120/119: Difference between revisions
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'''120/119''', the '''lynchisma''', is a [[small comma|small]] [[17-limit]] [[superparticular]] [[comma]] of about 14.49 [[cent]]s. It is the difference between [[20/17]] and [[7/6]], [[17/10]] and [[12/7]], or [[30/17]] and [[7/4]]. | '''120/119''', the '''lynchisma''', is a [[small comma|small]] [[17-limit]] [[superparticular]] [[comma]] of about 14.49 [[cent]]s. It is the difference between [[20/17]] and [[7/6]], [[17/10]] and [[12/7]], or [[30/17]] and [[7/4]]. | ||
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Since 120/119 factors as ([[225/224]])⋅([[256/255]]), it would make sense to temper them both out, so lynchic can be further tempered to a simple extension of [[marvel]] that adds prime 17 known as [[Marvel family #Char|char]], though it loses accuracy when compared to marvel. | Since 120/119 factors as ([[225/224]])⋅([[256/255]]), it would make sense to temper them both out, so lynchic can be further tempered to a simple extension of [[marvel]] that adds prime 17 known as [[Marvel family #Char|char]], though it loses accuracy when compared to marvel. | ||
=== Lynchic === | |||
[[Subgroup]]: 2.3.5.7.17 | |||
{{Mapping|legend=2| 1 0 0 0 3 | 0 1 0 0 1 | 0 0 1 0 1 | 0 0 0 1 -1 }} | |||
: mapping generators: ~2, ~3, ~5, ~7 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1198.9483{{c}}, ~3/2 = 702.1229{{c}}, ~5/4 = 386.5249{{c}}, ~7/4 = 973.6693{{c}} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8985{{c}}, ~5/4 = 385.5601{{c}}, ~7/4 = 973.5597{{c}} | |||
{{Optimal ET sequence|legend=1| 10, 12, 19, 22, 27g, 31, 41, 53, 198ddggg }} | |||
[[Badness]] (Sintel): 0.220 | |||
=== Lynchismic === | === Lynchismic === | ||
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| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]] | | ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]] | ||
|} | |} | ||
: | : mapping generators: ~2, ~3, ~5, ~7, ~11, ~13 | ||
: | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1198.9483{{c}}, ~3/2 = 702.1229{{c}}, ~5/4 = 386.5249{{c}}, ~7/4 = 973.6693{{c}}, ~11/8 = 554.4584{{c}}, ~13/8 = 843.6671{{c}} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8985{{c}}, ~5/4 = 385.5601{{c}}, ~7/4 = 973.5597{{c}}, ~11/8 = 553.3440{{c}}, ~13/8 = 842.6949{{c}} | |||
Optimal | {{Optimal ET sequence|legend=1| 19, 22, 26, 27eg, 31, 41, 49fg, 53, 65d, 84g, 92defg, 106g, 123dfgg, 128dg, 137gg, 145dgg, 171dgg }} | ||
[[Badness]] (Sintel): 0.603 | |||
== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:Lynchismic]] | |||
[[Category:Commas named after composers]] | [[Category:Commas named after composers]] | ||
[[Category:Commas named after music theorists]] | [[Category:Commas named after music theorists]] | ||