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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Technical data page}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
A '''subgroup temperament''' is a regular temperament defined on a [[just intonation subgroup]] that is not a full ''p''-limit group.  
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-02-20 12:42:06 UTC</tt>.<br>
: The original revision id was <tt>490785768</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]]
Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on [[Chromatic pairs]].


=2.3.7=
For temperaments that omit various prime harmonics, see:
* [[No-elevens subgroup temperaments]]
* [[No-sevens subgroup temperaments]]
* [[No-fives subgroup temperaments]]
* [[No-threes subgroup temperaments]]
* [[No-twos subgroup temperaments]] (additionally, [[Catalog of 3.5.7 subgroup rank two temperaments]]).


==[[Semaphore and Godzilla|Semaphore]]==
Below are some temperaments for composite subgroups and fractional subgroups. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on [[Chromatic pairs]].
Comma: 49/48


[[Lp tuning|POL2 generator]]: ~8/7~7/6 = 250.385
= Composite subgroup temperaments =
== 2.3.35 subgroup ==
=== Darian calendar ===
Darian calendar is described as 24 & 668 temperament in the 2.3.11.19 [[subgroup]] and is named after a certain calendar layout by the same name. The generator is close to the [[36/35]] quartertone, and this allows an extension to the 2.3.35.11.19 subgroup. 5 of them make [[11/8]], 8 of them make [[3/2]], and 6 of them make [[32/19]].


[[Gencom]]: [2 8/7; 49/48]
==== 2.3.11.19 subgroup ====
Gencom mapping: [&lt;1 2 0 3|, &lt;0 -2 0 -1|]
The temperament is simplest in this subgroup, although there is a tradeoff of breaking up the simplicity of the 36/35 quartertone.


Map: [&lt;1 2 3|, &lt;0 -2 -1|]
[[Subgroup]]: 2.3.11.19
EDOs: 5, 14, 19, 24, 67c, 91c
[[Tp tuning#T2%20tuning|RMS error]]: 2.523 cents


==Archy==
{{Mapping|legend=2| 4 5 13 18 | 0 8 5 -6 }}
Archy can be thought of as "no-5's [[dominant]]" or "no-5's [[superpyth]]". The name comes from the fact that it tempers out 64/63, the Archytas comma.


Comma: 64/63
: sval mapping generators: ~6291456/5285401, ~25289/24576


[[Lp tuning|POL2 generator]]: ~3/2 = 709.321
[[Optimal tuning]] ([[CTE]]): ~6291456/5285401 = 1\4, ~25289/24576 = 50.257


Gencom: [2 3/2; 64/63]
[[Support]]ing [[ET]]s: {{EDOs|24, 596, 620, 644, 668, 692, 716}}, ...
Gencom mapping: [&lt;1 1 0 4|, &lt;0 1 0 -2|]


Map: [&lt;1 2 2|, &lt;0 -1 2|]
==== 2.3.35.11.19 subgroup ====
EDOs: 5, 12, 17, 22, 27, 137bc
668edo does not map 36/35 consistently, with its own [[direct approximation]] being 27 steps while the direct approximations of its constituent odd harmonics do not sum to that same amount: 3/2, 8/5, and 8/7 are 391, 453, and 129 steps, respectively, and 391 + 391 + 453 + 129 - 668 - 668 = 28, ≠ 27.
[[Tp tuning#T2%20tuning|RMS error]]: 1.856 cents


==[[Slendric]]==
Subgroup: 2.3.35.11.19
Comma: 1029/1024


[[Lp tuning|POL2 generator]]: ~8/7 = 233.688
Sval mapping: {{mapping| 4 0 5 13 18 | 0 1 8 5 -6 }}


Gencom: [2 8/7; 1029/1024]
: sval mapping generators: ~2240/1881, ~36/35
Gencom mapping: [&lt;1 1 0 3|, &lt;0 3 0 -1|]


Map: [&lt;1 1 3|, &lt;0 3 -1|]
Optimal tuning (CTE): ~2240/1881 = 1\4, ~36/35 = 50.288
EDOs: 5, 21, 26, 31, 36, 77, 113, 190
[[Tp tuning#T2%20tuning|RMS error]]: 0.3202 cents


==Lee==
[[Support]]ing [[ET]]s: {{EDOs|24, 668}}, ...
Comma: 177147/175616


[[Lp tuning|POL2 generator]]: ~81/56 = 633.525
== 2.9.5.7 subgroup ==
See also [[Jubilismic clan #Antikythera|antikythera]] and [[Hemimean clan #Isra|isra]].  


