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 ==

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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 ==