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Semaphoresmic clan: Difference between revisions

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Move negri here
→Negri: update keys
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Negri tempers out the [[negri comma]] in the 5-limit, [[49/48]] and [[225/224]] in the 7-limit. It can be extended naturally to the 2.3.5.7.13 subgroup by adding [[91/90]] to the comma list; this will be discussed below under the title of negra.  
Negri tempers out the [[negri comma]] in the 5-limit, [[49/48]] and [[225/224]] in the 7-limit. It can be extended naturally to the 2.3.5.7.13 subgroup by adding [[91/90]] to the comma list; this will be discussed below under the title of negra.  


Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 16875/16384
[[Comma list]]: 16875/16384


[[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -4 3 }}]
[[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -4 3 }}]
: mapping generators: ~2, ~16/15


{{Multival|legend=1| 4 -3 -14 }}
{{Multival|legend=1| 4 -3 -14 }}


[[POTE generator]]: ~16/15 = 125.7549
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16/15 = 125.7549


{{Optimal ET sequence|legend=1| 9, 10, 19, 67c, 86c, 105c }}
{{Optimal ET sequence|legend=1| 9, 10, 19, 67c, 86c, 105c }}
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=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 49/48, 225/224
[[Comma list]]: 49/48, 225/224
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{{Multival|legend=1| 4 -3 2 -14 -8 13 }}
{{Multival|legend=1| 4 -3 2 -14 -8 13 }}


[[POTE generator]]: ~15/14 = 125.608
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~15/14 = 125.608


{{Optimal ET sequence|legend=1| 9, 10, 19, 48d, 67cdd, 86cdd }}
{{Optimal ET sequence|legend=1| 9, 10, 19, 48d, 67cdd, 86cdd }}
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[[Badness]]: 0.026483
[[Badness]]: 0.026483


==== Negra ====
==== 2.3.5.7.13 subgroup (negra) ====
This is the 2.3.5.7.13 extension of negri.
 
Subgroup: 2.3.5.7.13
Subgroup: 2.3.5.7.13


[[Comma list]]: 49/48, 65/64, 91/90
Comma list: 49/48, 65/64, 91/90


[[Sval]] [[mapping]]: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -3 }}]
Sval mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -3 }}]


[[Gencom]] [[mapping]]: [{{val| 1 2 2 3 0 4 }}, {{val| 0 -4 3 -2 0 -3 }}]
Gencom mapping: [{{val| 1 2 2 3 0 4 }}, {{val| 0 -4 3 -2 0 -3 }}]


[[Gencom]]: [2 14/13; 49/48 65/64 91/90]
: gencom: [2 14/13; 49/48 65/64 91/90]


[[POTE generator]]: ~14/13 = 125.567
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 125.567


{{Optimal ET sequence|legend=1| 9, 10, 19, 48df, 67cddf, 86cddff }}
{{Optimal ET sequence|legend=1| 9, 10, 19, 48df, 67cddf, 86cddff }}
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Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -5 }}]
Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -5 }}]


POTE generator: ~15/14 = 126.474
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 126.474


{{Optimal ET sequence|legend=1| 9, 10, 19 }}
{{Optimal ET sequence|legend=1| 9, 10, 19 }}
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Mapping: [{{val| 1 2 2 3 4 4 }}, {{val| 0 -4 3 -2 -5 -3 }}]
Mapping: [{{val| 1 2 2 3 4 4 }}, {{val| 0 -4 3 -2 -5 -3 }}]


POTE generator: ~14/13 = 126.431
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.431


{{Optimal ET sequence|legend=1| 9, 10, 19 }}
{{Optimal ET sequence|legend=1| 9, 10, 19 }}
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Mapping: [{{val| 1 2 2 3 2 }}, {{val| 0 -4 3 -2 14 }}]
Mapping: [{{val| 1 2 2 3 2 }}, {{val| 0 -4 3 -2 14 }}]


POTE generator: ~15/14 = 124.767
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 124.767


{{Optimal ET sequence|legend=1| 19, 29, 48d, 77cdd }}
{{Optimal ET sequence|legend=1| 19, 29, 48d, 77cdd }}
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Mapping: [{{val| 1 2 2 3 2 4 }}, {{val| 0 -4 3 -2 14 -3 }}]
Mapping: [{{val| 1 2 2 3 2 4 }}, {{val| 0 -4 3 -2 14 -3 }}]


