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Canopic clan: Difference between revisions

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{{Mapping|legend=1| 1 9 2 7 | 0 -23 1 -13 }}
{{Mapping|legend=1| 1 9 2 7 | 0 -23 1 -13 }}
: mapping generators: ~2, ~5/4
: mapping generators: ~2, ~5/4


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/4 = 386.863
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~5/4 = 386.863{{c}}


{{Optimal ET sequence|legend=1| 31, 90, 121, 152, 335d }}
{{Optimal ET sequence|legend=1| 31, 90, 121, 152, 335d }}


[[Badness]]: 0.051834
[[Badness]] (Smith): 0.051834


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 9 2 7 17 | 0 -23 1 -13 -42 }}
Mapping: {{mapping| 1 9 2 7 17 | 0 -23 1 -13 -42 }}


Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 386.856
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~5/4 = 386.856{{c}}


{{Optimal ET sequence|legend=1| 31, 90e, 121, 152, 335d, 487d }}
{{Optimal ET sequence|legend=0| 31, 90e, 121, 152, 335d, 487d }}


Badness: 0.019845
Badness (Smith): 0.019845


=== 13-limit ===
=== 13-limit ===
Line 77: Line 76:
Mapping: {{mapping| 1 9 2 7 17 -5 | 0 -23 1 -13 -42 27 }}
Mapping: {{mapping| 1 9 2 7 17 -5 | 0 -23 1 -13 -42 27 }}


Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 386.826
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~5/4 = 386.826{{c}}


{{Optimal ET sequence|legend=1| 31, 121, 152f, 425deff }}
{{Optimal ET sequence|legend=0| 31, 121, 152f, 425deff }}


Badness: 0.024839
Badness (Smith): 0.024839


=== 17-limit ===
=== 17-limit ===
Line 90: Line 89:
Mapping: {{mapping| 1 9 2 7 17 -5 -3 | 0 -23 1 -13 -42 27 22 }}
Mapping: {{mapping| 1 9 2 7 17 -5 -3 | 0 -23 1 -13 -42 27 22 }}


Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 386.812
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~5/4 = 386.812{{c}}


{{Optimal ET sequence|legend=1| 31, 121, 273defgg }}
{{Optimal ET sequence|legend=0| 31, 121, 273defgg }}


Badness: 0.021400
Badness (Smith): 0.021400


=== 19-limit ===
=== 19-limit ===
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Mapping: {{mapping| 1 9 2 7 17 -5 -3 -8 | 0 -23 1 -13 -42 27 22 38 }}
Mapping: {{mapping| 1 9 2 7 17 -5 -3 -8 | 0 -23 1 -13 -42 27 22 38 }}


Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 386.819
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~5/4 = 386.819{{c}}


{{Optimal ET sequence|legend=1| 31, 121, 152fg, 273defgg }}
{{Optimal ET sequence|legend=0| 31, 121, 152fg, 273defgg }}


Badness: 0.018413
Badness (Smith): 0.018413


== Kwai ==
== Kwai ==
Line 119: Line 118:


{{Mapping|legend=1| 1 0 -50 -40 | 0 1 33 27 }}
{{Mapping|legend=1| 1 0 -50 -40 | 0 1 33 27 }}
: mapping generators: ~2, ~3
: mapping generators: ~2, ~3


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.616
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 702.616{{c}}


{{Optimal ET sequence|legend=1| 41, 111, 152, 345, 497d }}
{{Optimal ET sequence|legend=1| 41, 111, 152, 345, 497d }}


[[Badness]]: 0.054476
[[Badness]] (Smith): 0.054476


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 0 -50 -40 32 | 0 1 33 27 -18 }}
Mapping: {{mapping| 1 0 -50 -40 32 | 0 1 33 27 -18 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.623
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.623{{c}}


{{Optimal ET sequence|legend=1| 29cd, 41, 111, 152 }}
{{Optimal ET sequence|legend=0| 29cd, 41, 111, 152 }}


Badness: 0.026219
Badness (Smith): 0.026219


==== 13-limit ====
==== 13-limit ====
Line 148: Line 146:
Mapping: {{mapping| 1 0 -50 -40 32 27 | 0 1 33 27 -18 -21 }}
Mapping: {{mapping| 1 0 -50 -40 32 27 | 0 1 33 27 -18 -21 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.644
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.644{{c}}


{{Optimal ET sequence|legend=1| 29cd, 41, 111, 152f }}
{{Optimal ET sequence|legend=0| 29cd, 41, 111, 152f }}


Badness: 0.024555
Badness (Smith): 0.024555


===== 17-limit =====
===== 17-limit =====
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Mapping: {{mapping| 1 0 -50 -40 32 27 58 | 0 1 33 27 -18 -21 -34 }}
Mapping: {{mapping| 1 0 -50 -40 32 27 58 | 0 1 33 27 -18 -21 -34 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.660
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.660{{c}}


{{Optimal ET sequence|legend=1| 29cdg, 41, 111, 152fg, 263dfg }}
{{Optimal ET sequence|legend=0| 29cdg, 41, 111, 152fg, 263dfg }}


Badness: 0.021950
Badness (Smith): 0.021950


===== 19-limit =====
===== 19-limit =====
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Mapping: {{mapping| 1 0 -50 -40 32 27 58 -56 | 0 1 33 27 -18 -21 -34 38 }}
Mapping: {{mapping| 1 0 -50 -40 32 27 58 -56 | 0 1 33 27 -18 -21 -34 38 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.657
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.657{{c}}


