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Starling family: Difference between revisions

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unchanged interval → unchanged-interval
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,160 edits
"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Line 27: Line 27:
: Eigenmonzos (unchanged-intervals): 2, 8/7, 4/3
: Eigenmonzos (unchanged-intervals): 2, 8/7, 4/3


{{Val list|legend=1| 7d, 8d, 12, 19, 27, 31, 46, 58, 77, 135c, 166c }}
{{Optimal ET sequence|legend=1| 7d, 8d, 12, 19, 27, 31, 46, 58, 77, 135c, 166c }}


[[Badness]]: 0.0699 × 10<sup>-3</sup>
[[Badness]]: 0.0699 × 10<sup>-3</sup>
Line 67: Line 67:
Mapping generators: ~2, ~3, ~5
Mapping generators: ~2, ~3, ~5


{{Val list|legend=1| 12e, 15, 19, 27, 31, 46, 77, 96d, 127d, 173d, 204de }}
{{Optimal ET sequence|legend=1| 12e, 15, 19, 27, 31, 46, 77, 96d, 127d, 173d, 204de }}


[[Badness]]: 0.677 × 10<sup>-3</sup>
[[Badness]]: 0.677 × 10<sup>-3</sup>
Line 91: Line 91:
: [[Eigenmonzo]]s (unchanged-intervals): 2, 7/6, 4/3
: [[Eigenmonzo]]s (unchanged-intervals): 2, 7/6, 4/3


{{Val list|legend=1| 12, 15, 19e, 27e, 31, 46, 58, 89, 135c, 193c, 224c }}
{{Optimal ET sequence|legend=1| 12, 15, 19e, 27e, 31, 46, 58, 89, 135c, 193c, 224c }}


[[Badness]]: 0.353 × 10<sup>-3</sup>
[[Badness]]: 0.353 × 10<sup>-3</sup>
Line 108: Line 108:
Mapping: [{{val| 1 0 0 -1 -5 0 }}, {{val| 0 1 0 -2 -2 -5 }}, {{val| 0 0 1 3 5 5 }}]
Mapping: [{{val| 1 0 0 -1 -5 0 }}, {{val| 0 1 0 -2 -2 -5 }}, {{val| 0 0 1 3 5 5 }}]


Vals: {{Val list| 12f, 19e, 27e, 31, 46, 58, 104c, 135c, 193cf }}
{{Optimal ET sequence|legend=1| 12f, 19e, 27e, 31, 46, 58, 104c, 135c, 193cf }}


Badness: 0.677 × 10<sup>-3</sup>
Badness: 0.677 × 10<sup>-3</sup>
Line 119: Line 119:
Mapping: [{{val| 1 0 0 -1 -5 9 }}, {{val| 0 1 0 -2 -2 4 }}, {{val| 0 0 1 3 5 -5 }}]
Mapping: [{{val| 1 0 0 -1 -5 9 }}, {{val| 0 1 0 -2 -2 4 }}, {{val| 0 0 1 3 5 -5 }}]


Vals: {{Val list| 12, 15, 27e, 31, 43, 58, 147cf, 205cceff, 263ccdeefff }}
{{Optimal ET sequence|legend=1| 12, 15, 27e, 31, 43, 58, 147cf, 205cceff, 263ccdeefff }}


Badness: 0.915 × 10<sup>-3</sup>
Badness: 0.915 × 10<sup>-3</sup>
Line 132: Line 132:
Mapping: [{{val| 1 0 0 -1 -5 -4 }}, {{val| 0 1 0 -2 -2 -1 }}, {{val| 0 0 1 3 5 4 }}]
Mapping: [{{val| 1 0 0 -1 -5 -4 }}, {{val| 0 1 0 -2 -2 -1 }}, {{val| 0 0 1 3 5 4 }}]


Vals: {{Val list| 12f, 15, 19e, 27eff, 31 }}
{{Optimal ET sequence|legend=1| 12f, 15, 19e, 27eff, 31 }}


Badness: 0.837 × 10<sup>-3</sup>
Badness: 0.837 × 10<sup>-3</sup>
Line 143: Line 143:
Mapping: [{{val| 1 0 0 -1 -5 2 }}, {{val| 0 1 0 -2 -2 4 }}, {{val| 0 0 1 3 5 -2 }}]
Mapping: [{{val| 1 0 0 -1 -5 2 }}, {{val| 0 1 0 -2 -2 4 }}, {{val| 0 0 1 3 5 -2 }}]