Map: [&lt;1 0 -3|, &lt;0 3 11|]
=== Commatose ===
EDOs: 17, 36, 89, 125, 161, 358, 519b
Commatose is a [[Dual-fifth temperaments|dual-fifth temperament]] which uses the Pythagorean comma as a generator. It was developed by [[Eliora]] to highlight the near-perfect expression of 9/8 by [[1789edo]], while at the same time the fact that it completely misses 3/2. It is described as the 460 & 1329 temperament. In the 13-limit extension 24 generators are equal to [[~]][[13/9]].
[[Tp tuning#T2%20tuning|RMS error]]: 0.3519 cents


==Skwares==
[[Subgroup]]: 2.9.5.7
Comma: 19683/19208


[[Lp tuning|POL2 generator]]: ~9/7 = 425.365 cents
[[Comma list]]: {{monzo| 28 -2 -19 8 }}, {{monzo| 9 -25 23 6 }}


Map: [&lt;1 3 6|, &lt;0 -4 -9|]
{{Mapping|legend=2| 1 9 6 13 | 0 -298 -188 -521 }}
EDOs: 14, 17, 31, 48, 79, 189b, 268bc, 347bc
[[Tp tuning#T2%20tuning|RMS error]]: 1.149 cents


=2.3.11=
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~531441/524288 = 23.4765


==Neutraltet==
{{Optimal ET sequence|legend=1| 460, 869, 1329 }}
Neutraltet can be thought of as 2.3.11 version of either [[mohajira]] or [[maqamic]], and is the temperament optimizing the [[neutral tetrad]].


Comma: 243/242
[[Badness]]: 0.611


[[Lp tuning|POL2 generator]]: ~11/9 = 350.525
==== 2.9.5.7.11 ====
Subgroup: 2.9.5.7.11


Gencom: [2 11/9; 243/242]
Comma list: {{monzo| -7 7 -3 2 -4 }}, {{monzo| 17 0 -13 1 3 }}, {{monzo| 11 -2 -6 7 -3 }}
Gencom mapping: [&lt;1 1 0 0 2|, &lt;0 2 0 0 5|]


Map: [&lt;1 1 2|, &lt;0 2 5|]
Sval mapping: {{mapping| 1 9 6 13 16 | 0 -298 -188 -521 -641 }}
EDOs: 7, 10, 17, 24, 41, 65, 89, 202, 291, 380
[[Tp tuning#T2%20tuning|RMS error]]: 0.3021 cents


[[xenharmonic/neutraltet7|Seven note albitonic scale]]
Optimal tuning (CTE): ~2 = 1\1, ~531441/524288 = 23.4767
[[xenharmonic/neutraltet10|Ten note chromatic scale]]
[[xenharmonic/neutraltet17|Seventeen note mega chromatic scale]]


=2.3.5.11=
{{Optimal ET sequence|legend=1| 460, 869e, 1329, 1789, 3118 }}


==Porkypine==
Badness: 0.165
Commas: 55/54, 100/99


[[Lp tuning|POL2 generator]]: ~10/9 = 164.078
==== 2.9.5.7.11.13 ====
Subgroup: 2.9.5.7.11.13


Gencom: [2 10/9; 55/54, 100/99]
Comma list: 123201/123200, 1016064/1015625, 2250423/2249390, 2599051/2598156
Gencom mapping: [&lt;1 2 3 0 4|, &lt;0 -3 -5 0 -4|]


Map: [&lt;1 2 3 4|, &lt;0 -3 -5 -4|]
Sval mapping: {{mapping| 0 9 6 13 16 10 | -298 -188 -521 -641 -322 }}
EDOs: 7, 15, 22, 37, 73cd, 95cd, 117bcd
[[Tp tuning#T2%20tuning|RMS error]]: 2.287 cents


==Mohaha==
Optimal tuning (CTE): ~2 = 1\1, ~3575/3528 = 23.4767
Commas: 81/80, 121/120


[[Lp tuning|POL2 generator]]: ~11/9 = 348.094
{{Optimal ET sequence|legend=1| 460, 869e, 1329, 1789, 3118 }}


