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Gammic family: Difference between revisions

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→Neptune: depends on whether you consider the 7- or 9-odd-limit as consonances
m Units, misc. cleanup, - redundant category
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{{Mapping|legend=1| 1 1 2 | 0 20 11 }}
{{Mapping|legend=1| 1 1 2 | 0 20 11 }}
: mapping generators: ~2, ~1990656/1953125
: mapping generators: ~2, ~1990656/1953125


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~1990656/1953125 = 35.0964
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~1990656/1953125 = 35.0964{{c}}


{{Optimal ET sequence|legend=1| 34, 103, 137, 171, 547, 718, 889, 1607 }}
{{Optimal ET sequence|legend=1| 34, 103, 137, 171, 547, 718, 889, 1607 }}


[[Badness]]: 0.087752
[[Badness]] (Smith): 0.087752


=== 2.3.5.17 subgroup ===
=== 2.3.5.17 subgroup ===
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{{Mapping|legend=1| 1 1 2 4 | 0 20 11 3 }}
{{Mapping|legend=1| 1 1 2 4 | 0 20 11 3 }}
: mapping generators: ~2, ~51/50
: mapping generators: ~2, ~51/50


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~51/50 = 35.1011
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~51/50 = 35.1011{{c}}


{{Optimal ET sequence|legend=1| 34, 103, 137, 171, 376, 547, 2564g, 3111cg, 3658cgg }}
{{Optimal ET sequence|legend=0| 34, 103, 137, 171, 376, 547, 2564g, 3111cg, 3658cgg }}


[[Badness]] (Sintel): 0.320
[[Badness]] (Sintel): 0.320
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{{Mapping|legend=1| 1 1 2 0 | 0 20 11 96 }}
{{Mapping|legend=1| 1 1 2 0 | 0 20 11 96 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~234375/229376 = 35.0904
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~234375/229376 = 35.0904{{c}}


{{Optimal ET sequence|legend=1| 34d, 171, 205, 1402, 1573, 1744, 1915 }}
{{Optimal ET sequence|legend=1| 34d, 171, 205, 1402, 1573, 1744, 1915 }}


[[Badness]]: 0.047362
[[Badness]] (Smith): 0.047362


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 1 2 0 2 | 0 20 11 96 50 }}
Mapping: {{mapping| 1 1 2 0 2 | 0 20 11 96 50 }}


Optimal tuning (POTE): ~2 = 1\1, ~45/44 = 35.089
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~45/44 = 35.089{{c}}


{{Optimal ET sequence|legend=1| 34d, 137d, 171 }}
{{Optimal ET sequence|legend=0| 34d, 137d, 171 }}


Badness: 0.097061
Badness (Smith): 0.097061


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 1 2 0 2 3 | 0 20 11 96 50 24 }}
Mapping: {{mapping| 1 1 2 0 2 3 | 0 20 11 96 50 24 }}


Optimal tuning (POTE): ~2 = 1\1, ~45/44 = 35.091
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~45/44 = 35.091{{c}}


{{Optimal ET sequence|legend=1| 34d, 137d, 171 }}
{{Optimal ET sequence|legend=0| 34d, 137d, 171 }}


Badness: 0.047822
Badness (Smith): 0.047822


=== 17-limit ===
=== 17-limit ===
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Mapping: {{mapping| 1 1 2 0 2 3 4 | 0 20 11 96 50 24 3 }}
Mapping: {{mapping| 1 1 2 0 2 3 4 | 0 20 11 96 50 24 3 }}


Optimal tuning (POTE): ~2 = 1\1, ~45/44 = 35.090
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~45/44 = 35.090{{c}}


{{Optimal ET sequence|legend=1| 34d, 137d, 171 }}
{{Optimal ET sequence|legend=0| 34d, 137d, 171 }}


Badness: 0.031466
Badness (Smith): 0.031466


== Gammy ==
== Gammy ==
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[[Mapping]]: {{mapping| 1 1 2 1 | 0 20 11 62 }}
[[Mapping]]: {{mapping| 1 1 2 1 | 0 20 11 62 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~1990656/1953125 = 34.984
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~1990656/1953125 = 34.984{{c}}


{{Optimal ET sequence|legend=1| 34d, 69d, 103, 240, 343b }}
{{Optimal ET sequence|legend=1| 34d, 69d, 103, 240, 343b }}