{{Optimal ET sequence|legend=1| 29cdgh, 41, 111, 152fg, 263dfgh }}
{{Optimal ET sequence|legend=0| 29cdgh, 41, 111, 152fg, 263dfgh }}


Badness: 0.016957
Badness (Smith): 0.016957


==== Hemikwai ====
==== Hemikwai ====
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Mapping: {{mapping| 1 0 -50 -40 32 -51 | 0 2 66 54 -36 69 }}
Mapping: {{mapping| 1 0 -50 -40 32 -51 | 0 2 66 54 -36 69 }}
: mapping generators: ~2, ~26/15
: mapping generators: ~2, ~26/15


Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 951.314
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~26/15 = 951.314{{c}}


{{Optimal ET sequence|legend=1| 82, 111, 193, 304d }}
{{Optimal ET sequence|legend=0| 82, 111, 193, 304d }}


Badness: 0.044108
Badness (Smith): 0.044108


===== 17-limit =====
===== 17-limit =====
Line 202: Line 199:
Mapping: {{mapping| 1 0 -50 -40 32 -51 -30 | 0 2 66 54 -36 69 43 }}
Mapping: {{mapping| 1 0 -50 -40 32 -51 -30 | 0 2 66 54 -36 69 43 }}


Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 951.314
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~26/15 = 951.314{{c}}


{{Optimal ET sequence|legend=1| 82, 111, 193, 304d }}
{{Optimal ET sequence|legend=0| 82, 111, 193, 304d }}


Badness: 0.025806
Badness (Smith): 0.025806


===== 19-limit =====
===== 19-limit =====
Line 215: Line 212:
Mapping: {{mapping| 1 0 -50 -40 32 -51 -30 -56 | 0 2 66 54 -36 69 43 76 }}
Mapping: {{mapping| 1 0 -50 -40 32 -51 -30 -56 | 0 2 66 54 -36 69 43 76 }}


Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 951.313
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~26/15 = 951.313{{c}}


{{Optimal ET sequence|legend=1| 82, 111, 193, 304dh }}
{{Optimal ET sequence|legend=0| 82, 111, 193, 304dh }}


Badness: 0.019146
Badness (Smith): 0.019146


== Pluto ==
== Pluto ==
{{Distinguish| plutus }}
{{Distinguish| Plutus }}


Pluto, named by [[Gene Ward Smith]] in 2010<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_18465.html Yahoo! Tuning Group | ''19-limit Pluto temperament'']</ref>, can be described as the 41 & 80 temperament. It is generated by a sharpened [[7/5]], and [[121edo|59\121]] is about perfect as a tuning.  
Pluto, named by [[Gene Ward Smith]] in 2010<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_18465.html Yahoo! Tuning Group | ''19-limit Pluto temperament'']</ref>, can be described as the {{nowrap| 41 & 80 }} temperament. It is generated by a sharpened [[7/5]], and [[121edo|59\121]] is about perfect as a tuning.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 232: Line 229:
{{Mapping|legend=1| 1 5 15 15 | 0 -7 -26 -25 }}
{{Mapping|legend=1| 1 5 15 15 | 0 -7 -26 -25 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 585.147
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~7/5 = 585.147{{c}}


{{Optimal ET sequence|legend=1| 39d, 41, 80, 121, 404bd }}
{{Optimal ET sequence|legend=1| 39d, 41, 80, 121, 404bd }}


[[Badness]]: 0.057514
[[Badness]] (Smith): 0.057514


=== 11-limit ===
=== 11-limit ===
Line 245: Line 242:
Mapping: {{mapping| 1 5 15 15 2 | 0 -7 -26 -25 3 }}
Mapping: {{mapping| 1 5 15 15 2 | 0 -7 -26 -25 3 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.114
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 585.114{{c}}


{{Optimal ET sequence|legend=1| 39d, 41, 80, 121 }}
{{Optimal ET sequence|legend=0| 39d, 41, 80, 121 }}


Badness: 0.029844
Badness (Smith): 0.029844


==== 13-limit ====
==== 13-limit ====
Line 258: Line 255:
Mapping: {{mapping| 1 5 15 15 2 -8 | 0 -7 -26 -25 3 24 }}
Mapping: {{mapping| 1 5 15 15 2 -8 | 0 -7 -26 -25 3 24 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.123
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 585.123{{c}}


{{Optimal ET sequence|legend=1| 39d, 41, 80, 121 }}
{{Optimal ET sequence|legend=0| 39d, 41, 80, 121 }}


Badness: 0.025717
Badness (Smith): 0.025717


===== 17-limit =====
===== 17-limit =====
Line 271: Line 268:
Mapping: {{mapping| 1 5 15 15 2 -8 -12 | 0 -7 -26 -25 3 24 33 }}
Mapping: {{mapping| 1 5 15 15 2 -8 -12 | 0 -7 -26 -25 3 24 33 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.116
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 585.116{{c}}


{{Optimal ET sequence|legend=1| 39d, 41, 80, 121 }}
{{Optimal ET sequence|legend=0| 39d, 41, 80, 121 }}


