}, ~11/9 = 344.410{{c}}, ~7/4 = 968.826{{c}}


{{Optimal ET sequence|legend=1| 77, 80, 87, 94, 167 }}
{{Optimal ET sequence|legend=1| 77, 80, 87, 94, 167 }}
Line 826: Line 792:
Mapping: {{mapping| 1 0 4 0 -1 4 6 | 0 1 3 0 2 -1 3 | 0 0 -5 0 1 1 -3 | 0 0 0 1 0 0 -1 }}
Mapping: {{mapping| 1 0 4 0 -1 4 6 | 0 1 3 0 2 -1 3 | 0 0 -5 0 1 1 -3 | 0 0 0 1 0 0 -1 }}


Optimal tuning (CTE): ~2 = 1＼1, ~3/2 = 702.713, ~11/9 = 344.403, ~7/4 = 969.193
Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~3/2 = 702.713{{c}}, ~11/9 = 344.403{{c}}, ~7/4 = 969.193{{c}}


{{Optimal ET sequence|legend=0| 77, 80, 87, 94, 167 }}
{{Optimal ET sequence|legend=0| 77, 80, 87, 94, 167 }}
Line 837: Line 803:
Mapping: {{mapping| 1 0 4 0 -1 4 6 2 | 0 1 3 0 2 -1 3 4 | 0 0 -5 0 1 1 -3 -1 | 0 0 0 1 0 0 -1 -1 }}
Mapping: {{mapping| 1 0 4 0 -1 4 6 2 | 0 1 3 0 2 -1 3 4 | 0 0 -5 0 1 1 -3 -1 | 0 0 0 1 0 0 -1 -1 }}


Optimal tuning (CTE): ~2 = 1＼1, ~3/2 = 702.736, ~11/9 = 344.417, ~7/4 = 969.159
Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~3/2 = 702.736{{c}}, ~11/9 = 344.417{{c}}, ~7/4 = 969.159{{c}}


{{Optimal ET sequence|legend=0| 77, 80, 87, 94, 167h }}
{{Optimal ET sequence|legend=0| 77, 80, 87, 94, 167h }}
Retrieved from "https://en.xen.wiki/w/Catalog_of_rank-4_temperaments"