Vals: {{Val list| 12, 15, 19e, 27e, 31f, 46 }}
{{Optimal ET sequence|legend=1| 12, 15, 19e, 27e, 31f, 46 }}


Badness: 0.991 × 10<sup>-3</sup>
Badness: 0.991 × 10<sup>-3</sup>
Line 167: Line 167:
: [[Eigenmonzo]]s (unchanged-intervals): 2, 8/7, 11/9
: [[Eigenmonzo]]s (unchanged-intervals): 2, 8/7, 11/9


{{Val list|legend=1| 7d, 8d, 12, 15, 19, 27e }} <nowiki>*</nowiki>
{{Optimal ET sequence|legend=1| 7d, 8d, 12, 15, 19, 27e }} <nowiki>*</nowiki>


<nowiki>*</nowiki> [[optimal patent val]]: [[34edo|34]]
<nowiki>*</nowiki> [[optimal patent val]]: [[34edo|34]]
Line 180: Line 180:
Mapping: [{{val| 1 0 0 -1 2 2 }}, {{val| 0 1 0 -2 -2 4 }}, {{val| 0 0 1 3 2 -2 }}]
Mapping: [{{val| 1 0 0 -1 2 2 }}, {{val| 0 1 0 -2 -2 4 }}, {{val| 0 0 1 3 2 -2 }}]


Vals: {{Val list| 7d, 8d, 12, 15, 19, 27e, 69bceef }} <nowiki>*</nowiki>
{{Optimal ET sequence|legend=1| 7d, 8d, 12, 15, 19, 27e, 69bceef }} <nowiki>*</nowiki>


<nowiki>*</nowiki> optimal patent val: [[34edo|34]]
<nowiki>*</nowiki> optimal patent val: [[34edo|34]]
Line 193: Line 193:
Mapping: [{{val| 1 0 0 -1 2 3 }}, {{val| 0 1 0 -2 -2 -1 }}, {{val| 0 0 1 3 2 1 }}]
Mapping: [{{val| 1 0 0 -1 2 3 }}, {{val| 0 1 0 -2 -2 -1 }}, {{val| 0 0 1 3 2 1 }}]


Vals: {{Val list| 7d, 8d, 12f, 15, 27eff }}
{{Optimal ET sequence|legend=1| 7d, 8d, 12f, 15, 27eff }}


Badness: 0.859 × 10<sup>-3</sup>
Badness: 0.859 × 10<sup>-3</sup>
Line 204: Line 204:
Mapping: [{{val| 1 0 0 -1 2 0 }}, {{val| 0 1 0 -2 -2 -5 }}, {{val| 0 0 1 3 2 5 }}]
Mapping: [{{val| 1 0 0 -1 2 0 }}, {{val| 0 1 0 -2 -2 -5 }}, {{val| 0 0 1 3 2 5 }}]


Vals: {{Val list| 7df, 8d, 12f, 19, 27e, 66cdeeef }}
{{Optimal ET sequence|legend=1| 7df, 8d, 12f, 19, 27e, 66cdeeef }}


Badness: 0.905 × 10<sup>-3</sup>
Badness: 0.905 × 10<sup>-3</sup>
Line 215: Line 215:
[[Mapping]]: [{{val| 1 0 0 -1 4 }}, {{val| 0 1 0 -2 7 }}, {{val| 0 0 1 3 -5 }}]
[[Mapping]]: [{{val| 1 0 0 -1 4 }}, {{val| 0 1 0 -2 7 }}, {{val| 0 0 1 3 -5 }}]


{{Val list|legend=1| 12e, 19, 27e, 31, 58, 89, 197c, 228c }}
{{Optimal ET sequence|legend=1| 12e, 19, 27e, 31, 58, 89, 197c, 228c }}


[[Badness]]: 0.648 × 10<sup>-3</sup>
[[Badness]]: 0.648 × 10<sup>-3</sup>
Line 226: Line 226:
Mapping: [{{val| 1 0 0 -1 4 0 }}, {{val| 0 1 0 -2 7 -5 }}, {{val| 0 0 1 3 -5 5 }}]
Mapping: [{{val| 1 0 0 -1 4 0 }}, {{val| 0 1 0 -2 7 -5 }}, {{val| 0 0 1 3 -5 5 }}]