Gencom: [2 11/9; 81/80 121/120]
Badness: 0.0564
Gencom mapping: [&lt;1 1 0 0 2|, &lt;0 2 8 0 5|]


Map: [&lt;1 1 0 2|, &lt;0 2 8 5|]
=== Daemotertiaschis ===
EDOs: 7, 10, 17, 24, 31, 55, 69d, 100d, 131bd
{{See also|Schismatic family#Tertiaschis}}
[[Tp tuning#T2%20tuning|RMS error]]: 1.392 cents
Daemotertiaschis is produced by taking every other generator of tertiaschis, and the subgroup is chosen so it tempers out exactly the same commas. It is notable due to offering a [[7L 4s|daemotonic 7L 4s]] scale of reasonable hardness (hence the name ― daemo- + tertiaschis), which is notoriously difficult to approximate with simple JI or RTT methods.


===Music===
Subgroup: 2.9.5.7.33.13.17
[[http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3|Mohaha10ping2]] by [[Billy Stiltner]]


=2.3.7.11=
Comma list: 325/324, 375/374, 385/384, 595/594, 10985/10976


==Ennea==
{{Mapping|legend=2|1 1 11 -16 13 -18 20|0 3 -12 26 -11 30 -22}}
Commas: 41503/41472, 43923/43904


[[Lp tuning|POL2 generator]]: ~99/98 = 17.6258
Optimal tuning (CTE): ~2 = 1\1, 33/20 = 867.982


Gencom: [2 99/98; 41503/41472, 43923/43904]
[[Support]]ing [[ET]]s: {{Optimal ET sequence|47, 65f, 112, 159, 206, 253}}
Gencom mapping: [&lt;1 14/9 0 25/9 31/9|, &lt;0 2 0 2 1|]


Sval map: [&lt;9 0 11 24|, &lt;0 2 2 1|]
=== Baldy ===
EDOs: 54, 63, 68, 72, 135, 342, 477, 525, 613, 681, 749, 817, 2159bcd, 3336bcd, 4153bcd
{{See also|Schismatic family #Garibaldi}}
[[Tp tuning#T2%20tuning|RMS error]]: 0.0383 cents
{{See also|No-threes subgroup temperaments #Frostburn}}


==Supra==
Baldy results from taking every other generator of the [[garibaldi]] temperament. One of the best extension is 2.9.5.7.13 subgroup with mapping 13/8 to +10 whole tones, as well as the cassandra temperament.
Commas: 64/63, 99/98


[[POTE tuning|POTE generator]]: ~3/2 = 707.192
[[Subgroup]]: 2.9.5.7


Gencom: [2 3/2; 64/63 99/98]
[[Comma list]]: 225/224, 3125/3087
Gencom mapping: [&lt;1 1 0 4 7|, &lt;0 1 0 -2 -6|]


Sval map: [&lt;1 0 6 13|, &lt;0 1 -2 -6|]
{{Mapping|legend=2| 1 3 3 4 | 0 1 -4 -7 }}
EDOs: 5, 12, 17, 39c, 56c
[[Tp tuning#T2%20tuning|RMS error]]: 1.977 cents


==Skwares==
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 204.170
Commas: 99/98, 243/242


[[POTE tuning|POTE generator]]: ~9/7 = 425.244
{{Optimal ET sequence|legend=1| 6, 29, 35, 41, 47 }}


Gencom: [2 9/7; 99/98 243/242]
Related temperament: [[Schismatic family #Garibaldi|Garibaldi]]
Gencom mapping: [&lt;1 3 0 6 7|, &lt;0 -4 0 -9 -10]]


Sval map: [&lt;1 3 6 7|, &lt;0 -4 -9 -10|]
==== 2.9.5.7.13 ====
EDOs: 14, 17, 31, 48, 79, 127, 206bcd
{{See also|Chromatic pairs #Baldy}}
[[Tp tuning#T2%20tuning|RMS error]]: 1.099 cents


==Hemif (11 limit)==
Baldy is every other step of [[garibaldi]], without the mapping of prime 11. It can be described as the 6 &amp; 35 temperament.
Commas: 243/242, 896/891


POTE generator: ~11/9 = 351.535
[[Subgroup]]: 2.9.5.7.13


Gencom: [2 11/9; 243/242 896/891]
[[Comma list]]: [[225/224]], [[325/324]], [[640/637]]
Gencom mapping: [&lt;1 1 0 -1 2|, &lt;0 2 0 13 5|]


