625/616: Difference between revisions
Create infobox |
Move the data for pakkanen here |
||
| (21 intermediate revisions by 6 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox Interval | {{Infobox Interval | ||
| | | Name = quadrikite comma, pakkanen comma | ||
| | | Color name = 1ury<sup>4</sup>-2, luruquadyo negative 2nd | ||
| | | Comma = yes | ||
}} | }} | ||
'''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 can be factored into simpler commas as ([[100/99]])⋅([[225/224]]). | |||
== 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.]] | |||
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:Quadrikite]] | |||
[[Category:Commas named for their regular temperament properties]] | |||
Latest revision as of 12:04, 2 July 2026
| Interval information |
pakkanen comma
625/616, the quadrikite comma or pakkanen comma (monzo: [-3 0 4 -1 -1⟩) is a small 11-limit (also 2.5.7.11-subgroup) comma measuring about 25.1 cents.
It can be factored into simpler commas as (100/99)⋅(225/224).
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
Subgroup-val mapping: [⟨1 0 0 -3], ⟨0 1 0 4], ⟨0 0 1 -1]]
- mapping generators: ~2, ~5, ~7
- WE: ~2 = 1200.6499 ¢, ~5/4 = 380.2990 ¢, ~7/4 = 969.2326 ¢
- error map: ⟨+0.650 -4.715 +1.706 +2.595]
- CWE: ~2 = 1200.0000 ¢, ~5/4 = 380.6249 ¢, ~7/4 = 969.6520 ¢
- error map: ⟨0.000 -5.689 +0.826 +1.530]
Optimal ET sequence: 6, 16, 22, 28, 29, 35, 41, 57, 63, 98c
Badness (Sintel): 0.573
Etymology
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.