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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>2012-07-25 12:55:15 UTC</tt>.<br>
: The original revision id was <tt>354768988</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
[[Lp tuning#L2 tuning|L2 error]]: 5.046 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.
[[Lp tuning#L2 tuning|L2 error]]: 3.713 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
[[Lp tuning#L2 tuning|L2 error]]: 0.6403 cents


=2.3.11=
[[Support]]ing [[ET]]s: {{EDOs|24, 668}}, ...


==Neutraltet==  
== 2.9.5.7 subgroup ==
Neutraltet can be thought of as 2.3.11 version of either [[mohajira]] or [[maqamic]], and is the temperament optimizing the [[neutral tetrad]].
See also [[Jubilismic clan #Antikythera|antikythera]] and [[Hemimean clan #Isra|isra]].  


Comma: 243/242
=== Commatose ===
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]].


[[Lp tuning|POL2 generator]]: ~11/9 = 350.525
[[Subgroup]]: 2.9.5.7


Gencom: [2 11/9; 243/242]
[[Comma list]]: {{monzo| 28 -2 -19 8 }}, {{monzo| 9 -25 23 6 }}
Gencom mapping: [&lt;1 1 0 0 2|, &lt;0 2 0 0 5|]


Map: [&lt;1 1 2|, &lt;0 2 5|]
{{Mapping|legend=2| 1 9 6 13 | 0 -298 -188 -521 }}
EDOs: 7, 10, 17, 24, 41, 65, 89, 202, 291, 380
[[Lp tuning#L2 tuning|L2 error]]: 0.6756 cents


[[xenharmonic/neutraltet7|Seven note albitonic scale]]
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~531441/524288 = 23.4765
[[xenharmonic/neutraltet10|Ten note chromatic scale]]
[[xenharmonic/neutraltet17|Seventeen note mega chromatic scale]]


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


==Porkypine==
[[Badness]]: 0.611
Commas: 55/54, 100/99


[[Lp tuning|POL2 generator]]: ~10/9 = 164.078
==== 2.9.5.7.11 ====
Subgroup: 2.9.5.7.11


Gencom: [2 10/9; 55/54, 100/99]
Comma list: {{monzo| -7 7 -3 2 -4 }}, {{monzo| 17 0 -13 1 3 }}, {{monzo| 11 -2 -6 7 -3 }}
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| 1 9 6 13 16 | 0 -298 -188 -521 -641 }}
EDOs: 7, 15, 22, 37, 73cd, 95cd, 117bcd
[[Lp tuning#L2 tuning|L2 error]]: 5.114 cents


==Mohaha==
Optimal tuning (CTE): ~2 = 1\1, ~531441/524288 = 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: 0.165
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|]
==== 2.9.5.7.11.13 ====
EDOs: 7, 10, 17, 24, 31, 69d, 100d, 131bd
Subgroup: 2.9.5.7.11.13
[[Lp tuning#L2 tuning|L2 error]]: 3.113 cents


===Music===
Comma list: 123201/123200, 1016064/1015625, 2250423/2249390, 2599051/2598156
[[http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3|Mohaha10ping2]] by [[Billy Stiltner]]


=2.3.7.11=
Sval mapping: {{mapping| 0 9 6 13 16 10 | -298 -188 -521 -641 -322 }}


==Ennea==
Optimal tuning (CTE): ~2 = 1\1, ~3575/3528 = 23.4767
Commas: 41503/41472, 43923/43904


[[Lp tuning|POL2 generator]]: ~99/98 = 17.6258
{{Optimal ET sequence|legend=1| 460, 869e, 1329, 1789, 3118 }}


Gencom: [2 99/98; 41503/41472, 43923/43904]
Badness: 0.0564
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|]
=== Daemotertiaschis ===
EDOs: 54, 63, 68, 72, 135, 342, 477, 525, 613, 681, 749, 817, 2159bcd, 3336bcd, 4153bcd
{{See also|Schismatic family#Tertiaschis}}
[[Lp tuning#L2 tuning|L2 error]]: 0.0857 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.