Sval map: [&lt;1 1 -1 2|, &lt;0 2 13 5|]
{{Mapping|legend=2| 1 0 15 25 -28 | 0 1 -4 -7 10 }}
EDOs: 7, 17, 41, 58, 99d
[[Tp tuning#T2%20tuning|RMS error]]: 0.6108 cents


=2.3.7.11.13=
{{Mapping|legend=3| 1 3/2 3 4 0 2 | 0 1/2 -4 -7 0 10 }}


==Suhajira==
: [[gencom]]: [2 9/8; 225/224 325/324 640/637]
Commas: 64/63, 78/77, 144/143


Gencom: [2 11/9; 64/63 78/77 144/143]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 204.090
Gencom map: [&lt;1 1 0 4 2 4|, &lt;0 2 0 -4 5 -1|]


[[Tp tuning|POT2 generator]]: ~11/9 = 353.775
{{Optimal ET sequence|legend=1| 6, 11, 17, 23, 29, 35, 41, 47, 100, 147, 488cd, 635cd }}


Map: [&lt;1 1 4 2 4|, &lt;0 2 -4 5 -1|]
[[Tp tuning #T2 tuning|RMS error]]: 0.5999 cents
EDOs: 7, 10, 17, 44d, 61cd, 78cd
[[Tp tuning#T2%20tuning|RMS error]]: 1.953 cents


==Hemif==
Related temperament: [[Schismatic family #Garibaldi|Cassandra]]
Commas: 144/143, 243/242, 364/363
Related temperament: [[xenharmonic/Breedsmic temperaments|Hemififths]], namo


[[Tp tuning|POT2 generator]]: ~11/9 = 351.691
==== Baldanders ====
Baldanders results from taking every other generator of the andromeda, with mapping 11/8 to -9 whole tones.


[[Gencom]]: [2 11/9; 144/143 243/242 364/363]
Subgroup: 2.9.5.7.11
Gencom map: [&lt;1 1 0 -1 2 4|, &lt;0 2 0 13 5 -1|]


Map: [&lt;1 1 -1 2 4|, &lt;0 2 13 5 -1|]
Comma list: 100/99, 225/224, 245/242
EDOs: 7, 10, 17, 24, 41, 58
[[Tp tuning#T2%20tuning|RMS error]]: 0.7167 cents


==Skwares==
{{Mapping|legend=2| 1 3 3 4 5 | 0 1 -4 -7 -9 }}
Commas: 78/77, 99/98, 243/242


[[Tp tuning|POT2 generator]]: ~9/7 = 424.457
Optimal tuning (POTE): ~2 = 1\1, ~9/8 = 204.743


Map: [&lt;1 3 6 7 9|, &lt;0 -4 -9 -10 -15|]
{{Optimal ET sequence|legend=1| 6, 23de, 29, 35, 41 }}
EDOs: 17, 48e, 65de, 82c, 147ce
[[Tp tuning#T2%20tuning|RMS error]]: 1.769 cents


==Leapfrog==
Related temperament: [[Schismatic family #Garibaldi|Andromeda]]
Commas: 169/168, 352/351, 364/363


[[Lp tuning|POL2 generator]]: ~3/2 = 704.745 cents
===== 2.9.5.7.11.13 =====
Subgroup: 2.9.5.7.11.13


Gencom: [2 3/2; 169/169 352/351 364/363]
Comma list: 100/99, 144/143, 225/224, 245/242
Gencom mapping: [&lt;1 1 0 -6 -3 -1|, &lt;0 1 0 15 11 8|]


Sval map: [&lt;1 0 -21 -14 -9|, &lt;0 1 15 11 8|]
{{Mapping|legend=2| 1 3 3 4 5 2 | 0 1 -4 -7 -9 10 }}
EDOs: 17, 46, 63
[[Tp tuning#T2%20tuning|RMS error]]: 0.7541 cents


==Bleu==
Optimal tuning (POTE): ~2 = 1\1, ~9/8 = 204.414
Group: 2.3.7.11.13
Commas: 78/77, 99/98, 144/143
Sval name: 9&amp;17


[[Tp tuning|POL2 generator]]: ~13/12 = 139.990
{{Optimal ET sequence|legend=1| 6, 23def, 29f, 35, 41, 47 }}


