No-elevens subgroup temperaments: Difference between revisions
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{{Technical data page}} | |||
This is a collection of [[subgroup temperament]]s which omit the prime harmonic of 11. | This is a collection of [[subgroup temperament]]s which omit the prime harmonic of 11. | ||
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[[Tp tuning #T2 tuning|RMS error]]: 2.318 cents | [[Tp tuning #T2 tuning|RMS error]]: 2.318 cents | ||
== Beet == | |||
Being describable as [[mynucumic]] [[archy]] [[biome]], this temperament has the logic common to 13-limit [[beatles]], [[Archytas_clan#Ringo|ringo]] and [[Archytas_clan#Beetle|beetle]]; in other words, they all only differ by the mapping of 11. The mapping of 11 provided by [[ares]] is seen as the canonic extension of [[beatles]] to the 11-limit. If you want a good patent val tuning, [[27edo]] is about as good as you're going to get if you want the major third to have a good chance at being able to function contextually as both a ~[[9/7]] and ~[[13/10]], assuming you're targeting the no-11's [[13-odd-limit]]. | |||
The [[S-expression]]-based comma list of this temperament is {[[64/63|S8]], [[169/168|S13]], [[196/195|S14]]}. | |||
Subgroup: 2.3.5.7.13 | |||
Comma list: 64/63, 91/90, 196/195 | |||
Mapping: {{mapping| 1 1 5 4 4 | 0 2 -9 -4 -1 }} | |||
Optimal tuning ([[CTE]]): ~16/13 = 356.645 | |||
{{Optimal ET sequence|legend=1| 10, 27, 37 }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 2.067 cents | |||
== Meanpop == | == Meanpop == | ||
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[[Tp tuning #T2 tuning|RMS error]]: 0.1347 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.1347 cents | ||
== Garibaldia == | |||
: <small>''See also: [[No-sevens subgroup temperaments #Photia]] and [[No-sevens subgroup temperaments #Nestoria|#Nestoria]]''</small> | |||
Subgroup: 2.3.5.7.17 | |||
[[Comma list]]: 120/119, 225/224, 1458/1445 | |||
[[Gencom]]: [2 4/3; 120/119 225/224 1458/1445] | |||
[[Gencom|Gencom mapping]]: [{{val|1 2 -1 -3 0 0 7}}, {{val|0 -1 8 14 0 0 -7}}] | |||
[[Mapping|Sval mapping]]: [{{val|1 2 -1 -3 7}}, {{val|0 -1 8 14 -7}}] | |||
[[Tp tuning|POL2 generator]]: ~3/2 = 701.862 | |||
{{Optimal ET sequence|legend=1| 12, 29, 41, 53 }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 0.8796 cents | |||
Related temperament: [[Garibaldi]] | |||
=== 2.3.5.7.17.19 === | |||
Subgroup: 2.3.5.7.17.19 | |||
[[Comma list]]: 120/119, 171/170, 190/189, 225/224 | |||
[[Gencom]]: [2 4/3; 120/119 171/170 190/189 225/224] | |||
[[Gencom|Gencom mapping]]: [{{val|1 2 -1 -3 0 0 7 3}}, {{val|0 -1 8 14 0 0 -7 3}}] | |||
[[Mapping|Sval mapping]]: [{{val|1 2 -1 -3 7 3}}, {{val|0 -1 8 14 -7 3}}] | |||
[[Tp tuning|POL2 generator]]: ~3/2 = 701.880 | |||
{{Optimal ET sequence|legend=1| 12, 29, 41, 53 }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 0.9338 cents | |||
== Devisemi == | |||
: <small>''See also: [[No-sevens subgroup temperaments #Devisemi]]''</small> | |||
Subgroup: 2.3.5.7.19 | |||
[[Comma list]]: 190/189, 245/243, 361/360 | |||
[[Gencom]]: [2 19/18; 190/189 245/243 361/360] | |||
[[Gencom|Gencom mapping]]: [{{val|1 1 1 2 0 0 0 3}}, {{val|0 8 18 11 0 0 0 17}}] | |||
[[Mapping|Sval mapping]]: [{{val|1 1 1 2 3}}, {{val|0 8 18 11 17}}] | |||
[[Tp tuning|POL2 generator]]: ~19/18 = 88.075 | |||
{{Optimal ET sequence|legend=1| 14c, 27, 41, 68, 109 }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 0.5780 cents | |||
Related temperament: [[Tetracot family|octacot]] | |||
== Pontia == | |||
: <small>''See also: [[No-sevens subgroup temperaments #Nestoria]]''</small> | |||
Subgroup: 2.3.5.7.19 | |||
[[Comma list]]: 361/360, 513/512, 4375/4374 | |||
[[Gencom]]: [2 4/3; 361/360 513/512 4375/4374] | |||
[[Gencom|Gencom mapping]]: [{{val|1 2 -1 19 0 0 0 3}}, {{val|0 -1 8 -39 0 0 0 3}}] | |||
[[Mapping|Sval mapping]]: [{{val|1 2 -1 19 3}}, {{val|0 -1 8 -39 3}}] | |||
[[Tp tuning|POL2 generator]]: ~3/2 = 701.748 | |||
{{Optimal ET sequence|legend=1| 53, 118, 171 }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 0.1763 cents | |||
Related temperament: [[Pontiac]] | |||
== Cotoneum == | == Cotoneum == | ||
: <small>''For full 19-limit extensions, see [[ | : <small>''For full 19-limit extensions, see [[Garischismic clan #Cotoneum]].''</small> | ||
Subgroup: 2.3.5.7.19 | Subgroup: 2.3.5.7.19 | ||
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[[Tp tuning #T2 tuning|RMS error]]: 0.1852 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.1852 cents | ||
== Devimarvel (rank 3) == | |||
{{see also|Marvel family}} | |||
Subgroup: 2.3.5.7.19 | |||
[[Comma list]]: 225/224, 400/399 | |||
[[Mapping|Sval mapping]]: [{{val|1 0 0 -5 9}}, {{val|0 1 0 2 -3}}, {{val|0 0 1 2 0}}] | |||
[[Tp tuning|POL2 generator]]: ~3/2 = 700.971, ~5/4 = 383.639 | |||
{{Optimal ET sequence|legend=1| 12, 19, 22, 31, 41, 53, 72, 94, 125 }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 0.3779 cents | |||
== Devichrome (rank 4) == | |||
Subgroup: 2.3.5.7.19 | |||
[[Comma list]]: [[400/399]] | |||
[[Mapping|Sval mapping]]: [{{val|1 0 0 0 4}}, {{val|0 1 0 0 -1}}, {{val|0 0 1 0 2}}, {{val|0 0 0 1 -1}}] | |||
[[Tp tuning|POL2 generator]]: ~3/2 = 702.536, ~5/4 = 386.216, ~7/4 = 970.081 | |||
{{Optimal ET sequence|legend=1| 12, 19, 22, 26, 27, 31, 41, 53, 68, 72, 94, 99, 140, 152, 345 }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 0.1886 cents | |||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Subgroup temperaments]] | [[Category:Subgroup temperaments]] | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||