Parimo: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Ratio = 1771561/1771470

~~| Monzo = -1 -11 -1 0 6~~

~~| Cents = 0.08893~~

| Name = parimo

| Color name = satribilo-agu comma

| ~~FJS name =~~

| Comma = yes

~~| Sound~~ =

}}

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''' ~~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 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]].

== Temperaments ==

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=== Parimic ===

Subgroup: 2.3.5.7.11

[[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|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

: mapping generators: ~2, ~3, ~18/11, ~7

[[POTE ~~generator~~]]s: ~3/2 = 701.9581, ~18/11 = 852.6073

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~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 }}

{{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 }}

[[Badness]]: 0.0279 × 10<sup>-6</sup>

=== Tritomere ===

Subgroup: 2.3.5.11

[[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

: sval mapping generators: ~2, ~3, ~18/11

[[POTE ~~generator~~]]s: ~3/2 = 701.9581, ~18/11 = 852.6073

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~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 }}

{{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 }}

[[Badness]]: 0.00712 × 10<sup>-3</sup>

== Etymology ==

It is yet to be found out how this comma was named. However, as [[Petr Pařízek]] was the first to take note of it<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_100716.html Yahoo! Tuning Group | ''The two smallest commas I have found so far'']</ref> and as it was tempered out in the [[mohaha]] temperament, it could be conjectured that the name was a contraction of ''Pařízek'' and ''mohaha''.

== See also ==

* [[Unnoticeable comma]]

[[Category:~~11-limit~~]]

== Notes ==

[[Category:~~Unnoticeable commas~~]]

[[Category:Commas named after composers]]

[[Category:Commas named after music theorists]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
 | Ratio = 1771561/1771470
-| Monzo = -1 -11 -1 0 6
-| Cents = 0.08893
 | Name = parimo
 | Color name = satribilo-agu comma
-| FJS name =
+| Comma = yes
-| Sound =
 }}
+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''' 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 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]].
 == Temperaments ==
@@ Line 16: / Line 11: @@
 === Parimic ===
-Subgroup: 2.3.5.7.11
+[[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|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
+: mapping generators: ~2, ~3, ~18/11, ~7
-[[POTE generator]]s: ~3/2 = 701.9581, ~18/11 = 852.6073
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~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 }}
+{{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 }}
 [[Badness]]: 0.0279 × 10<sup>-6</sup>
 === Tritomere ===
-Subgroup: 2.3.5.11
+[[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 }}]
+{{Mapping|legend=2| 1 0 5 1 | 0 1 1 2 | 0 0 -6 -1 }}
-Sval mapping generators: ~2, ~3, ~18/11
+: sval mapping generators: ~2, ~3, ~18/11
-[[POTE generator]]s: ~3/2 = 701.9581, ~18/11 = 852.6073
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~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 }}
+{{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 }}
 [[Badness]]: 0.00712 × 10<sup>-3</sup>
+== Etymology ==
+It is yet to be found out how this comma was named. However, as [[Petr Pařízek]] was the first to take note of it<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_100716.html Yahoo! Tuning Group | ''The two smallest commas I have found so far'']</ref> and as it was tempered out in the [[mohaha]] temperament, it could be conjectured that the name was a contraction of ''Pařízek'' and ''mohaha''.
 == See also ==
 * [[Unnoticeable comma]]
-[[Category:11-limit]]
+== Notes ==
-[[Category:Unnoticeable commas]]
+[[Category:Commas named after composers]]
+[[Category:Commas named after music theorists]]