[[Gencom]]: [2 13/12; 78/77 99/98 144/143]
== 2.3.25 subgroup ==
Gencom map: [&lt;1 1 0 2 3 3|, &lt;0 5 0 7 4 6|]


Map: [&lt;1 1 2 3 3|, &lt;0 5 7 4 6|]
=== Shrub ===
EDOs: [[xenharmonic/17edo|17]], [[xenharmonic/43edo|43]], [[xenharmonic/60edo|60c]]
This is a restriction of diaschismic which omits the tritone to produce a diatonic scale. True to its name, it generates a [[shrubmajor]] third (~425c) in quarter-comma tuning.
[[Tp tuning#T2%20tuning|RMS error]]: 1.752 cents


==Parapyth (Rank 3)==
Subgroup: 2.3.25
Commas: 352/351, 364/363


[[Lp tuning|POL2 tuning]]: &lt;1200.000 1903.856 (2787.774) 3369.907 4154.482 4442.913|
Edo join: 17 & 12


The gencom below gives [[Margo Schulter]]'s favored basis
Comma list: [[2048/2025]]
Gencom: [2 3/2 28/27; 352/351 364/363]
Gencom mapping: [&lt;1 1 0 1 4 6|, &lt;0 1 0 3 -1 -4|, &lt;0 0 0 1 1 1|]


Sval map: [&lt;1 0 0 7 12|, &lt;0 1 0 -4 -7|, &lt;0 0 1 1 1|]
{{Mapping|legend=2| 1 1 7| 0 1 -4}}
EDOs: 17, 41, 46, 58, 87, 104
[[Tp tuning#T2%20tuning|RMS error]]: 0.3789 cents


=2.3.5.11=
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 705.136


==Larry==  
==== 2.3.23.25.41 subgroup ====
Commas: 243/242, 4000/3993
''See also: [[Reversed meantone]]''
Related temperaments: [[Gravity family#Gravity|gravity]], [[Gravity family#Harry|harry]]


POTE generator: ~40/27 = 683.166
Edo join: 17 & 12


Gencom: [2 40/27; 243/242 4000/3993]
Comma list: 2048/2025, 576/575, 82/81
Gencom mapping: [&lt;1 5 12 0 12|, &lt;0 -6 -17 0 -15|]


Map: [&lt;1 5 12 12|, &lt;0 -6 -17 -15|]
{{Mapping|legend=2| 1 1 1 7 3| 0 1 6 -4 4}}
EDOs: 7, 58, 65, 137, 202
[[Tp tuning#T2%20tuning|RMS error]]: 0.3025 cents


=2.9.7.11=
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 705.264


==Machine==  
===== Sburb =====
Commas: 64/63, 99/98
This temperament sets the [[octave reduction|octave-reduced]] 413th harmonic (413/256, 827.998{{c}}) to the diminished seventh.


[[POTE tuning|POTE generator]]: ~8/7 = 214.384
Subgroup: 2.3.7.23.25.41.59


Gencom: [2 8/7; 64/63 99/98]
Edo join: 17 & 12
Gencom mapping: [&lt;1 3/2 0 3 4|, &lt;0 1/2 0 -1 -3|]


[[Smonzos and Svals|Sval map]]: [&lt;1 0 6 13|, &lt;0 1 -1 -3|]
Comma list: 64/63, 225/224, 162/161, 82/81, 177/175
EDOs: 5, 6, 11, 17, 28
[[Tp tuning#T2%20tuning|RMS error]]: 1.977 cents


==Apparatus==
{{Mapping|legend=2| 1 1 4 1 7 3 10| 0 1 -2 6 -4 4 -7}}
Commas: 41503/41472, 322102/321489


[[POTE tuning|POTE generator]]: ~77/72 = 115.570
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 706.387


Gencom: [2 77/72; 41503/41472 322102/321489]
== 2.9.5.11 subgroup ==
Gencom mapping: [&lt;1 5/2 0 3 5|, &lt;0 -19/2 0 -2 -16|]
=== Glacial ===
{{See also| Chromatic pairs #Glacial }}


[[Smonzos and Svals|Sval map]]: [&lt;1 5 3 5|, &lt;0 -19 -2 -16|]
[[Subgroup]]: 2.9.5.11.13
EDOs: 10, 21, 31, 52, 83, 135, 353, 488, 623
[[Tp tuning#T2%20tuning|RMS error]]: 0.0673 cents