==Supra==
Subgroup: 2.9.5.7.33.13.17
Commas: 64/63, 99/98


[[POTE tuning|POTE generator]]: ~3/2 = 707.192
Comma list: 325/324, 375/374, 385/384, 595/594, 10985/10976


Gencom: [2 3/2; 64/63 99/98]
{{Mapping|legend=2|1 1 11 -16 13 -18 20|0 3 -12 26 -11 30 -22}}
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|]
Optimal tuning (CTE): ~2 = 1\1, 33/20 = 867.982
EDOs: 5, 12, 17, 39c, 56c
[[Lp tuning#L2 tuning|L2 error]]: 4.421 cents


==Skwares==
[[Support]]ing [[ET]]s: {{Optimal ET sequence|47, 65f, 112, 159, 206, 253}}
Commas: 99/98, 243/242


[[POTE tuning|POTE generator]]: ~9/7 = 425.244
=== Baldy ===
{{See also|Schismatic family #Garibaldi}}
{{See also|No-threes subgroup temperaments #Frostburn}}


Gencom: [2 9/7; 99/98 243/242]
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.
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|]
[[Subgroup]]: 2.9.5.7
EDOs: 14, 17, 31, 48, 79, 127, 206bcd
[[Lp tuning#L2 tuning|L2 error]]: 2.457 cents


==Hemif==
[[Comma list]]: 225/224, 3125/3087
Commas: 243/242, 896/891


POTE generator: ~11/9 = 351.535
{{Mapping|legend=2| 1 3 3 4 | 0 1 -4 -7 }}


Gencom: [2 11/9; 243/242 896/891]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 204.170
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|]
{{Optimal ET sequence|legend=1| 6, 29, 35, 41, 47 }}
EDOs: 7, 17, 41, 58, 99d
[[Lp tuning#L2 tuning|L2 error]]: 1.366 cents


=2.5.7.11=
Related temperament: [[Schismatic family #Garibaldi|Garibaldi]]


==Larry==  
==== 2.9.5.7.13 ====
Commas: 243/242, 4000/3993
{{See also|Chromatic pairs #Baldy}}
Related temperaments: [[Gravity family#Gravity|gravity]], [[Gravity family#Harry|harry]]


POTE generator: ~40/27 = 683.166
Baldy is every other step of [[garibaldi]], without the mapping of prime 11. It can be described as the 6 &amp; 35 temperament.  


Gencom: [2 40/27; 243/242 4000/3993]
[[Subgroup]]: 2.9.5.7.13
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|]
[[Comma list]]: [[225/224]], [[325/324]], [[640/637]]
EDOs: 7, 58, 65, 137, 202
[[Lp tuning#L2 tuning|L2 error]]: 0.6765 cents


=2.9.7.11=
{{Mapping|legend=2| 1 0 15 25 -28 | 0 1 -4 -7 10 }}


==Machine==
{{Mapping|legend=3| 1 3/2 3 4 0 2 | 0 1/2 -4 -7 0 10 }}
Commas: 64/63, 99/98


[[POTE tuning|POTE generator]]: ~8/7 = 214.384
: [[gencom]]: [2 9/8; 225/224 325/324 640/637]


Gencom: [2 8/7; 64/63 99/98]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 204.090
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|]
{{Optimal ET sequence|legend=1| 6, 11, 17, 23, 29, 35, 41, 47, 100, 147, 488cd, 635cd }}
EDOs: 5, 6, 11, 17, 28
[[Lp tuning#L2 tuning|L2 error]]: 4.421 cents


==Apparatus==
[[Tp tuning #T2 tuning|RMS error]]: 0.5999 cents
Commas: 41503/41472, 322102/321489


[[POTE tuning|POTE generator]]: ~77/72 = 115.570
Related temperament: [[Schismatic family #Garibaldi|Cassandra]]


Gencom: [2 77/72; 41503/41472 322102/321489]
==== Baldanders ====
Gencom mapping: [&lt;1 5/2 0 3 5|, &lt;0 -19/2 0 -2 -16|]
Baldanders results from taking every other generator of the andromeda, with mapping 11/8 to -9 whole tones.


