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Sensamagic clan: Difference between revisions

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Sensi tempers out [[126/125]], [[686/675]] and [[4375/4374]] in addition to [[245/243]], and can be described as the 19 & 27 temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 2.3.5.7.13 sensi (sensation) tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and [[mos scale]]s of 8-, 11-, 19- and 27-tones are available.  
Sensi tempers out [[126/125]], [[686/675]] and [[4375/4374]] in addition to [[245/243]], and can be described as the 19 & 27 temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 2.3.5.7.13 sensi (sensation) tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and [[mos scale]]s of 8-, 11-, 19- and 27-tones are available.  


=== Septimal sensi ===
=== Septimal sensi ===
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{{Multival|legend=1| 7 9 13 -2 1 5 }}
{{Multival|legend=1| 7 9 13 -2 1 5 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~9/7 = 443.3166
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~9/7 = 443.3166
* [[POTE]]: ~2 = 1\1, ~9/7 = 443.383


[[Minimax tuning]]:  
[[Minimax tuning]]:  
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Mapping: {{mapping| 1 6 8 11 -6 | 0 -7 -9 -13 15 }}
Mapping: {{mapping| 1 6 8 11 -6 | 0 -7 -9 -13 15 }}


Optimal tuning (CTE): ~2 = 1\1, ~9/7 = 443.2987
Optimal tunings:
* CTE: ~2 = 1\1, ~9/7 = 443.2987
* POTE: ~2 = 1\1, ~9/7 = 443.294


{{Optimal ET sequence|legend=1| 19, 27, 46, 111d }}
{{Optimal ET sequence|legend=1| 19, 27, 46, 111d }}
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Mapping: {{mapping| 1 6 8 11 -6 10 | 0 -7 -9 -13 15 -10 }}
Mapping: {{mapping| 1 6 8 11 -6 10 | 0 -7 -9 -13 15 -10 }}


Optimal tuning (CTE): ~2 = 1\1, ~9/7 = 443.3658
Optimal tunings:
* CTE: ~2 = 1\1, ~9/7 = 443.3658
* POTE: ~2 = 1\1, ~9/7 = 443.321


{{Optimal ET sequence|legend=1| 19, 27, 46, 111df }}
{{Optimal ET sequence|legend=1| 19, 27, 46, 111df }}
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Mapping: {{mapping| 1 6 8 11 -6 10 -6 | 0 -7 -9 -13 15 -10 16 }}
Mapping: {{mapping| 1 6 8 11 -6 10 -6 | 0 -7 -9 -13 15 -10 16 }}


Optimal tuning (CTE): ~2 = 1\1, ~9/7 = 443.3775
Optimal tunings:
* CTE: ~2 = 1\1, ~9/7 = 443.3775
* POTE: ~2 = 1\1, ~9/7 = 443.365


{{Optimal ET sequence|legend=1| 19, 27, 46 }}
{{Optimal ET sequence|legend=1| 19, 27, 46 }}
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Mapping: {{mapping| 1 6 8 11 23 | 0 -7 -9 -13 -31 }}
Mapping: {{mapping| 1 6 8 11 23 | 0 -7 -9 -13 -31 }}


Optimal tuning (CTE): ~2 = 1\1, ~9/7 = 443.4783
Optimal tunings:
* CTE: ~2 = 1\1, ~9/7 = 443.4783
* POTE: ~2 = 1\1, ~9/7 = 443.626


{{Optimal ET sequence|legend=1| 19e, 27e, 46, 119c }}
{{Optimal ET sequence|legend=1| 19e, 27e, 46, 119c }}
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Mapping: {{mapping| 1 6 8 11 23 10 | 0 -7 -9 -13 -31 -10 }}
Mapping: {{mapping| 1 6 8 11 23 10 | 0 -7 -9 -13 -31 -10 }}


Optimal tuning (CTE): ~2 = 1\1, ~9/7 = 443.5075
Optimal tunings:
* CTE: ~2 = 1\1, ~9/7 = 443.5075
* POTE: ~2 = 1\1, ~9/7 = 443.559


{{Optimal ET sequence|legend=1| 19e, 27e, 46 }}
{{Optimal ET sequence|legend=1| 19e, 27e, 46 }}
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Mapping: {{mapping| 1 6 8 11 23 10 23 | 0 -7 -9 -13 -31 -10 -30 }}
Mapping: {{mapping| 1 6 8 11 23 10 23 | 0 -7 -9 -13 -31 -10 -30 }}


Optimal tuning (CTE): ~2 = 1\1, ~9/7 = 443.5050
Optimal tunings:
* CTE: ~2 = 1\1, ~9/7 = 443.5050
* POTE: ~2 = 1\1, ~9/7 = 443.551


{{Optimal ET sequence|legend=1| 19eg, 27eg, 46 }}
{{Optimal ET sequence|legend=1| 19eg, 27eg, 46 }}
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Mapping: {{mapping| 1 6 8 11 6 | 0 -7 -9 -13 -4 }}
Mapping: {{mapping| 1 6 8 11 6 | 0 -7 -9 -13 -4 }}