Badness: 0.021463
Badness (Smith): 0.021463


===== 19-limit =====
===== 19-limit =====
Line 284: Line 281:
Mapping: {{mapping| 1 5 15 15 2 -8 -12 14 | 0 -7 -26 -25 3 24 33 -20 }}
Mapping: {{mapping| 1 5 15 15 2 -8 -12 14 | 0 -7 -26 -25 3 24 33 -20 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.109
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 585.109{{c}}


{{Optimal ET sequence|legend=1| 39d, 41, 80, 121 }}
{{Optimal ET sequence|legend=0| 39d, 41, 80, 121 }}


Badness: 0.017650
Badness (Smith): 0.017650


==== Orcus ====
==== Orcus ====
Line 297: Line 294:
Mapping: {{mapping| 1 5 15 15 2 12 | 0 -7 -26 -25 3 -17 }}
Mapping: {{mapping| 1 5 15 15 2 12 | 0 -7 -26 -25 3 -17 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.111
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 585.111{{c}}


{{Optimal ET sequence|legend=1| 39df, 41, 80f, 121ff }}
{{Optimal ET sequence|legend=0| 39df, 41, 80f, 121ff }}


Badness: 0.033441
Badness (Smith): 0.033441


=== Plutino ===
=== Plutino ===
Line 310: Line 307:
Mapping: {{mapping| 1 5 15 15 22 | 0 -7 -26 -25 -38 }}
Mapping: {{mapping| 1 5 15 15 22 | 0 -7 -26 -25 -38 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.283
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 585.283{{c}}


{{Optimal ET sequence|legend=1| 39dee, 41 }}
{{Optimal ET sequence|legend=0| 39dee, 41 }}


Badness: 0.057966
Badness (Smith): 0.057966


==== 13-limit ====
==== 13-limit ====
Line 323: Line 320:
Mapping: {{mapping| 1 5 15 15 22 12 | 0 -7 -26 -25 -38 -17 }}
Mapping: {{mapping| 1 5 15 15 22 12 | 0 -7 -26 -25 -38 -17 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.232
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 585.232{{c}}


{{Optimal ET sequence|legend=1| 39deef, 41 }}
{{Optimal ET sequence|legend=0| 39deef, 41 }}


Badness: 0.040182
Badness (Smith): 0.040182


== Mirkat ==
== Mirkat ==
Line 336: Line 333:
{{Mapping|legend=1| 3 2 1 2 | 0 6 13 14 }}
{{Mapping|legend=1| 3 2 1 2 | 0 6 13 14 }}


[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~10/9 = 183.539
[[Optimal tuning]] ([[POTE]]): ~63/50 = 400.000{{c}}, ~10/9 = 183.539{{c}}


{{Optimal ET sequence|legend=1| 39d, 72, 111, 183, 255 }}
{{Optimal ET sequence|legend=1| 39d, 72, 111, 183, 255 }}


[[Badness]]: 0.059376
[[Badness]] (Smith): 0.059376


=== 11-limit ===
=== 11-limit ===
Line 349: Line 346:
Mapping: {{mapping| 3 2 1 2 9 | 0 6 13 14 3 }}
Mapping: {{mapping| 3 2 1 2 9 | 0 6 13 14 3 }}


Optimal tuning (POTE): ~63/50 = 1\3, ~10/9 = 183.528
Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~10/9 = 183.528{{c}}


{{Optimal ET sequence|legend=1| 39d, 72, 111, 183, 255 }}
{{Optimal ET sequence|legend=0| 39d, 72, 111, 183, 255 }}


Badness: 0.022126
Badness (Smith): 0.022126


=== 13-limit ===
=== 13-limit ===
Line 362: Line 359:
Mapping: {{mapping| 3 2 1 2 9 1 | 0 6 13 14 3 22 }}
Mapping: {{mapping| 3 2 1 2 9 1 | 0 6 13 14 3 22 }}


Optimal tuning (POTE): ~63/50 = 1\3, ~10/9 = 183.577
Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~10/9 = 183.577{{c}}


{{Optimal ET sequence|legend=1| 39df, 72, 111, 183 }}
{{Optimal ET sequence|legend=0| 39df, 72, 111, 183 }}


Badness: 0.018632
Badness (Smith): 0.018632


=== 17-limit ===
=== 17-limit ===
Line 375: Line 372:
Mapping: {{mapping| 3 2 1 2 9 1 4 | 0 6 13 14 3 22 18 }}
Mapping: {{mapping| 3 2 1 2 9 1 4 | 0 6 13 14 3 22 18 }}


Optimal tuning (POTE): ~34/27 = 1\3, ~10/9 = 183.579
Optimal tuning (POTE): ~34/27 = 400.000{{c}}, ~10/9 = 183.579{{c}}


{{Optimal ET sequence|legend=1| 39dfg, 72, 111, 183 }}
{{Optimal ET sequence|legend=0| 39dfg, 72, 111, 183 }}


Badness: 0.011775
Badness (Smith): 0.011775


== Eris ==
== Eris ==
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{{Mapping|legend=1| 1 10 0 6 | 0 -29 8 -11 }}
{{Mapping|legend=1| 1 10 0 6 | 0 -29 8 -11 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~60/49 = 348.216
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~60/49 = 348.216{{c}}


{{Optimal ET sequence|legend=1| 31, 131, 162, 193, 224, 1823cd, 2271cd }}
{{Optimal ET sequence|legend=1| 31, 131, 162, 193, 224, 1823cd, 2271cd }}