==Mechanism==
[[Comma list]]: 45/44, 65/64, 81/80
Commas: 896/891, 26411/26244


[[POTE tuning|POTE generator]]: ~9/7 = 438.465
{{Mapping|legend=2| 1 0 -4 -6 10 | 0 1 2 3 -2 }}


Gencom: [2 9/7; 896/891 26411/26244]
{{Mapping|legend=3| 1 3/2 2 0 3 4 | 0 1/2 2 0 3 -2 }}
Gencom mapping: [&lt;1 5/2 0 5 2|, &lt;0 -5/2 0 -6 4|]


[[Smonzos and Svals|Sval map]]: [&lt;1 5 5 2|, &lt;0 -5 -6 4|]
: [[gencom]]: [2 9/8; 45/44 65/64 81/80]
EDOs: 8, 11, 30, 41, 52
[[Tp tuning#T2%20tuning|RMS error]]: 0.4262 cents


=2.9.15.7.11.13=
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 186.151


==Stacks (aka 2magic)==
{{Optimal ET sequence|legend=1| 6, 13, 45be, 58bce, 71bce, 84bce }}
Commas: 100/99, 105/104, 144/143, 196/195


[[Lp tuning|POL2 generator]]: ~9/7 = 438.977
[[Tp tuning #T2 tuning|RMS error]]: 2.887 cents


Gencom: [2 9/7; 100/99 105/104 144/143 196/195]
Music:
Gencom mapping: [&lt;1 5/2 5/2 5 2 7|, &lt;0 -5/2 -1/2 -6 4 -9|]
* ''[[Thundersnow]]'' - [[Sevish]] (2021)


Sval map: [&lt;1 0 2 -1 6 -2|, &lt;0 5 3 6 -4 9|]
== 2.9.7 subgroup ==
EDOs: 11, 30, 41, 153cdef, 194cdef, 235cdef
=== Mabon ===
[[Tp tuning#T2%20tuning|RMS error]]: 1.540 cents
Derived from a [http://individual.utoronto.ca/kalendis/leap/index.htm#se calendar leap cycle built for the autumn equinox], hence the name. Defined as the 11 & 62 temperament.


===2.9.15.7.11 stacks===
Subgroup: 2.9.7
Commas: 100/99, 225/224, 245/243


[[Lp tuning|POL2 generator]]: ~9/7 = 438.607
Comma basis: 44957696/43046721


Gencom: [2 9/7; 100/99 225/224 245/243]
Sval mapping: [{{val|1 1 -3}}, {{val|0 3 8}}]
Gencom mapping: [&lt;1 5/2 5/2 5 2|, &lt;0 -5/2 -1/2 -6 4|]


Sval map: [&lt;1 0 2 -1 6|, &lt;0 5 3 6 -4|]
Optimal tuning (CTE): ~729/448 = 870.792
EDOs: 8, 11, 30, 41, 52, 93, 145, 342bce,
[[Tp tuning#T2%20tuning|RMS error]]: 1.226 cents


===2.9.15.7 stacks===
{{Optimal ET sequence|legend=1|7d, 11, 18d, 29, 40, 62}}, ...
Commas: 225/224, 245/243


[[Lp tuning|POL2 generator]]: ~9/7 = 439.296
==== 2.9.7.11 subgroup ====
Subgroup: 2.9.7.11


Gencom: [2 9/7; 225/224 245/243]
Comma basis: 896/891, 1331/1296
Gencom mapping: [&lt;1 5/2 5/2 5|, &lt;0 -5/2 -1/2 -6|]


Sval map: [&lt;1 0 2 -1|, &lt;0 5 3 6|]
Sval mapping: [{{val|1 1 -3 2}}, {{val|0 3 8 2}}]
EDOs: 8, 11, 30, 41, 71, 93, 112c, 134c, 175c
[[Tp tuning#T2%20tuning|RMS error]]: 1.074 cents


=2.9.21=
Optimal tuning (CTE): ~16/11 = 870.966
==A-team==
Commas: 1029/1024


[[Lp tuning|POL2 generator]]: ~21/16 = 467.375
{{Optimal ET sequence|legend=1| 7d, 11, 40, 51, 62 }}


