625/616: Difference between revisions
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'''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. | '''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 is the difference between [[25/22]] and [[28/25]]. | ||
It can be factored into simpler commas as ([[100/99]])⋅([[225/224]]). | It can be factored into simpler commas as ([[100/99]])⋅([[225/224]]). | ||
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== Temperaments == | == 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. | [[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=3| 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 == | == Etymology == | ||