[[Smonzos and Svals|Sval map]]: [&lt;1 5 3 5|, &lt;0 -19 -2 -16|]
Subgroup: 2.9.5.7.11
EDOs: 10, 21, 31, 52, 83, 135, 353, 488, 623
[[Lp tuning#L2 tuning|L2 error]]: 0.1505 cents


==Mechanism==
Comma list: 100/99, 225/224, 245/242
Commas: 896/891, 26411/26244


[[POTE tuning|POTE generator]]: ~9/7 = 438.465
{{Mapping|legend=2| 1 3 3 4 5 | 0 1 -4 -7 -9 }}


Gencom: [2 9/7; 896/891 26411/26244]
Optimal tuning (POTE): ~2 = 1\1, ~9/8 = 204.743
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|]
{{Optimal ET sequence|legend=1| 6, 23de, 29, 35, 41 }}
EDOs: 8, 11, 30, 41, 52
[[Lp tuning#L2 tuning|L2 error]]: 0.9531 cents


=2.9.15.7.11.13=
Related temperament: [[Schismatic family #Garibaldi|Andromeda]]


==Stacks (aka 2magic)==  
===== 2.9.5.7.11.13 =====
Commas: 100/99, 105/104, 144/143, 196/195
Subgroup: 2.9.5.7.11.13


[[Lp tuning|POL2 generator]]: ~9/7 = 438.977
Comma list: 100/99, 144/143, 225/224, 245/242


Gencom: [2 9/7; 100/99 105/104 144/143 196/195]
{{Mapping|legend=2| 1 3 3 4 5 2 | 0 1 -4 -7 -9 10 }}
Gencom mapping: [&lt;1 5/2 5/2 5 2 7|, &lt;0 -5/2 -1/2 -6 4 -9|]


Sval map: [&lt;1 0 2 -1 6 -2|, &lt;0 5 3 6 -4 9|]
Optimal tuning (POTE): ~2 = 1\1, ~9/8 = 204.414
EDOs: 11, 30, 41, 153cdef, 194cdef, 235cdef
[[Lp tuning#L2 tuning|L2 error]]: 3.772 cents


===2.9.15.7.11 stacks===
{{Optimal ET sequence|legend=1| 6, 23def, 29f, 35, 41, 47 }}
Commas: 100/99, 225/224, 245/243


[[Lp tuning|POL2 generator]]: ~9/7 = 438.607
== 2.3.25 subgroup ==


Gencom: [2 9/7; 100/99 225/224 245/243]
=== Shrub ===
Gencom mapping: [&lt;1 5/2 5/2 5 2|, &lt;0 -5/2 -1/2 -6 4|]
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.


Sval map: [&lt;1 0 2 -1 6|, &lt;0 5 3 6 -4|]
Subgroup: 2.3.25
EDOs: 8, 11, 30, 41, 52, 93, 145, 342bce,
[[Lp tuning#L2 tuning|L2 error]]: 2.741 cents


===2.9.15.7 stacks===
Edo join: 17 & 12
Commas: 225/224, 245/243


[[Lp tuning|POL2 generator]]: ~9/7 = 439.296
Comma list: [[2048/2025]]


Gencom: [2 9/7; 225/224 245/243]
{{Mapping|legend=2| 1 1 7| 0 1 -4}}
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|]
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 705.136
EDOs: 8, 11, 30, 41, 71, 93, 112c, 134c, 175c
[[Lp tuning#L2 tuning|L2 error]]: 2.149 cents


=2.9.21=
==== 2.3.23.25.41 subgroup ====
==A-team==  
''See also: [[Reversed meantone]]''
Commas: 1029/1024