Vals: {{Val list| 8d, 19, 27e, 31, 50, 58, 166cef, 224ceeff }}
{{Optimal ET sequence|legend=1| 8d, 19, 27e, 31, 50, 58, 166cef, 224ceeff }}


Badness: 0.821 × 10<sup>-3</sup>
Badness: 0.821 × 10<sup>-3</sup>
Line 237: Line 237:
[[Mapping]]: [{{val| 1 0 1 2 2 }}, {{val| 0 1 1 1 1 }}, {{val| 0 0 -2 -6 -1 }}]
[[Mapping]]: [{{val| 1 0 1 2 2 }}, {{val| 0 1 1 1 1 }}, {{val| 0 0 -2 -6 -1 }}]


{{Val list|legend=1| 7d, 8d, 15, 23de, 24d, 31, 46, 77 }}
{{Optimal ET sequence|legend=1| 7d, 8d, 15, 23de, 24d, 31, 46, 77 }}


[[Badness]]: 0.699 × 10<sup>-3</sup>
[[Badness]]: 0.699 × 10<sup>-3</sup>
Line 248: Line 248:
Mapping: [{{val| 1 0 1 2 2 2 }}, {{val| 0 1 1 1 1 1 }}, {{val| 0 0 -2 -6 -1 -1 }}]
Mapping: [{{val| 1 0 1 2 2 2 }}, {{val| 0 1 1 1 1 1 }}, {{val| 0 0 -2 -6 -1 -1 }}]


Vals: {{Val list| 7d, 8d, 15, 23de, 24d, 31 }}
{{Optimal ET sequence|legend=1| 7d, 8d, 15, 23de, 24d, 31 }}


Badness: 1.093 × 10<sup>-3</sup>
Badness: 1.093 × 10<sup>-3</sup>
Line 259: Line 259:
[[Mapping]]: [{{val| 1 0 0 -1 -3 }}, {{val| 0 1 0 -2 7 }}, {{val| 0 0 1 3 -2 }}]
[[Mapping]]: [{{val| 1 0 0 -1 -3 }}, {{val| 0 1 0 -2 7 }}, {{val| 0 0 1 3 -2 }}]


{{Val list|legend=1| 7d, 12e, 19e, 27e, 39d, 46, 119c }}
{{Optimal ET sequence|legend=1| 7d, 12e, 19e, 27e, 39d, 46, 119c }}


[[Badness]]: 1.585 × 10<sup>-3</sup>
[[Badness]]: 1.585 × 10<sup>-3</sup>
Line 270: Line 270:
Mapping: [{{val| 1 0 0 -1 -3 2 }}, {{val| 0 1 0 -2 7 4 }}, {{val| 0 0 1 3 -2 -2 }}]
Mapping: [{{val| 1 0 0 -1 -3 2 }}, {{val| 0 1 0 -2 7 4 }}, {{val| 0 0 1 3 -2 -2 }}]


Vals: {{Val list| 7d, 12e, 19e, 27e, 46 }}
{{Optimal ET sequence|legend=1| 7d, 12e, 19e, 27e, 46 }}


Badness: 1.588 × 10<sup>-3</sup>
Badness: 1.588 × 10<sup>-3</sup>
Line 281: Line 281:
[[Mapping]]: [{{val| 1 1 0 -3 2 }}, {{val| 0 2 0 -4 5 }}, {{val| 0 0 1 3 0 }}]
[[Mapping]]: [{{val| 1 1 0 -3 2 }}, {{val| 0 2 0 -4 5 }}, {{val| 0 0 1 3 0 }}]


{{Val list|legend=1| 24d, 27e, 31, 58, 89, 154, 185 }}
{{Optimal ET sequence|legend=1| 24d, 27e, 31, 58, 89, 154, 185 }}


[[Badness]]: 0.933 × 10<sup>-3</sup>
[[Badness]]: 0.933 × 10<sup>-3</sup>
Line 292: Line 292:
Mapping: [{{val| 1 1 0 -3 2 -5 }}, {{val| 0 2 0 -4 5 -10 }}, {{val| 0 0 1 3 0 5 }}]
Mapping: [{{val| 1 1 0 -3 2 -5 }}, {{val| 0 2 0 -4 5 -10 }}, {{val| 0 0 1 3 0 5 }}]


Vals: {{Val list| 27e, 31, 58, 96d, 154 }}
{{Optimal ET sequence|legend=1| 27e, 31, 58, 96d, 154 }}


[[Category:Temperament families]]
[[Category:Temperament families]]
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