Optimal tuning (CTE): ~2 = 1\1, ~9/7 = 443.1886
Optimal tunings:
* CTE: ~2 = 1\1, ~9/7 = 443.1886
* POTE: ~2 = 1\1, ~9/7 = 443.962


{{Optimal ET sequence|legend=1| 8d, 19, 27e }}
{{Optimal ET sequence|legend=1| 8d, 19, 27e }}
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Mapping: {{mapping| 1 6 8 11 6 10 | 0 -7 -9 -13 -4 -10 }}
Mapping: {{mapping| 1 6 8 11 6 10 | 0 -7 -9 -13 -4 -10 }}


Optimal tuning (CTE): ~2 = 1\1, ~9/7 = 443.2863
Optimal tunings:
* CTE: ~2 = 1\1, ~9/7 = 443.2863
* POTE: ~2 = 1\1, ~9/7 = 443.945


{{Optimal ET sequence|legend=1| 8d, 19, 27e }}
{{Optimal ET sequence|legend=1| 8d, 19, 27e }}
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Mapping: {{mapping| 1 6 8 11 11 | 0 -7 -9 -13 -12 }}
Mapping: {{mapping| 1 6 8 11 11 | 0 -7 -9 -13 -12 }}


Optimal tuning (CTE): ~2 = 1\1, ~9/7 = 443.7814
Optimal tunings:
* CTE: ~2 = 1\1, ~9/7 = 443.7814
* POTE: ~2 = 1\1, ~9/7 = 443.518


{{Optimal ET sequence|legend=1| 8d, 19e, 27 }}
{{Optimal ET sequence|legend=1| 8d, 19e, 27 }}
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Mapping: {{mapping| 1 6 8 11 11 11 | 0 -7 -9 -13 -12 -11 }}
Mapping: {{mapping| 1 6 8 11 11 11 | 0 -7 -9 -13 -12 -11 }}


Optimal tuning (CTE): ~2 = 1\1, ~9/7 = 443.7877
Optimal tunings:
* CTE: ~2 = 1\1, ~9/7 = 443.7877
* POTE: ~2 = 1\1, ~9/7 = 443.506


{{Optimal ET sequence|legend=1| 8d, 19e, 27 }}
{{Optimal ET sequence|legend=1| 8d, 19e, 27 }}
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: mapping generators: ~99/70, ~11/10
: mapping generators: ~99/70, ~11/10


Optimal tuning (CTE): ~99/70 = 1\2, ~11/10 = 156.6312
Optimal tunings:
* CTE: ~99/70 = 1\2, ~11/10 = 156.6312
* POTE: ~99/70 = 1\2, ~11/10 = 156.692


{{Optimal ET sequence|legend=1| 8d, …, 38d, 46 }}
{{Optimal ET sequence|legend=1| 8d, …, 38d, 46 }}
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Mapping: {{mapping| 2 5 7 9 9 10 | 0 -7 -9 -13 -8 -10 }}
Mapping: {{mapping| 2 5 7 9 9 10 | 0 -7 -9 -13 -8 -10 }}


Optimal tuning (CTE): ~55/39 = 1\2, ~11/10 = 156.5584
Optimal tunings:
* CTE: ~55/39 = 1\2, ~11/10 = 156.5584
* POTE: ~55/39 = 1\2, ~11/10 = 156.725


{{Optimal ET sequence|legend=1| 8d, …, 38df, 46 }}
{{Optimal ET sequence|legend=1| 8d, …, 38df, 46 }}
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Mapping: {{mapping| 2 5 7 9 9 10 10 | 0 -7 -9 -13 -8 -10 -7 }}
Mapping: {{mapping| 2 5 7 9 9 10 10 | 0 -7 -9 -13 -8 -10 -7 }}


Optimal tuning (CTE): ~17/12 = 1\2, ~11/10 = 156.5534
Optimal tunings:
* CTE: ~17/12 = 1\2, ~11/10 = 156.5534


{{Optimal ET sequence|legend=1| 8d, …, 38df, 46 }}
{{Optimal ET sequence|legend=1| 8d, …, 38df, 46 }}
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: mapping generators: ~2, ~44/25
: mapping generators: ~2, ~44/25


Optimal tuning (CTE): ~2 = 1\1, ~25/22 = 221.5981
Optimal tunings:
* CTE: ~2 = 1\1, ~25/22 = 221.5981
* POTE: ~2 = 1\1, ~25/22 = 221.605


{{Optimal ET sequence|legend=1| 27e, 38d, 65 }}
{{Optimal ET sequence|legend=1| 27e, 38d, 65 }}
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Mapping: {{mapping| 1 13 17 24 32 30 | 0 -14 -18 -26 -35 -30 }}
Mapping: {{mapping| 1 13 17 24 32 30 | 0 -14 -18 -26 -35 -30 }}


Optimal tuning (CTE): ~2 = 1\1, ~25/22 = 221.6333
Optimal tunings:
* CTE: ~2 = 1\1, ~25/22 = 221.6333
* POTE: ~2 = 1\1, ~25/22 = 221.556


{{Optimal ET sequence|legend=1| 27e, 38df, 65f }}
{{Optimal ET sequence|legend=1| 27e, 38df, 65f }}
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