[[Badness]]: 0.230839
[[Badness]] (Smith): 0.230839


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 1 2 1 2 | 0 20 11 62 50 }}
Mapping: {{mapping| 1 1 2 1 2 | 0 20 11 62 50 }}


Optimal tuning (POTE): ~2 = 1\1, ~45/44 = 34.985
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~45/44 = 34.985{{c}}


{{Optimal ET sequence|legend=1| 34d, 69de, 103, 240, 343be }}
{{Optimal ET sequence|legend=0| 34d, 69de, 103, 240, 343be }}


Badness: 0.065326
Badness (Smith): 0.065326


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 1 2 1 2 3 | 0 20 11 62 50 24 }}
Mapping: {{mapping| 1 1 2 1 2 3 | 0 20 11 62 50 24 }}


Optimal tuning (POTE): ~2 = 1\1, ~45/44 = 34.988
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~45/44 = 34.988{{c}}


{{Optimal ET sequence|legend=1| 34d, 69de, 103, 240, 343be }}
{{Optimal ET sequence|legend=0| 34d, 69de, 103, 240, 343be }}


Badness: 0.033418
Badness (Smith): 0.033418


=== 17-limit ===
=== 17-limit ===
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Mapping: {{mapping| 1 1 2 1 2 3 4 | 0 20 11 62 50 24 3 }}
Mapping: {{mapping| 1 1 2 1 2 3 4 | 0 20 11 62 50 24 3 }}


Optimal tuning (POTE): ~2 = 1\1, ~45/44 = 34.997
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~45/44 = 34.997{{c}}


{{Optimal ET sequence|legend=1| 34d, 69de, 103, 137, 240 }}
{{Optimal ET sequence|legend=0| 34d, 69de, 103, 137, 240 }}


Badness: 0.025030
Badness (Smith): 0.025030


== Neptune ==
== Neptune ==
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{{Mapping|legend=1| 1 21 13 13 | 0 -40 -22 -21 }}
{{Mapping|legend=1| 1 21 13 13 | 0 -40 -22 -21 }}
: mapping generators: 2, ~7/5
: mapping generators: 2, ~7/5


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 582.452
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~7/5 = 582.452{{c}}


{{Optimal ET sequence|legend=1| 35, 68, 103, 171, 1094, 1265, 1436, 1607, 1778 }}
{{Optimal ET sequence|legend=1| 35, 68, 103, 171, 1094, 1265, 1436, 1607, 1778 }}


[[Badness]]: 0.023427
[[Badness]] (Smith): 0.023427


==== 2.3.5.7.17 subgroup ====
==== 2.3.5.7.17 subgroup ====
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{{Mapping|legend=1| 1 21 13 13 7 | 0 -40 -22 -21 -6 }}
{{Mapping|legend=1| 1 21 13 13 7 | 0 -40 -22 -21 -6 }}
: mapping generators: ~2, ~7/5
: mapping generators: ~2, ~7/5


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, 7/5 = 582.450
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, 7/5 = 582.450{{c}}


{{Optimal ET sequence|legend=1| 35, 68, 103, 171, 581, 752, 923, 1094 }}
{{Optimal ET sequence|legend=0| 35, 68, 103, 171, 581, 752, 923, 1094 }}


[[Badness]] (Sintel): 0.404
[[Badness]] (Sintel): 0.404
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{{Mapping|legend=1| 1 21 13 13 7 20 | 0 -40 -22 -21 -6 -31 }}
{{Mapping|legend=1| 1 21 13 13 7 20 | 0 -40 -22 -21 -6 -31 }}
: mapping generators: ~2, ~7/5
: mapping generators: ~2, ~7/5


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, 7/5 = 582.451
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, 7/5 = 582.451{{c}}


{{Optimal ET sequence|legend=1| 35, 68, 103, 171, 752k, 923k, 1094k, 1265kk }}
{{Optimal ET sequence|legend=0| 35, 68, 103, 171, 752k, 923k, 1094k, 1265kk }}


[[Badness]] (Sintel): 0.393
[[Badness]] (Sintel): 0.393
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Mapping: {{mapping| 1 21 13 13 2 | 0 -40 -22 -21 3 }}
Mapping: {{mapping| 1 21 13 13 2 | 0 -40 -22 -21 3 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 582.475
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 582.475{{c}}


