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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.  


Line 16: Line 17:
[[Tp tuning|POL2 generator]]: ~4/3 = 486.255
[[Tp tuning|POL2 generator]]: ~4/3 = 486.255


{{Val list|legend=1| 5, 32, 37 }}
{{Optimal ET sequence|legend=1| 5, 32, 37 }}


[[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 ==
: <small>''For full 13-limit extensions, see [[Meantone family #Septimal meantone]].''</small>
Subgroup: 2.3.5.7.13
[[Comma list]]: 81/80, 105/104, 126/125
[[Gencom]]: [2 4/3; 81/80 105/104 126/125]
[[Gencom|Gencom mapping]]: [{{val|1 2 4 7 0 10}}, {{val|0 -1 -4 -10 0 -15}}]
[[Mapping|Sval mapping]]: [{{val|1 2 4 7 10}}, {{val|0 -1 -4 -10 -15}}]
[[Tp tuning|POL2 generator]]: ~3/2 = 695.988
{{Optimal ET sequence|legend=1| 12f, 19, 31, 50 }}
[[Tp tuning #T2 tuning|RMS error]]: 1.421 cents


== Sensi (aka sensation) ==
== Sensi (aka sensation) ==
Line 35: Line 72:
[[Tp tuning|POL2 generator]]: ~9/7 = 443.322
[[Tp tuning|POL2 generator]]: ~9/7 = 443.322


{{Val list|legend=1| 19, 27, 46, 111de, 157de }}
{{Optimal ET sequence|legend=1| 19, 27, 46, 111de, 157de }}


[[Tp tuning #T2 tuning|RMS error]]: 1.321 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.321 cents
== Decic ==
: <small>''For full 13- and 17-limit extensions, see [[Cloudy clan #Decic]].''</small>
Subgroup: 2.3.5.7.13
[[Comma list]]: 105/104, 196/195, 8281/8192
[[Gencom]]: [2 49/48; 105/104 196/195 8281/8192]
[[Gencom|Gencom mapping]]: [{{val|10 16 23 28 0 37}}, {{val|0 -1 1 0 0 0}}]
[[Mapping|Sval mapping]]: [{{val|10 16 23 28 37}}, {{val|0 -1 1 0 0}}]
[[Tp tuning|POL2 generator]]: ~49/48 = 21.1859
{{Optimal ET sequence|legend=1| 10, 30b, 40, 50, 60, 110d, 170cdd }}
[[Tp tuning #T2 tuning|RMS error]]: 1.122 cents
=== 2.3.5.7.13.17 ===
Subgroup: 2.3.5.7.13.17
[[Comma list]]: 105/104, 170/169, 196/195, 289/288
[[Gencom]]: [2 49/48; 105/104 170/169 196/195 289/288]
[[Gencom|Gencom mapping]]: [{{val|10 16 23 28 0 37 41}}, {{val|0 -1 1 0 0 0 -1}}]
[[Mapping|Sval mapping]]: [{{val|10 16 23 28 37 41}}, {{val|0 -1 1 0 0 -1}}]
[[Tp tuning|POL2 generator]]: ~49/48 = 21.1836
{{Optimal ET sequence|legend=1| 10, 30bg, 40, 50, 60, 110dg, 170cddg }}
[[Tp tuning #T2 tuning|RMS error]]: 1.038 cents


== Quartonic ==
== Quartonic ==
Line 54: Line 127:
[[Tp tuning|POL2 generator]]: ~36/35 = 45.1821
[[Tp tuning|POL2 generator]]: ~36/35 = 45.1821


{{Val list|legend=1| 26, 27, 53 }}
{{Optimal ET sequence|legend=1| 26, 27, 53 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.7439 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.7439 cents
== Unicorn ==
: <small>''For full 13-limit extensions, see [[Unicorn family]].''</small>
Subgroup: 2.3.5.7.13
[[Comma list]]: 126/125, 196/195, 676/675
[[Gencom]]: [2 28/27; 126/125, 196/195, 676/675]
[[Gencom|Gencom mapping]]: [{{val|1 2 3 4 0 5}}, {{val|0 -8 -13 -23 0 -25}}]
[[Mapping|Sval mapping]]: [{{val|1 2 3 4 5}}, {{val|0 -8 -13 -23 -25}}]
[[Tp tuning|POL2 generator]]: ~28/27 = 62.294
{{Optimal ET sequence|legend=1| 19, 39df, 58, 77 }}
[[Tp tuning #T2 tuning|RMS error]]: 0.7092 cents


