Parimo: Difference between revisions
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
Rework intro and update keys |
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The '''parimo''' ([[ratio]]: 1771561/1771470, {{monzo|legend=1| -1 -11 -1 0 6 }}) is an [[Unnoticeable comma|unnoticeable]] [[11-limit]] [[comma]] with a value of approximately 0.09{{cent}}. It is the amount by which an [[octave-reduced]] stack of six [[11/9]] neutral thirds exceeds [[5/3]], as well as the amount by which a stack of three [[243/242|rastmas]] falls short of a [[81/80|syntonic comma]]. | |||
The '''parimo''' | |||
== Temperaments == | == Temperaments == | ||
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=== Parimic === | === Parimic === | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 1771561/1771470 | [[Comma list]]: 1771561/1771470 | ||
{{Mapping|legend=1| 1 0 5 0 1 | 0 1 1 0 2 | 0 0 -6 0 -1 | 0 0 0 1 0 }} | |||
: mapping generators: ~2, ~3, ~18/11, ~7 | |||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 701.9581, ~18/11 = 852.6073 | ||
{{Optimal ET sequence|legend=1| 14c, 17c, 24, 31, 90e, 107cde, 114e, 121, 145, 152, 311, 342, 836, 1178, 1354, 1506, 1817, 1848, 2684, 3665, 4007, 4501, 4843, 6349, 6691, 21921, 28612, 35303, 48343, 63573, 70264e, 76955e, 98876e, 105567e }} | {{Optimal ET sequence|legend=1| 14c, 17c, 24, 31, 90e, 107cde, 114e, 121, 145, 152, 311, 342, 836, 1178, 1354, 1506, 1817, 1848, 2684, 3665, 4007, 4501, 4843, 6349, 6691, 21921, 28612, 35303, 48343, 63573, 70264e, 76955e, 98876e, 105567e }} | ||
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=== Tritomere === | === Tritomere === | ||
Subgroup: 2.3.5.11 | [[Subgroup]]: 2.3.5.11 | ||
[[Comma list]]: 1771561/1771470 | [[Comma list]]: 1771561/1771470 | ||
{{Mapping|legend=2| 1 0 5 1 | 0 1 1 2 | 0 0 -6 -1 }} | |||
: sval mapping generators: ~2, ~3, ~18/11 | |||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 701.9581, ~18/11 = 852.6073 | ||
{{Optimal ET sequence|legend=1| 7, 17c, 24, 31, 69e, 90e, 97, 107ce, 114e, 121, 145, 152, 311, 335, 342, 494, 677, 1019, 1171, 3855, 4349, 5026, 5520, 6691, 7862, 36474, 37645, 44336, 45507, 53369, 61231 }} | {{Optimal ET sequence|legend=1| 7, 17c, 24, 31, 69e, 90e, 97, 107ce, 114e, 121, 145, 152, 311, 335, 342, 494, 677, 1019, 1171, 3855, 4349, 5026, 5520, 6691, 7862, 36474, 37645, 44336, 45507, 53369, 61231 }} |