{{Optimal ET sequence|legend=1| 35, 68, 103, 171e, 274e, 445ee }}
{{Optimal ET sequence|legend=0| 35, 68, 103, 171e, 274e, 445ee }}


Badness: 0.063602
Badness (Smith): 0.063602


==== 13-limit ====
==== 13-limit ====
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Mapping: {{mapping| 1 21 13 13 2 27 | 0 -40 -22 -21 3 -48 }}
Mapping: {{mapping| 1 21 13 13 2 27 | 0 -40 -22 -21 3 -48 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 582.480
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 582.480{{c}}


{{Optimal ET sequence|legend=1| 35f, 68, 103, 171e, 274e }}
{{Optimal ET sequence|legend=0| 35f, 68, 103, 171e, 274e }}


Badness: 0.037156
Badness (Smith): 0.037156


==== 17-limit ====
==== 17-limit ====
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Mapping: {{mapping| 1 21 13 13 2 27 7 | 0 -40 -22 -21 3 -48 -6 }}
Mapping: {{mapping| 1 21 13 13 2 27 7 | 0 -40 -22 -21 3 -48 -6 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 582.475
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 582.475{{c}}


{{Optimal ET sequence|legend=1| 35f, 68, 103, 171e, 274e, 445ee }}
{{Optimal ET sequence|legend=0| 35f, 68, 103, 171e, 274e, 445ee }}


Badness: 0.025909
Badness (Smith): 0.025909


=== Salacia ===
=== Salacia ===
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Mapping: {{mapping| 1 21 13 13 52 | 0 -40 -22 -21 -100 }}
Mapping: {{mapping| 1 21 13 13 52 | 0 -40 -22 -21 -100 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 582.478
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 582.478{{c}}


{{Optimal ET sequence|legend=1| 68e, 103, 171, 274, 719be, 993bcde, 1267bbcde }}
{{Optimal ET sequence|legend=0| 68e, 103, 171, 274, 719be, 993bcde, 1267bbcde }}


Badness: 0.069721
Badness (Smith): 0.069721


==== 13-limit ====
==== 13-limit ====
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Mapping: {{mapping| 1 21 13 13 52 27 | 0 -40 -22 -21 -100 -48 }}
Mapping: {{mapping| 1 21 13 13 52 27 | 0 -40 -22 -21 -100 -48 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 582.477
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 582.477{{c}}


{{Optimal ET sequence|legend=1| 68e, 103, 171, 274, 719be, 993bcde }}
{{Optimal ET sequence|legend=0| 68e, 103, 171, 274, 719be, 993bcde }}


Badness: 0.034977
Badness (Smith): 0.034977


==== 17-limit ====
==== 17-limit ====
Line 268: Line 263:
Mapping: {{mapping| 1 21 13 13 52 27 7 | 0 -40 -22 -21 -100 -48 -6 }}
Mapping: {{mapping| 1 21 13 13 52 27 7 | 0 -40 -22 -21 -100 -48 -6 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 582.475
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 582.475{{c}}


{{Optimal ET sequence|legend=1| 68e, 103, 171, 274, 445e, 719be, 1164bcdeef }}
{{Optimal ET sequence|legend=0| 68e, 103, 171, 274, 445e, 719be, 1164bcdeef }}


Badness: 0.024577
Badness (Smith): 0.024577


=== Poseidon ===
=== Poseidon ===
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Mapping: {{mapping| 2 2 4 5 8 | 0 40 22 21 -37 }}
Mapping: {{mapping| 2 2 4 5 8 | 0 40 22 21 -37 }}
: mapping generators: ~99/70, ~99/98
: mapping generators: ~99/70, ~99/98


Optimal tuning (POTE): ~2 = 1\1, ~99/98 = 17.545
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~99/98 = 17.545{{c}}


{{Optimal ET sequence|legend=1| 68, 206b, 274, 342 }}
{{Optimal ET sequence|legend=0| 68, 206b, 274, 342 }}


Badness: 0.041727
Badness (Smith): 0.041727


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Gammic family| ]] <!-- main article -->
[[Category:Gammic family| ]] <!-- main article -->
[[Category:Gammic| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Gammic_family"