[[Badness]]: 0.074719
[[Badness]] (Smith): 0.074719


=== 11-limit ===
=== 11-limit ===
Line 403: Line 400:
Mapping: {{mapping| 1 10 0 6 20 | 0 -29 8 -11 -57 }}
Mapping: {{mapping| 1 10 0 6 20 | 0 -29 8 -11 -57 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 348.219
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/9 = 348.219{{c}}


{{Optimal ET sequence|legend=1| 31, 193, 224, 703, 927d, 1151cd }}
{{Optimal ET sequence|legend=0| 31, 193, 224, 703, 927d, 1151cd }}


Badness: 0.027621
Badness (Smith): 0.027621


=== 13-limit ===
=== 13-limit ===
Line 416: Line 413:
Mapping: {{mapping| 1 10 0 6 20 -14 | 0 -29 8 -11 -57 61 }}
Mapping: {{mapping| 1 10 0 6 20 -14 | 0 -29 8 -11 -57 61 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 348.213
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/9 = 348.213{{c}}


{{Optimal ET sequence|legend=1| 31, 193, 224 }}
{{Optimal ET sequence|legend=0| 31, 193, 224 }}


Badness: 0.025137
Badness (Smith): 0.025137


== Subsemifourth ==
== Subsemifourth ==
Line 428: Line 425:


{{Mapping|legend=1| 1 39 27 45 | 0 -47 -31 -53 }}
{{Mapping|legend=1| 1 39 27 45 | 0 -47 -31 -53 }}
: mapping generators: ~2, ~125/72
: mapping generators: ~2, ~125/72


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~144/125 = 244.719
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~144/125 = 244.719{{c}}


{{Optimal ET sequence|legend=1| 49, 103, 152, 255, 407 }}
{{Optimal ET sequence|legend=1| 49, 103, 152, 255, 407 }}


[[Badness]]: 0.135173
[[Badness]] (Smith): 0.135173


=== 11-limit ===
=== 11-limit ===
Line 444: Line 440:
Mapping: {{mapping| 1 39 27 45 56 | 0 -47 -31 -53 -66 }}
Mapping: {{mapping| 1 39 27 45 56 | 0 -47 -31 -53 -66 }}


Optimal tuning (POTE): ~2 = 1\1, ~121/105 = 244.719
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~121/105 = 244.719{{c}}


{{Optimal ET sequence|legend=1| 49, 103, 152, 255, 407, 966d }}
{{Optimal ET sequence|legend=0| 49, 103, 152, 255, 407, 966d }}


Badness: 0.034276
Badness (Smith): 0.034276


=== 13-limit ===
=== 13-limit ===
Line 457: Line 453:
Mapping: {{mapping| 1 39 27 45 56 65 | 0 -47 -31 -53 -66 -77 }}
Mapping: {{mapping| 1 39 27 45 56 65 | 0 -47 -31 -53 -66 -77 }}


Optimal tuning (POTE): ~2 = 1\1, ~15/13 = 244.714
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/13 = 244.714{{c}}


{{Optimal ET sequence|legend=1| 49f, 103, 152f, 255, 407f, 662df }}
{{Optimal ET sequence|legend=0| 49f, 103, 152f, 255, 407f, 662df }}


Badness: 0.028387
Badness (Smith): 0.028387


== Septendesemi ==
== Septendesemi ==
The name ''septendesemi'' means a septendecimal semitone ([[17/16]]). The septendesemi temperament (80 &amp; 103) tempers out the mirkwai comma and 1959552/1953125 (''parkleiness'' comma, zotritrigu) in the 7-limit. [[183edo]] provides an excellent tuning for 7, 11, 13, and 17-limit septendesemi.
The name ''septendesemi'' means a septendecimal semitone ([[17/16]]). The septendesemi temperament (80 & 103) tempers out the mirkwai comma and 1959552/1953125 (''parkleiness'' comma, zotritrigu) in the 7-limit. [[183edo]] provides an excellent tuning for 7-, 11-, 13-, and 17-limit septendesemi.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 471: Line 467:


{{Mapping|legend=1| 1 39 37 53 | 0 -41 -38 -55 }}
{{Mapping|legend=1| 1 39 37 53 | 0 -41 -38 -55 }}
: mapping generators: ~2, ~648/343
: mapping generators: ~2, ~648/343


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~343/324 = 104.916
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~343/324 = 104.916{{c}}


{{Optimal ET sequence|legend=1| 80, 103, 183 }}
{{Optimal ET sequence|legend=0| 80, 103, 183 }}


[[Badness]]: 0.146795
[[Badness]] (Smith): 0.146795


=== 11-limit ===
=== 11-limit ===
Line 487: Line 482:
Mapping: {{mapping| 1 39 37 53 50 | 0 -41 -38 -55 -51 }}
Mapping: {{mapping| 1 39 37 53 50 | 0 -41 -38 -55 -51 }}


Optimal tuning (POTE): ~2 = 1\1, ~35/33 = 104.916
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~35/33 = 104.916{{c}}


{{Optimal ET sequence|legend=1| 80, 103, 183 }}
{{Optimal ET sequence|legend=0| 80, 103, 183 }}


Badness: 0.041554
Badness (Smith): 0.041554


=== 13-limit ===
=== 13-limit ===
Line 500: Line 495:
Mapping: {{mapping| 1 39 37 53 50 11 | 0 -41 -38 -55 -51 -8 }}
Mapping: {{mapping| 1 39 37 53 50 11 | 0 -41 -38 -55 -51 -8 }}