== Septidiasemi ==
== Septidiasemi ==
Line 73: Line 165:
[[Tp tuning|POL2 generator]]: ~15/14 = 119.297
[[Tp tuning|POL2 generator]]: ~15/14 = 119.297


{{Val list|legend=1| 10, 151, 161, 171 }}
{{Optimal ET sequence|legend=1| 10, 151, 161, 171 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.2002 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.2002 cents
Line 90: Line 182:
[[Tp tuning|POL2 generator]]: ~15/14 = 119.297
[[Tp tuning|POL2 generator]]: ~15/14 = 119.297


{{Val list|legend=1| 10, 151, 161, 171 }}
{{Optimal ET sequence|legend=1| 10, 151, 161, 171 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.1867 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.1867 cents
Line 109: Line 201:
[[Tp tuning|POL2 generator]]: ~3/2 = 701.773
[[Tp tuning|POL2 generator]]: ~3/2 = 701.773


{{Val list|legend=1| 53, 118, 171, 224, 395 }}
{{Optimal ET sequence|legend=1| 53, 118, 171, 224, 395 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.1525 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.1525 cents
Line 126: Line 218:
[[Tp tuning|POL2 generator]]: ~3/2 = 701.764
[[Tp tuning|POL2 generator]]: ~3/2 = 701.764


{{Val list|legend=1| 53, 118, 171, 395, 566… }}
{{Optimal ET sequence|legend=1| 53, 118, 171, 395, 566… }}


[[Tp tuning #T2 tuning|RMS error]]: 0.1696 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.1696 cents
Line 145: Line 237:
[[Tp tuning|POL2 generator]]: ~10/9 = 182.471
[[Tp tuning|POL2 generator]]: ~10/9 = 182.471


{{Val list|legend=1| 46, 125, 171, 388 }}
{{Optimal ET sequence|legend=1| 46, 125, 171, 388 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.1442 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.1442 cents
Line 162: Line 254:
[[Tp tuning|POL2 generator]]: ~10/9 = 182.471
[[Tp tuning|POL2 generator]]: ~10/9 = 182.471


{{Val list|legend=1| 46, 125, 171, 388 }}
{{Optimal ET sequence|legend=1| 46, 125, 171, 388 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.1341 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.1341 cents
Line 181: Line 273:
[[Tp tuning|POL2 generator]]: ~117/112 = 77.173
[[Tp tuning|POL2 generator]]: ~117/112 = 77.173


{{Val list|legend=1| 31, 109, 140, 171, 311 }}
{{Optimal ET sequence|legend=1| 31, 109, 140, 171, 311 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.1383 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.1383 cents
Line 198: Line 290:
[[Tp tuning|POL2 generator]]: ~68/65 = 77.177
[[Tp tuning|POL2 generator]]: ~68/65 = 77.177


{{Val list|legend=1| 31, 109f, 140, 171, 311 }}
{{Optimal ET sequence|legend=1| 31, 109f, 140, 171, 311 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.1367 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.1367 cents
Line 217: Line 309:
[[Tp tuning|POL2 generator]]: ~105/104 = 16.4240
[[Tp tuning|POL2 generator]]: ~105/104 = 16.4240


{{Val list|legend=1| 28, 56, 84, 140, 224, 364 }}
{{Optimal ET sequence|legend=1| 28, 56, 84, 140, 224, 364 }}


[[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 [[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
Line 236: Line 408:
[[Tp tuning|POL2 generator]]: ~3/2 = 702.319
[[Tp tuning|POL2 generator]]: ~3/2 = 702.319


{{Val list|legend=1| 41, 176, 217 }}
{{Optimal ET sequence|legend=1| 41, 176, 217 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.1852 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.1852 cents


[[Category:Regular temperament theory]]
== Devimarvel (rank 3) ==
[[Category:Temperament collection]]
{{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:Pages with mostly numerical content]]
[[Category:Subgroup temperaments]]
[[Category:Subgroup temperaments]]
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/No-elevens_subgroup_temperaments"