Parimo: Difference between revisions
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The '''parimo''' is an [[11-limit]] [[unnoticeable comma]] with a ratio of '''1771561/1771470''' = {{Monzo|-1 -11 -1 0 6}} and a value of approximately 0.09 [[cent|cents]]. It is the amount by which a stack of three [[243/242|rastmas]] falls short of a [[81/80|syntonic comma]]. Tempering it out leads to a form of '''parimic temperament''', which can be said to be the undecimal counterpart of the [[metric microtemperaments|metric temperament]] in that the syntonic comma is split into three equal parts in both systems. However, in parimic temperament, the parts represent different intervals – one part represents the [[243/242|rastma]], and two represent the [[121/120|biyatisma]]. | The '''parimo''' is an [[11-limit]] [[unnoticeable comma]] with a ratio of '''1771561/1771470''' = {{Monzo|-1 -11 -1 0 6}} and a value of approximately 0.09 [[cent|cents]]. It is the amount by which a stack of three [[243/242|rastmas]] falls short of a [[81/80|syntonic comma]]. | ||
== Temperaments == | |||
Tempering it out leads to a form of '''parimic temperament''', which can be said to be the undecimal counterpart of the [[metric microtemperaments|metric temperament]] in that the syntonic comma is split into three equal parts in both systems. However, in parimic temperament, the parts represent different intervals – one part represents the [[243/242|rastma]], and two represent the [[121/120|biyatisma]]. The corresponding 2.3.5.11 subgroup temperament is '''tritomere'''. | |||
=== Parimic === | |||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 1771561/1771470 | |||
[[Mapping]]: [{{val| 1 0 5 0 1 }}, {{val| 0 1 1 0 2 }}, {{val| 0 0 -6 0 -1 }}, {{val| 0 0 0 1 0 }}] | |||
Mapping generators: ~2, ~3, ~18/11, ~7 | |||
[[POTE generator]]s: ~3/2 = 701.9581, ~18/11 = 852.6073 | |||
{{Val list|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 }} | |||
[[Badness]]: 0.0279 × 10<sup>-6</sup> | |||
=== Tritomere === | |||
Subgroup: 2.3.5.11 | |||
[[Comma list]]: 1771561/1771470 | |||
[[Sval]] [[mapping]]: [{{val| 1 0 5 1 }}, {{val| 0 1 1 2 }}, {{val| 0 0 -6 -1 }}] | |||
Sval mapping generators: ~2, ~3, ~18/11 | |||
[[POTE generator]]s: ~3/2 = 701.9581, ~18/11 = 852.6073 | |||
{{Val list|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 }} | |||
[[Badness]]: 0.00712 × 10<sup>-3</sup> | |||
== See also == | == See also == | ||
Revision as of 16:26, 8 December 2021
| Interval information |
The parimo is an 11-limit unnoticeable comma with a ratio of 1771561/1771470 = [-1 -11 -1 0 6⟩ and a value of approximately 0.09 cents. It is the amount by which a stack of three rastmas falls short of a syntonic comma.
Temperaments
Tempering it out leads to a form of parimic temperament, which can be said to be the undecimal counterpart of the metric temperament in that the syntonic comma is split into three equal parts in both systems. However, in parimic temperament, the parts represent different intervals – one part represents the rastma, and two represent the biyatisma. The corresponding 2.3.5.11 subgroup temperament is tritomere.
Parimic
Subgroup: 2.3.5.7.11
Comma list: 1771561/1771470
Mapping: [⟨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 generators: ~3/2 = 701.9581, ~18/11 = 852.6073
Badness: 0.0279 × 10-6
Tritomere
Subgroup: 2.3.5.11
Comma list: 1771561/1771470
Sval mapping: [⟨1 0 5 1], ⟨0 1 1 2], ⟨0 0 -6 -1]]
Sval mapping generators: ~2, ~3, ~18/11
POTE generators: ~3/2 = 701.9581, ~18/11 = 852.6073
Badness: 0.00712 × 10-3