Optimal tuning (POTE): ~2 = 1\1, ~35/33 = 104.908
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~35/33 = 104.908{{c}}


{{Optimal ET sequence|legend=1| 80, 103, 183, 469f, 652def }}
{{Optimal ET sequence|legend=0| 80, 103, 183, 469f, 652def }}


Badness: 0.027908
Badness (Smith): 0.027908


=== 17-limit ===
=== 17-limit ===
Line 513: Line 508:
Mapping: {{mapping| 1 39 37 53 50 11 5 | 0 -41 -38 -55 -51 -8 -1 }}
Mapping: {{mapping| 1 39 37 53 50 11 5 | 0 -41 -38 -55 -51 -8 -1 }}


Optimal tuning (POTE): ~2 = 1\1, ~17/16 = 104.909
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~17/16 = 104.909{{c}}


{{Optimal ET sequence|legend=1| 80, 103, 183, 469f, 652def }}
{{Optimal ET sequence|legend=0| 80, 103, 183, 469f, 652def }}


Badness: 0.020128
Badness (Smith): 0.020128


== Gaster ==
== Gaster ==
Line 523: Line 518:
{{Main| Gaster temperament }}
{{Main| Gaster temperament }}


The ''gaster'' temperament (111 &amp; 113) tempers out {{monzo| -70 72 -19 }} (quadbila-negu) in the 5-limit; mirkwai comma (16875/16807) and [[scheme comma]] (14348907/14336000) in the 7-limit. The word "[[Wiktionary: gaster|gaster]]" means [[Wiktionary: abdomen|abdomen]] or [[Wiktionary: stomach|stomach]], but also a restructuring of the words "gassormic tritone", which is a generator of this temperament. This temperament is sufficient to obtain high prime limit harmonics like a stomach, so that patent vals [[111edo|111]], [[113edo|113]] and [[224edo|224]] support it even in the 41-limit.
The gaster temperament (111 & 113) tempers out {{monzo| -70 72 -19 }} (quadbila-negu) in the 5-limit; mirkwai comma (16875/16807) and [[scheme comma]] (14348907/14336000) in the 7-limit. The word "[[Wiktionary: gaster|gaster]]" means [[Wiktionary: abdomen|abdomen]] or [[Wiktionary: stomach|stomach]], but also a restructuring of the words "gassormic tritone", which is a generator of this temperament. This temperament is sufficient to obtain high prime limit harmonics like a stomach, so that patent vals [[111edo|111]], [[113edo|113]] and [[224edo|224]] support it even in the 41-limit.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 531: Line 526:
{{Mapping|legend=1| 1 11 38 37 | 0 -19 -72 -69 }}
{{Mapping|legend=1| 1 11 38 37 | 0 -19 -72 -69 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~800/567 = 594.641
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~800/567 = 594.641{{c}}


{{Optimal ET sequence|legend=1| 111, 224 }}
{{Optimal ET sequence|legend=1| 111, 224 }}


[[Badness]]: 0.154521
[[Badness]] (Smith): 0.154521


=== 11-limit ===
=== 11-limit ===
Line 544: Line 539:
Mapping: {{mapping| 1 11 38 37 -1 | 0 -19 -72 -69 9 }}
Mapping: {{mapping| 1 11 38 37 -1 | 0 -19 -72 -69 9 }}


Optimal tuning (POTE): ~2 = 1\1, ~512/363 = 594.639
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~512/363 = 594.639{{c}}


{{Optimal ET sequence|legend=1| 111, 224, 783d, 1007d, 1231dd }}
{{Optimal ET sequence|legend=0| 111, 224, 783d, 1007d, 1231dd }}


Badness: 0.054060
Badness (Smith): 0.054060


=== 13-limit ===
=== 13-limit ===
Line 557: Line 552:
Mapping: {{mapping| 1 11 38 37 -1 26 | 0 -19 -72 -69 9 -45 }}
Mapping: {{mapping| 1 11 38 37 -1 26 | 0 -19 -72 -69 9 -45 }}


Optimal tuning (POTE): ~2 = 1\1, ~55/39 = 594.639
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~55/39 = 594.639{{c}}


{{Optimal ET sequence|legend=1| 111, 224, 783df, 1007df, 1231ddf }}
{{Optimal ET sequence|legend=0| 111, 224, 783df, 1007df, 1231ddf }}


Badness: 0.024882
Badness (Smith): 0.024882


=== 17-limit ===
=== 17-limit ===
Line 570: Line 565:
Mapping: {{mapping| 1 11 38 37 -1 26 14 | 0 -19 -72 -69 9 -45 -20 }}
Mapping: {{mapping| 1 11 38 37 -1 26 14 | 0 -19 -72 -69 9 -45 -20 }}


Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.636
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~24/17 = 594.636{{c}}


{{Optimal ET sequence|legend=1| 111, 224, 559dgg }}
{{Optimal ET sequence|legend=0| 111, 224, 559dgg }}


Badness: 0.021436
Badness (Smith): 0.021436


=== 19-limit ===
=== 19-limit ===
Line 583: Line 578:
Mapping: {{mapping| 1 11 38 37 -1 26 14 32 | 0 -19 -72 -69 9 -45 -20 -56 }}
Mapping: {{mapping| 1 11 38 37 -1 26 14 32 | 0 -19 -72 -69 9 -45 -20 -56 }}


Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.636
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~24/17 = 594.636{{c}}


{{Optimal ET sequence|legend=1| 111, 224 }}
{{Optimal ET sequence|legend=0| 111, 224 }}


Badness: 0.018370
Badness (Smith): 0.018370


=== 23-limit ===
=== 23-limit ===
Line 596: Line 591:
Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 | 0 -19 -72 -69 9 -45 -20 -56 -5 }}
Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 | 0 -19 -72 -69 9 -45 -20 -56 -5 }}


Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.641
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~24/17 = 594.641{{c}}


{{Optimal ET sequence|legend=1| 111, 224 }}
{{Optimal ET sequence|legend=0| 111, 224 }}


Badness: 0.017619
Badness (Smith): 0.017619


=== 29-limit ===
=== 29-limit ===
Line 609: Line 604:
Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 -11 | 0 -19 -72 -69 9 -45 -20 -56 -5 32 }}
Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 -11 | 0 -19 -72 -69 9 -45 -20 -56 -5 32 }}


Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.646
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~24/17 = 594.646{{c}}


{{Optimal ET sequence|legend=1| 111, 113, 224 }}
{{Optimal ET sequence|legend=0| 111, 113, 224 }}


Badness: 0.016815
Badness (Smith): 0.016815


=== 31-limit ===
=== 31-limit ===
Line 622: Line 617:
Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 -11 0 | 0 -19 -72 -69 9 -45 -20 -56 -5 32 10 }}
Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 -11 0 | 0 -19 -72 -69 9 -45 -20 -56 -5 32 10 }}


Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.644
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~24/17 = 594.644{{c}}


{{Optimal ET sequence|legend=1| 111, 113, 224 }}
{{Optimal ET sequence|legend=0| 111, 113, 224 }}


Badness: 0.014790
Badness (Smith): 0.014790


=== 37-limit ===
=== 37-limit ===
Line 635: Line 630:
Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 -11 0 -27 | 0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65 }}
Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 -11 0 -27 | 0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65 }}


Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.644
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~24/17 = 594.644{{c}}


{{Optimal ET sequence|legend=1| 111, 113, 224 }}
{{Optimal ET sequence|legend=0| 111, 113, 224 }}


Badness: 0.014377
Badness (Smith): 0.014377


=== 41-limit ===
=== 41-limit ===
Line 648: Line 643:
Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 -11 0 -27 45 | 0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65 -80 }}
Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 -11 0 -27 45 | 0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65 -80 }}


Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.643
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~24/17 = 594.643{{c}}


{{Optimal ET sequence|legend=1| 111, 113, 224 }}
{{Optimal ET sequence|legend=0| 111, 113, 224 }}


Badness: 0.012858
Badness (Smith): 0.012858


== Subsedia ==
== Subsedia ==
The generator for ''subsedia'' (10 &amp; 111) is 0.5 cents flat of [[15/14]]-wide semitone and tempers out the mirkwai comma and 65536/64827 (''buzzardisma'', saquadru comma). In this temperament, three generators makes ~[[16/13]], five of them equals ~[[24/17]], twelve of them equals ~[[16/7]], sixteen of them equals ~[[3/1]], and 45 of them equals ~22/1.
The generator for subsedia (10 & 111) is 0.5 cents flat of [[15/14]]-wide semitone and tempers out the mirkwai comma and [[buzzardsma]]. In this temperament, three generators makes ~[[16/13]], five of them equals ~[[24/17]], twelve of them equals ~[[16/7]], sixteen of them equals ~[[3/1]], and 45 of them equals ~22/1.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 663: Line 658:
{{Mapping|legend=1| 1 0 5 4 | 0 16 -27 -12 }}
{{Mapping|legend=1| 1 0 5 4 | 0 16 -27 -12 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~15/14 = 118.965
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~15/14 = 118.965{{c}}


{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d }}
{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d }}


[[Badness]]: 0.157658
[[Badness]] (Smith): 0.157658


=== 11-limit ===
=== 11-limit ===
Line 676: Line 671:
Mapping: {{mapping| 1 0 5 4 -1 | 0 16 -27 -12 45 }}
Mapping: {{mapping| 1 0 5 4 -1 | 0 16 -27 -12 45 }}


Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 118.968
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/14 = 118.968{{c}}


{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d }}
{{Optimal ET sequence|legend=0| 10, 101, 111, 121, 232d }}


Badness: 0.066838
Badness (Smith): 0.066838


=== 13-limit ===
=== 13-limit ===
Line 689: Line 684:
Mapping: {{mapping| 1 0 5 4 -1 4 | 0 16 -27 -12 45 -3 }}
Mapping: {{mapping| 1 0 5 4 -1 4 | 0 16 -27 -12 45 -3 }}


Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 118.968
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/14 = 118.968{{c}}


{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d }}
{{Optimal ET sequence|legend=0| 10, 101, 111, 121, 232d }}


Badness: 0.031635
Badness (Smith): 0.031635


=== 17-limit ===
=== 17-limit ===
Line 702: Line 697:
Mapping: {{mapping| 1 0 5 4 -1 4 3 | 0 16 -27 -12 45 -3 11 }}
Mapping: {{mapping| 1 0 5 4 -1 4 3 | 0 16 -27 -12 45 -3 11 }}


Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 118.968
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/14 = 118.968{{c}}


{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232dg }}
{{Optimal ET sequence|legend=0| 10, 101, 111, 121, 232dg }}


