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31st-octave temperaments: Difference between revisions

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{{Technical data page}}
{{Infobox fractional-octave|31}}
{{Infobox fractional-octave|31}}
This page collects rank-2 temperaments with a period that is 1/31 of an octave.
This page collects rank-2 temperaments with a period that is 1/31 of an octave.
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[[Mapping]]: [{{val| 31 49 72 87 }}, {{val| 0 1 0 0 }}]
[[Mapping]]: [{{val| 31 49 72 87 }}, {{val| 0 1 0 0 }}]
{{Multival|legend=1| 31 0 0 -72 -87 0 }}


[[POTE generator]]: ~1029/1024 = 5.1551
[[POTE generator]]: ~1029/1024 = 5.1551
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Mapping: [{{val| 31 49 72 87 107 }}, {{val| 0 1 0 0 2 }}]
Mapping: [{{val| 31 49 72 87 107 }}, {{val| 0 1 0 0 2 }}]
{{Multival|legend=1| 31 0 0 62 -72 -87 -9 0 144 174 }}


POTE generator: ~385/384 = 4.9377
POTE generator: ~385/384 = 4.9377
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Mapping: [{{val| 31 49 72 87 107 115 }}, {{val| 0 1 0 0 2 -2 }}]
Mapping: [{{val| 31 49 72 87 107 115 }}, {{val| 0 1 0 0 2 -2 }}]
{{Multival|legend=1| 31 0 0 62 -62 -72 -87 -9 -213 0 144 -144 174 -174 -444 }}


POTE generator: ~385/384 = 5.1703
POTE generator: ~385/384 = 5.1703
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[[Mapping]]: [{{val| 31 49 72 87 107 }}, {{val| 0 0 0 0 1 }}]
[[Mapping]]: [{{val| 31 49 72 87 107 }}, {{val| 0 0 0 0 1 }}]
Wedgie: {{multival| 0 0 0 31 0 0 49 0 72 87 }}


[[POTE generator]]: ~176/175 = 6.519
[[POTE generator]]: ~176/175 = 6.519
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Mapping: [{{val| 31 49 72 87 107 115 }}, {{val| 0 0 0 0 1 0 }}]
Mapping: [{{val| 31 49 72 87 107 115 }}, {{val| 0 0 0 0 1 0 }}]
Wedgie: {{multival| 0 0 0 31 0 0 0 49 0 0 72 0 87 0 -115 }}


POTE generator: ~66/65 = 9.171
POTE generator: ~66/65 = 9.171
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Mapping: [{{val| 31 49 72 87 107 115 }}, {{val| 0 0 0 0 1 -1 }}]
Mapping: [{{val| 31 49 72 87 107 115 }}, {{val| 0 0 0 0 1 -1 }}]
Wedgie: {{multival| 0 0 0 31 -31 0 0 49 -49 0 72 -72 87 -87 -222 }}


POTE generator: ~196/195 = 10.120
POTE generator: ~196/195 = 10.120
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{{Mapping|legend=1| 31 49 72 87 107 115 | 0 0 0 0 0 -1 }}
{{Mapping|legend=1| 31 49 72 87 107 115 | 0 0 0 0 0 -1 }}
Wedgie: {{multival| 0 0 0 0 31 0 0 0 49 0 0 72 0 87 107 }}


[[Optimal tuning]] ([[CTE]]): ~45/44 = 1\31, ~13/8 = 840.5276 (~144/143 = 11.0853)
[[Optimal tuning]] ([[CTE]]): ~45/44 = 1\31, ~13/8 = 840.5276 (~144/143 = 11.0853)
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