625/616: Difference between revisions

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{{Infobox Interval

| ~~Ratio~~ = ~~625/616~~

| Name = quadrikite comma, pakkanen comma

| ~~Monzo~~ = ~~-3 0~~ 4 -~~1 -1~~

| Color name = 1ury<sup>4</sup>-2, luruquadyo negative 2nd

~~| Cents = 25.1110066~~

| Comma = yes

| ~~Name~~ = ~~Quadrikite comma~~

}}

~~The~~ '''quadrikite comma''' ~~was discovered by~~ [[~~User:Frostburn~~|~~Lumi Pakkanen~~]] ~~and Praveen Venkataramana when prompted to create a temperament that could be called~~ [[No-~~threes_subgroup_temperaments#Xeimtionic|xeimtionic~~]] ~~that produces a~~ [[~~6L 5s~~]] ~~MOS pattern so that the pattern could be named ''xeimtonic''~~. ~~The name ''quarikite'' comes from the fact that a gap of four strings on the Kite guitar can be both 625/256 and 77/32 when this comma is tempered out~~.

'''625/616''', the '''quadrikite comma''' or '''pakkanen comma''' ({{monzo|legend=1| -3 0 4 -1 -1 }}) is a [[small comma|small]] [[11-limit]] (also 2.5.7.11-[[subgroup]]) [[comma]] measuring about 25.1 [[cent]]s.

It ~~needs to~~ be ~~paired with the '''frostma''' 245~~/~~242 to produce the~~ [[~~No-threes_subgroup_temperaments#Xeimtionic|xeimtionic~~]] ~~temperament (pronounced ''zeem-tee-onic''~~) ~~for the desired 6L 5s MOS pattern~~.

It can be factored into simpler commas as ([[100/99]])⋅([[225/224]]).

~~All of~~ this ~~was inspired by an AI generated picture of~~ ''~~xenharmonic music theory~~'' ~~featuring something that looks like~~ the ~~word~~ ''~~XEIMTIONC~~''.

== Temperaments ==

[[Tempering out]] this comma in the 11-limit leads to the rank-4 '''quadrikite''' temperament, or in the 2.5.7.11 subgroup, the rank-3 '''pakkanen''' temperament.

=== Pakkanen ===

[[Subgroup]]: 2.5.7.11

[[Comma list]]: 625/616

: mapping generators: ~2, ~5, ~7

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.6499{{c}}, ~5/4 = 380.2990{{c}}, ~7/4 = 969.2326{{c}}

: [[error map]]: {{val| +0.650 -4.715 +1.706 +2.595 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 380.6249{{c}}, ~7/4 = 969.6520{{c}}

: error map: {{val| 0.000 -5.689 +0.826 +1.530 }}

{{Optimal ET sequence|legend=1| 6, 16, 22, 28, 29, 35, 41, 57, 63, 98c }}

[[Badness]] (Sintel): 0.573

== Etymology ==

[[File:Xeimtionic.png|thumb|AI generated image of xenharmonic music theory.]]

[[~~Category:Small commas~~]]

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

This comma was discovered by [[Lumi Pakkanen]] and [[Praveen Venkataramana]] when prompted to create a temperament that could be called ''xeimtionic'' that produces a [[6L 5s]] mos pattern so that the pattern could be named ''xeimtonic''. The name ''quadrikite'' comes from the fact that a gap of four strings on the Kite guitar can be both 625/256 and 77/32 when this comma is tempered out. It was originally intended to be paired with the frostma [[245/242]] to produce the [[frostburn]] temperament as this was to be called ''xeimtionic'' (pronounced ''zeem-tee-onic'') for the desired 6L 5s mos pattern. All of this was inspired by an AI generated picture of ''xenharmonic music theory'' featuring something that looks like the word ''XEIMTIONC'', but the name was not used for [[TAMNAMS]] after all to remain temperament agnostic.

[[Category:~~Rational intervals~~]]

[[Category:Quadrikite]]

[[Category:Commas named for their regular temperament properties]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 625/616
+| Name = quadrikite comma, pakkanen comma
-| Monzo = -3 0 4 -1 -1
+| Color name = 1ury<sup>4</sup>-2, luruquadyo negative 2nd
-| Cents = 25.1110066
+| Comma = yes
-| Name = Quadrikite comma
 }}
-The '''quadrikite comma''' was discovered by [[User:Frostburn|Lumi Pakkanen]] and Praveen Venkataramana when prompted to create a temperament that could be called [[No-threes_subgroup_temperaments#Xeimtionic|xeimtionic]] that produces a [[6L 5s]] MOS pattern so that the pattern could be named ''xeimtonic''. The name ''quarikite'' comes from the fact that a gap of four strings on the Kite guitar can be both 625/256 and 77/32 when this comma is tempered out.
+'''625/616''', the '''quadrikite comma''' or '''pakkanen comma''' ({{monzo|legend=1| -3 0 4 -1 -1 }}) is a [[small comma|small]] [[11-limit]] (also 2.5.7.11-[[subgroup]]) [[comma]] measuring about 25.1 [[cent]]s.
-It needs to be paired with the '''frostma''' 245/242 to produce the [[No-threes_subgroup_temperaments#Xeimtionic|xeimtionic]] temperament (pronounced ''zeem-tee-onic'') for the desired 6L 5s MOS pattern.
+It can be factored into simpler commas as ([[100/99]])⋅([[225/224]]).
-All of this was inspired by an AI generated picture of ''xenharmonic music theory'' featuring something that looks like the word ''XEIMTIONC''.
+== Temperaments ==
+[[Tempering out]] this comma in the 11-limit leads to the rank-4 '''quadrikite''' temperament, or in the 2.5.7.11 subgroup, the rank-3 '''pakkanen''' temperament.
+=== Pakkanen ===
+[[Subgroup]]: 2.5.7.11
+[[Comma list]]: 625/616
+{{Mapping|legend=2| 1 0 0 -3 | 0 1 0 4 | 0 0 1 -1 }}
+: mapping generators: ~2, ~5, ~7
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.6499{{c}}, ~5/4 = 380.2990{{c}}, ~7/4 = 969.2326{{c}}
+: [[error map]]: {{val| +0.650 -4.715 +1.706 +2.595 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 380.6249{{c}}, ~7/4 = 969.6520{{c}}
+: error map: {{val| 0.000 -5.689 +0.826 +1.530 }}
+{{Optimal ET sequence|legend=1| 6, 16, 22, 28, 29, 35, 41, 57, 63, 98c }}
+[[Badness]] (Sintel): 0.573
+== Etymology ==
 [[File:Xeimtionic.png|thumb|AI generated image of xenharmonic music theory.]]
-[[Category:Small commas]]
-[[Category:11-limit]]
+This comma was discovered by [[Lumi Pakkanen]] and [[Praveen Venkataramana]] when prompted to create a temperament that could be called ''xeimtionic'' that produces a [[6L 5s]] mos pattern so that the pattern could be named ''xeimtonic''. The name ''quadrikite'' comes from the fact that a gap of four strings on the Kite guitar can be both 625/256 and 77/32 when this comma is tempered out. It was originally intended to be paired with the frostma [[245/242]] to produce the [[frostburn]] temperament as this was to be called ''xeimtionic'' (pronounced ''zeem-tee-onic'') for the desired 6L 5s mos pattern. All of this was inspired by an AI generated picture of ''xenharmonic music theory'' featuring something that looks like the word ''XEIMTIONC'', but the name was not used for [[TAMNAMS]] after all to remain temperament agnostic.
-[[Category:Rational intervals]]
+[[Category:Quadrikite]]
+[[Category:Commas named for their regular temperament properties]]