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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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== Cotoneum ==
== Cotoneum ==
: <small>''For full 19-limit extensions, see [[Hemimage temperaments #Cotoneum]].''</small>
: <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


== Beet ==
== Devimarvel (rank 3) ==
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]] if you're targetting the no-11's [[13-odd-limit]].
{{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 }}


The S-expression-based comma list of this temperament is {S8, S12, S13}
[[Tp tuning #T2 tuning|RMS error]]: 0.3779 cents


Subgroup: 2.3.5.7.13
== Devichrome (rank 4) ==
Subgroup: 2.3.5.7.19


Comma list: 64/63, 686/675, 512/507
[[Comma list]]: [[400/399]]


Mapping: {{mapping| 1 1 5 4 4 | 0 2 -9 -4 -1 }}
[[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}}]


Optimal tuning ([[CTE]]): 356.645
[[Tp tuning|POL2 generator]]: ~3/2 = 702.536, ~5/4 = 386.216, ~7/4 = 970.081


All [[patent val]] [[EDO]] tunings: 10, 27, 37
{{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]]
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