Parimo: Difference between revisions

(10 intermediate revisions by 6 users not shown)

Line 1:

{{Infobox Interval

~~| Icon =~~

| Ratio = 1771561/1771470

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

~~| Cents = 0.08893~~

| Name = parimo

| Color name =

| 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 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]].

== 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|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

[[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 }}

[[Badness]]: 0.0279 × 10<sup>-6</sup>

=== Tritomere ===

[[Subgroup]]: 2.3.5.11

[[Comma list]]: 1771561/1771470

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

[[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 }}

[[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 comma~~]]

[[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 =
+| 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 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]].
+== 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|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
+[[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 }}
+[[Badness]]: 0.0279 × 10<sup>-6</sup>
+=== Tritomere ===
+[[Subgroup]]: 2.3.5.11
+[[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
+[[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 }}
+[[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 comma]]
+[[Category:Commas named after composers]]
+[[Category:Commas named after music theorists]]