Gencom: [2 21/16; 1029/1024]
== 2.9.7.11 subgroup ==
Gencom mapping: [&lt;1 1 0 3|, &lt;0 3/2 0 -1/2|]
=== Apparatus ===
[[Subgroup]]: 2.9.7.11


Sval map: [&lt;1 2 4|, &lt;0 3 1|]
[[Comma list]]: 41503/41472, 322102/321489
EDOs: 5, 13, 18, 41, 59, 77, 95
[[Tp tuning#T2%20tuning|RMS error]]: 0.3202 cents


=2.3.7/5.11/5.13/5=
{{Mapping|legend=2| 1 5 3 5 | 0 -19 -2 -16 }}
==Historical==
Subgroup: 2.3.7/5.11/5.13/5
Commas: 364/363, 441/440, 1001/1000


[[Lp tuning|POL2 generator]]: ~21/20 = 83.016
: mapping generators: ~2, ~77/72


[[Gencom]]: [2 21/20; 364/363 441/440 1001/1000]
{{Mapping|legend=3| 1 5/2 0 3 5 | 0 -19/2 0 -2 -16 }}
Gencom map: [&lt;1 2 -3/4 -3/4 1/4 5/4|, &lt;0 -6 0 7 2 -9|]


Sval map: [&lt;1 2 0 1 2|, &lt;0 -6 7 2 -9|]
: [[gencom]]: [2 77/72; 41503/41472 322102/321489]
EDOs: 14, 29, 72, 101, 130, 159
[[Tp tuning#T2%20tuning|RMS error]]: 0.2562 cents


=2.3.7.11/5.13=
[[Optimal tuning]] ([[CTE]]): ~77/72 = 115.5685
==Hypnosis==
Subgroup: 2.3.7.11/5.13
Commas: 169/168, 540/539, 729/728
Related temperament: [[Swetismic temperaments#Hypnos-13-limit|hypnos]], [[Hemifamity temperaments#Tricot-13-limit|tricot]]


[[Gencom]]: [2 13/9; 169/168, 540/539, 729/728]
{{Optimal ET sequence|legend=1| 10e, 21, 31, 52, 83, 135, 353, 488, 623 }}
Gencom map: [&lt;1 0 -4 -3 4 0|, &lt;0 3 13/2 11 -13/2 7|]


Sval map: [&lt;1 0 -3 8 0|, &lt;0 3 11 -13 7|]
[[Badness]]: 0.00263
EDOs: 17, 36, 118e, 125e, 161e, 197e
 
[[Tp tuning#T2%20tuning|RMS error]]: 0.5379 cents</pre></div>
=== Joan ===
<h4>Original HTML content:</h4>
{{See also| Chromatic pairs #Joan }}
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Subgroup temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:80:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt;&lt;a href=
 
Joan is related to [[casablanca]] as well as to [[orwell]].
 
[[Subgroup]]: 2.9.7.11
 
[[Comma list]]: 99/98, 9317/9216
 
{{Mapping|legend=2| 1 0 1 3 | 0 7 4 1 }}
 
{{Mapping|legend=3| 1 0 0 1 3 | 0 7/2 0 4 1 }}
 
: [[gencom]]: [2 11/8; 99/98 9317/9216]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 542.672 cents
 
{{Optimal ET sequence|legend=1| 11, 20, 31, 42, 115bd, 157bd }}
 
[[Tp tuning #T2 tuning|RMS error]]: 1.424 cents
 
=== Machine ===
Machine is every other step of [[supra]], most interesting for its scale patterns.
 
[[Subgroup]]: 2.9.7.11
 
[[Comma list]]: 64/63, 99/98
 
{{Mapping|legend=2| 1 0 6 13 | 0 1 -1 -3 }}
 
: sval mapping generators: ~2, ~9
 
{{Mapping|legend=3| 1 3/2 0 3 4 | 0 1/2 0 -1 -3 }}
 
: [[gencom]]: [2 8/7; 64/63 99/98]
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~9/8 = 216.9128
* [[POTE]]: ~2 = 1\1, ~9/8 = 214.3843
 
{{Optimal ET sequence|legend=1| 5, 6, 11, 17, 28 }}
 
[[Badness]]: 0.00233
 
=== Penta a.k.a. mechanism ===
Penta or mechanism is the 8 &amp; 11 temperament in the 2.9.7.11 subgroup.
 