[[Lp tuning|POL2 generator]]: ~21/16 = 467.375
Edo join: 17 & 12


Gencom: [2 21/16; 1029/1024]
Comma list: 2048/2025, 576/575, 82/81
Gencom mapping: [&lt;1 1 0 3|, &lt;0 3/2 0 -1/2|]


Sval map: [&lt;1 2 4|, &lt;0 3 1|]
{{Mapping|legend=2| 1 1 1 7 3| 0 1 6 -4 4}}
EDOs: 5, 13, 18, 41, 59, 77, 95
[[Lp tuning#L2 tuning|L2 error]]: 0.6403


=2.3.7/5.11/5.13/5=
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 705.264
==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
===== Sburb =====
This temperament sets the [[octave reduction|octave-reduced]] 413th harmonic (413/256, 827.998{{c}}) to the diminished seventh.


[[Gencom]]: [2 21/20; 364/363 441/440 1001/1000]
Subgroup: 2.3.7.23.25.41.59
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|]
Edo join: 17 & 12
EDOs: 14, 29, 72, 101, 130, 159
 
[[Lp tuning#L2 tuning|L2 error]]: 0.6274 cents
Comma list: 64/63, 225/224, 162/161, 82/81, 177/175
</pre></div>
 
<h4>Original HTML content:</h4>
{{Mapping|legend=2| 1 1 4 1 7 3 10| 0 1 -2 6 -4 4 -7}}
<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:58:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&
 
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 706.387
 
== 2.9.5.11 subgroup ==
=== Glacial ===
{{See also| Chromatic pairs #Glacial }}
 
[[Subgroup]]: 2.9.5.11.13
 
[[Comma list]]: 45/44, 65/64, 81/80
 
{{Mapping|legend=2| 1 0 -4 -6 10 | 0 1 2 3 -2 }}
 
{{Mapping|legend=3| 1 3/2 2 0 3 4 | 0 1/2 2 0 3 -2 }}
 
: [[gencom]]: [2 9/8; 45/44 65/64 81/80]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 186.151
 
{{Optimal ET sequence|legend=1| 6, 13, 45be, 58bce, 71bce, 84bce }}
 
[[Tp tuning #T2 tuning|RMS error]]: 2.887 cents
 
Music:
* ''[[Thundersnow]]'' - [[Sevish]] (2021)
 
== 2.9.7 subgroup ==
=== Mabon ===
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.
 
Subgroup: 2.9.7
 
Comma basis: 44957696/43046721
 
Sval mapping: [{{val|1 1 -3}}, {{val|0 3 8}}]
 
Optimal tuning (CTE): ~729/448 = 870.792
 
{{Optimal ET sequence|legend=1|7d, 11, 18d, 29, 40, 62}}, ...
 
==== 2.9.7.11 subgroup ====
Subgroup: 2.9.7.11
 
Comma basis: 896/891, 1331/1296
 
Sval mapping: [{{val|1 1 -3 2}}, {{val|0 3 8 2}}]
 
Optimal tuning (CTE): ~16/11 = 870.966
 
{{Optimal ET sequence|legend=1| 7d, 11, 40, 51, 62 }}
 
== 2.9.7.11 subgroup ==
=== Apparatus ===
[[Subgroup]]: 2.9.7.11
 
[[Comma list]]: 41503/41472, 322102/321489
 
{{Mapping|legend=2| 1 5 3 5 | 0 -19 -2 -16 }}
 
: mapping generators: ~2, ~77/72
 
{{Mapping|legend=3| 1 5/2 0 3 5 | 0 -19/2 0 -2 -16 }}
 
: [[gencom]]: [2 77/72; 41503/41472 322102/321489]
 
[[Optimal tuning]] ([[CTE]]): ~77/72 = 115.5685
 
{{Optimal ET sequence|legend=1| 10e, 21, 31, 52, 83, 135, 353, 488, 623 }}
 
[[Badness]]: 0.00263
 
=== Joan ===
{{See also| Chromatic pairs #Joan }}
 
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
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