Badness: 0.019707
Badness (Smith): 0.019707


=== 19-limit ===
=== 19-limit ===
Line 715: Line 710:
Mapping: {{mapping| 1 0 5 4 -1 4 3 10 | 0 16 -27 -12 45 -3 11 -58 }}
Mapping: {{mapping| 1 0 5 4 -1 4 3 10 | 0 16 -27 -12 45 -3 11 -58 }}


Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 118.964
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/14 = 118.964{{c}}


{{Optimal ET sequence|legend=1| 10, 101h, 111, 121, 232dg }}
{{Optimal ET sequence|legend=0| 10, 101h, 111, 121, 232dg }}


Badness: 0.017935
Badness (Smith): 0.017935


== Hemiseptisix ==
== Hemiseptisix ==
The name ''hemiseptisix'' means a half of septimal major sixth ([[12/7]]). The hemiseptisix temperament (103 &amp; 121) tempers out the mirkwai comma and 95703125/95551488 (''pontiqak'' comma, lazozotritriyo) in the 7-limit. [[224edo]] provides an excellent tuning for 7-, 11-, and 13-limit hemiseptisix.
The name ''hemiseptisix'' means a half of septimal major sixth ([[12/7]]). The hemiseptisix temperament (103 & 121) tempers out the mirkwai comma and 95703125/95551488 (''pontiqak'' comma, lazozotritriyo) in the 7-limit. [[224edo]] provides an excellent tuning for 7-, 11-, and 13-limit hemiseptisix.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 729: Line 724:


{{Mapping|legend=1| 1 34 17 34 | 0 -53 -24 -51 }}
{{Mapping|legend=1| 1 34 17 34 | 0 -53 -24 -51 }}
: mapping generators: ~2, ~75/49
: mapping generators: ~2, ~75/49


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~98/75 = 466.071
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~98/75 = 466.071{{c}}


{{Optimal ET sequence|legend=1| 103, 121, 224 }}
{{Optimal ET sequence|legend=1| 103, 121, 224 }}


[[Badness]]: 0.162826
[[Badness]] (Smith): 0.162826


=== 11-limit ===
=== 11-limit ===
Line 745: Line 739:
Mapping: {{mapping| 1 34 17 34 53 | 0 -53 -24 -51 -81 }}
Mapping: {{mapping| 1 34 17 34 53 | 0 -53 -24 -51 -81 }}


Optimal tuning (POTE): ~2 = 1\1, ~55/42 = 466.070
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~55/42 = 466.070{{c}}


{{Optimal ET sequence|legend=1| 103, 121, 224 }}
{{Optimal ET sequence|legend=0| 103, 121, 224 }}


Badness: 0.043381
Badness (Smith): 0.043381


=== 13-limit ===
=== 13-limit ===
Line 758: Line 752:
Mapping: {{mapping| 1 34 17 34 53 30 | 0 -53 -24 -51 -81 -43 }}
Mapping: {{mapping| 1 34 17 34 53 30 | 0 -53 -24 -51 -81 -43 }}


Optimal tuning (POTE): ~2 = 1\1, ~55/42 = 466.071
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~55/42 = 466.071{{c}}


{{Optimal ET sequence|legend=1| 103, 121, 224 }}
{{Optimal ET sequence|legend=0| 103, 121, 224 }}


Badness: 0.021127
Badness (Smith): 0.021127


=== 17-limit ===
=== 17-limit ===
Line 771: Line 765:
Mapping: {{mapping| 1 34 17 34 53 30 31 | 0 -53 -24 -51 -81 -43 -44 }}
Mapping: {{mapping| 1 34 17 34 53 30 31 | 0 -53 -24 -51 -81 -43 -44 }}


Optimal tuning (POTE): ~2 = 1\1, ~17/13 = 466.074
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~17/13 = 466.074{{c}}


{{Optimal ET sequence|legend=1| 103, 121, 224 }}
{{Optimal ET sequence|legend=0| 103, 121, 224 }}


Badness: 0.018611
Badness (Smith): 0.018611


== Browser ==
== Browser ==
{{See also| Sensipent family }}
This can also be considered a [[non-over-1 temperament]], with considerable scope for harmony in the 2.5/3.7/3.11/3.13/3.17/3 subgroup with MOSes of 8, 15, 23, and 31 notes despite no harmonics from the root. It can be considered a detemperament of 8et, with a generator very slightly sharp of 1\8.
This can also be considered a [[non-over-1 temperament]], with considerable scope for harmony in the 2.5/3.7/3.11/3.13/3.17/3 subgroup with MOSes of 8, 15, 23, and 31 notes despite no harmonics from the root. It can be considered a detemperament of 8et, with a generator very slightly sharp of 1\8.
{{See also| Sensipent family }}


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 787: Line 782:
{{Mapping|legend=1| 1 6 8 10 | 0 -35 -45 -57 }}
{{Mapping|legend=1| 1 6 8 10 | 0 -35 -45 -57 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/45 = 151.399
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~49/45 = 151.399{{c}}


{{Optimal ET sequence|legend=1| 103, 111, 214 }}
{{Optimal ET sequence|legend=1| 103, 111, 214 }}


[[Badness]]: 0.180645
[[Badness]] (Smith): 0.180645


=== 11-limit ===
=== 11-limit ===
Line 800: Line 795:
Mapping: {{mapping| 1 6 8 10 8 | 0 -35 -45 -57 -36 }}
Mapping: {{mapping| 1 6 8 10 8 | 0 -35 -45 -57 -36 }}


Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 151.405
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 151.405{{c}}


{{Optimal ET sequence|legend=1| 103, 214 }}
{{Optimal ET sequence|legend=0| 103, 214 }}


Badness: 0.057634
Badness (Smith): 0.057634


=== 13-limit ===
=== 13-limit ===
Line 813: Line 808:
Mapping: {{mapping| 1 6 8 10 8 9 | 0 -35 -45 -57 -36 -42 }}
Mapping: {{mapping| 1 6 8 10 8 9 | 0 -35 -45 -57 -36 -42 }}


Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 151.403
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 151.403{{c}}


{{Optimal ET sequence|legend=1| 103, 111, 214 }}
{{Optimal ET sequence|legend=0| 103, 111, 214 }}


Badness: 0.028822
Badness (Smith): 0.028822


=== 17-limit ===
=== 17-limit ===
Line 826: Line 821:
Mapping: {{mapping| 1 6 8 10 8 9 8 | 0 -35 -45 -57 -36 -42 -31 }}
Mapping: {{mapping| 1 6 8 10 8 9 8 | 0 -35 -45 -57 -36 -42 -31 }}


Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 151.397
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 151.397{{c}}


{{Optimal ET sequence|legend=1| 103, 111, 214 }}
{{Optimal ET sequence|legend=0| 103, 111, 214 }}


Badness: 0.020384
Badness (Smith): 0.020384


=== 19-limit ===
=== 19-limit ===
Line 839: Line 834:
Mapping: {{mapping| 1 6 8 10 8 9 8 18 | 0 -35 -45 -57 -36 -42 -31 -109 }}
Mapping: {{mapping| 1 6 8 10 8 9 8 18 | 0 -35 -45 -57 -36 -42 -31 -109 }}


Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 151.396
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 151.396{{c}}


{{Optimal ET sequence|legend=1| 103h, 111, 214 }}
{{Optimal ET sequence|legend=0| 103h, 111, 214 }}


Badness: 0.017570
Badness (Smith): 0.017570


== Grazer ==
== Grazer ==
Line 851: Line 846:


{{Mapping|legend=1| 1 34 47 58 | 0 -37 -51 -63 }}
{{Mapping|legend=1| 1 34 47 58 | 0 -37 -51 -63 }}
: mapping generators: ~2, ~90/49
: mapping generators: ~2, ~90/49


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/45 = 148.719
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~49/45 = 148.719{{c}}


{{Optimal ET sequence|legend=1| 113, 121, 234 }}
{{Optimal ET sequence|legend=1| 113, 121, 234 }}


[[Badness]]: 0.217166
[[Badness]] (Smith): 0.217166


=== 11-limit ===
=== 11-limit ===
Line 867: Line 861:
Mapping: {{mapping| 1 34 47 58 35 | 0 -37 -51 -63 -36 }}
Mapping: {{mapping| 1 34 47 58 35 | 0 -37 -51 -63 -36 }}


Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 148.729
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 148.729{{c}}


{{Optimal ET sequence|legend=1| 113, 121, 234, 355e, 589cee }}
{{Optimal ET sequence|legend=0| 113, 121, 234, 355e, 589cee }}


Badness: 0.076062
Badness (Smith): 0.076062


=== 13-limit ===
=== 13-limit ===
Line 880: Line 874:
Mapping: {{mapping| 1 34 47 58 35 44 | 0 -37 -51 -63 -36 -46 }}
Mapping: {{mapping| 1 34 47 58 35 44 | 0 -37 -51 -63 -36 -46 }}


Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 148.729
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 148.729{{c}}


{{Optimal ET sequence|legend=1| 113, 121, 234, 355e, 589cee }}
{{Optimal ET sequence|legend=0| 113, 121, 234, 355e, 589cee }}


Badness: 0.036248
Badness (Smith): 0.036248


=== 17-limit ===
=== 17-limit ===
Line 893: Line 887:
Mapping: {{mapping| 1 34 47 58 35 44 33 | 0 -37 -51 -63 -36 -46 -33 }}
Mapping: {{mapping| 1 34 47 58 35 44 33 | 0 -37 -51 -63 -36 -46 -33 }}


Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 148.735
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 148.735{{c}}


{{Optimal ET sequence|legend=1| 113, 121, 234g, 355eg }}
{{Optimal ET sequence|legend=0| 113, 121, 234g, 355eg }}


Badness: 0.025410
Badness (Smith): 0.025410


=== 19-limit ===
=== 19-limit ===
Line 906: Line 900:
Mapping: {{mapping| 1 34 47 58 35 44 33 6 | 0 -37 -51 -63 -36 -46 -33 -2 }}
Mapping: {{mapping| 1 34 47 58 35 44 33 6 | 0 -37 -51 -63 -36 -46 -33 -2 }}


Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 148.727
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 148.727{{c}}


{{Optimal ET sequence|legend=1| 113, 121, 234g, 355eg, 589ceegg }}
{{Optimal ET sequence|legend=0| 113, 121, 234g, 355eg, 589ceegg }}


Badness: 0.022574
Badness (Smith): 0.022574


== Notes ==
== References ==


[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Mirkwai clan| ]] <!-- main article -->
[[Category:Mirkwai clan| ]] <!-- main article -->
[[Category:Mirkwai| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Canopic_clan"