[[Subgroup]]: 2.9.7.11
 
[[Comma list]]: 896/891, 26411/26244
 
{{Mapping|legend=2| 1 0 -1 6 | 0 5 6 -4 }}
 
: sval mapping generators: ~2, ~14/9
 
{{Mapping|legend=3| 1 5/2 0 5 2 | 0 -5/2 0 -6 4 }}
 
: [[gencom]]: [2 9/7; 896/891 26411/26244]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~14/9 = 761.3782
 
{{Optimal ET sequence|legend=1| 8, 11, 30, 41, 52 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.4262 cents
 
[[Badness]]: 0.00439
 
Scales: [[penta5]], [[penta8]], [[penta11]], [[penta19]]
 
== 2.9.7.13.17 subgroup ==
 
=== Novisept ===
Novisept is generated by a one-cent-flat 9/7, such that stacking 5 of them gives you 7/4. It can be formed by doubling both generator and period of [[gizzard]].
 
[[Subgroup]]: 2.9.7.13.17
 
[[Comma list]]: 729/728, 442/441, 833/832
 
{{Mapping|legend=2| 1 1 1 -1 3| 0 6 5 13 3 }}
 
[[Optimal tuning]] ([[CWE]]): ~2 = 1\1, ~9/7 = 433.836
 
Badness (Dirichlet): 0.142
 
== 2.9.11 subgroup ==
=== Demon ===
Demon is a temperament which equates 3 [[11/9]] with [[16/9]], or equivalently 3 [[18/11]] with [[9/8]], tempering out [[1331/1296]]. This results in [[11/9]] being tuned flat to a supraminor third, and [[27/22]] being tuned sharp to a submajor third. It was discovered by [[User:CompactStar|CompactStar]] while searching for temperaments assosciated with the [[7L 4s]] ("daemotonic") MOS, known for its lack of representation of simple temperaments. The optimal tuning for demon temperament is near the basic tuning of 7L 4s (13\18), and indeed [[18edo]] supports demon temperament.
 
[[Subgroup]]: 2.9.11
 
[[Comma list]]: [[1331/1296]]
 
{{Mapping|legend=2|1 1 2|0 3 2}}
 
[[Optimal tuning]] ([[CTE]]): ~[[18/11]] = 870.060
 
{{Optimal ET sequence|legend=1|4, 7, 11, 18, 29, 76e}}
 
=== Genius ===
 
Named after the genius in Roman religion, following the demon (daimon) in Greek mythology.
 
[[Subgroup]]: 2.9.11
 
[[Comma list]]: [[131769/131072]]
 
{{Mapping|legend=2|1 1 4|0 4 -1}}
 
[[Optimal tuning]] ([[CTE]]): ~[[16/11]] = 650.863
 
{{Optimal ET sequence|legend=1|9, 11, 24, 59, 83, 142, 225, 367}}[-11], 592[-11], 959[-9, --11], 1326[-9, --11]
 
== 2.9.15.7 subgroup ==
=== Stacks (a.k.a. 2magic) ===
Stacks, the 11 &amp; 30 temperament in the 2.9.15.7.11.13 subgroup, is every other step of [[magic]].
 
[[Subgroup]]: 2.9.15.7
 
[[Comma list]]: 225/224, 245/243
 
{{Mapping|legend=2| 1 0 2 -1 | 0 5 3 6 }}
 
: sval mapping generators: ~2, ~14/9
 
{{Mapping|legend=3| 1 5/2 5/2 5 | 0 -5/2 -1/2 -6 }}
 
: [[gencom]]: [2 9/7; 225/224 245/243]
 
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~14/9 = 760.704
 
{{Optimal ET sequence|legend=1| 8, 11, 30, 41, 71, 93, 112c, 134c, 175c }}
 
[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
 
==== 2.9.15.7.11 ====
Subgroup: 2.9.15.7.11
 
Comma list: 100/99, 225/224, 245/243
 
Sval mapping: {{mapping| 1 0 2 -1 6 | 0 5 3 6 -4 }}
 
Gencom mapping: {{mapping| 1 5/2 5/2 5 2 | 0 -5/2 -1/2 -6 4 }}
 
: gencom: [2 9/7; 100/99 225/224 245/243]
 
Optimal tuning (subgroup POTE): ~2 =
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