POTE generator: ~14/13 = 124.716
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 124.716


{{Optimal ET sequence|legend=1| 19, 29, 48df, 77cddf }}
{{Optimal ET sequence|legend=1| 19, 29, 48df, 77cddf }}
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Mapping: [{{val| 1 2 2 3 3 }}, {{val| 0 -4 3 -2 4 }}]
Mapping: [{{val| 1 2 2 3 3 }}, {{val| 0 -4 3 -2 4 }}]


POTE generator: ~15/14 = 127.039
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 127.039


{{Optimal ET sequence|legend=1| 9, 19e }}
{{Optimal ET sequence|legend=1| 9, 19e }}
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Mapping: [{{val| 1 2 2 3 3 4 }}, {{val| 0 -4 3 -2 4 -3 }}]
Mapping: [{{val| 1 2 2 3 3 4 }}, {{val| 0 -4 3 -2 4 -3 }}]


POTE generator: ~14/13 = 127.039
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 127.039


{{Optimal ET sequence|legend=1| 9, 19e }}
{{Optimal ET sequence|legend=1| 9, 19e }}
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Mapping: [{{val| 1 2 2 3 5 }}, {{val| 0 -4 3 -2 -15 }}]
Mapping: [{{val| 1 2 2 3 5 }}, {{val| 0 -4 3 -2 -15 }}]


POTE generator: ~15/14 = 124.539
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 124.539


{{Optimal ET sequence|legend=1| 10, 19e, 29, 77cddee }}
{{Optimal ET sequence|legend=1| 10, 19e, 29, 77cddee }}
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Mapping: [{{val| 1 2 2 3 5 4 }}, {{val| 0 -4 3 -2 -15 -3 }}]
Mapping: [{{val| 1 2 2 3 5 4 }}, {{val| 0 -4 3 -2 -15 -3 }}]


POTE generator: ~14/13 = 124.545
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 124.545


{{Optimal ET sequence|legend=1| 10, 19e, 29, 77cddeef }}
{{Optimal ET sequence|legend=1| 10, 19e, 29, 77cddeef }}
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Mapping: [{{val| 1 6 -1 5 4 }}, {{val| 0 -8 6 -4 -1 }}]
Mapping: [{{val| 1 6 -1 5 4 }}, {{val| 0 -8 6 -4 -1 }}]


POTE generator: ~11/8 = 537.186
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 537.186


{{Optimal ET sequence|legend=1| 9, 20, 29, 38d, 67cdde }}
{{Optimal ET sequence|legend=1| 9, 20, 29, 38d, 67cdde }}
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Mapping: [{{val| 1 6 -1 5 4 7 }}, {{val| 0 -8 6 -4 -1 -6 }}]
Mapping: [{{val| 1 6 -1 5 4 7 }}, {{val| 0 -8 6 -4 -1 -6 }}]


POTE generator: ~11/8 = 537.208
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 537.208


{{Optimal ET sequence|legend=1| 9, 20, 29, 38df, 67cddef }}
{{Optimal ET sequence|legend=1| 9, 20, 29, 38df, 67cddef }}
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Mapping: [{{val| 1 6 -1 5 4 7 -2 }}, {{val| 0 -8 6 -4 -1 -6 11 }}]
Mapping: [{{val| 1 6 -1 5 4 7 -2 }}, {{val| 0 -8 6 -4 -1 -6 11 }}]


POTE generator: ~11/8 = 537.230
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 537.230


{{Optimal ET sequence|legend=1| 9, 20g, 29g, 38df, 67cddefg }}
{{Optimal ET sequence|legend=1| 9, 20g, 29g, 38df, 67cddefg }}
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Mapping: [{{val| 1 6 -1 5 4 7 -2 7 }}, {{val| 0 -8 6 -4 -1 -6 11 -5 }}]
Mapping: [{{val| 1 6 -1 5 4 7 -2 7 }}, {{val| 0 -8 6 -4 -1 -6 11 -5 }}]


POTE generator: ~11/8 = 537.214
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 537.214


{{Optimal ET sequence|legend=1| 9, 20g, 29g, 38df, 67cddefgh }}
{{Optimal ET sequence|legend=1| 9, 20g, 29g, 38df, 67cddefgh }}
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