Subgroup temperaments: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
__FORCETOC__
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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|Chromatic pairs]].
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2016-09-23 16:44:41 UTC</tt>.<br>
: The original revision id was <tt>593183188</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=  
=2.3.7=


==[[Semaphore and Godzilla|Semaphore]]==  
==[[Semaphore_and_Godzilla|Semaphore]]==
Comma: 49/48
Comma: 49/48


[[Lp tuning|POL2 generator]]: ~8/7~7/6 = 250.385
[[Lp_tuning|POL2 generator]]: ~8/7~7/6 = 250.385
 
[[Gencom|Gencom]]: [2 8/7; 49/48]


[[Gencom]]: [2 8/7; 49/48]
Gencom mapping: [&lt;1 2 0 3|, &lt;0 -2 0 -1|]
Gencom mapping: [&lt;1 2 0 3|, &lt;0 -2 0 -1|]


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


==Archy==  
[[Tp_tuning#T2 tuning|RMS error]]: 2.523 cents
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.
 
==Archy==
Archy can be thought of as "no-5's [[dominant|dominant]]" or "no-5's [[Superpyth|superpyth]]". The name comes from the fact that it tempers out 64/63, the Archytas comma.


Comma: 64/63
Comma: 64/63


[[Lp tuning|POL2 generator]]: ~3/2 = 709.321
[[Lp_tuning|POL2 generator]]: ~3/2 = 709.321


Gencom: [2 3/2; 64/63]
Gencom: [2 3/2; 64/63]
Gencom mapping: [&lt;1 1 0 4|, &lt;0 1 0 -2|]
Gencom mapping: [&lt;1 1 0 4|, &lt;0 1 0 -2|]


Map: [&lt;1 2 2|, &lt;0 -1 2|]
Map: [&lt;1 2 2|, &lt;0 -1 2|]
EDOs: 5, 12, 17, 22, 27, 137bc
EDOs: 5, 12, 17, 22, 27, 137bc
[[Tp tuning#T2%20tuning|RMS error]]: 1.856 cents


==[[Slendric]]==  
[[Tp_tuning#T2 tuning|RMS error]]: 1.856 cents
 
==[[Slendric|Slendric]]==
Comma: 1029/1024
Comma: 1029/1024


[[Lp tuning|POL2 generator]]: ~8/7 = 233.688
[[Lp_tuning|POL2 generator]]: ~8/7 = 233.688


Gencom: [2 8/7; 1029/1024]
Gencom: [2 8/7; 1029/1024]
Gencom mapping: [&lt;1 1 0 3|, &lt;0 3 0 -1|]
Gencom mapping: [&lt;1 1 0 3|, &lt;0 3 0 -1|]


Map: [&lt;1 1 3|, &lt;0 3 -1|]
Map: [&lt;1 1 3|, &lt;0 3 -1|]
EDOs: 5, 21, 26, 31, 36, 77, 113, 190
EDOs: 5, 21, 26, 31, 36, 77, 113, 190
[[Tp tuning#T2%20tuning|RMS error]]: 0.3202 cents


==Lee==  
[[Tp_tuning#T2 tuning|RMS error]]: 0.3202 cents
 
==Lee==
Comma: 177147/175616
Comma: 177147/175616


[[Lp tuning|POL2 generator]]: ~81/56 = 633.525
[[Lp_tuning|POL2 generator]]: ~81/56 = 633.525


Map: [&lt;1 0 -3|, &lt;0 3 11|]
Map: [&lt;1 0 -3|, &lt;0 3 11|]
EDOs: 17, 36, 89, 125, 161, 358, 519b
EDOs: 17, 36, 89, 125, 161, 358, 519b
[[Tp tuning#T2%20tuning|RMS error]]: 0.3519 cents


==Skwares==  
[[Tp_tuning#T2 tuning|RMS error]]: 0.3519 cents
 
==Skwares==
Comma: 19683/19208
Comma: 19683/19208


[[Lp tuning|POL2 generator]]: ~9/7 = 425.365 cents
[[Lp_tuning|POL2 generator]]: ~9/7 = 425.365 cents


Map: [&lt;1 3 6|, &lt;0 -4 -9|]
Map: [&lt;1 3 6|, &lt;0 -4 -9|]
EDOs: 14, 17, 31, 48, 79, 189b, 268bc, 347bc
EDOs: 14, 17, 31, 48, 79, 189b, 268bc, 347bc
[[Tp tuning#T2%20tuning|RMS error]]: 1.149 cents


=2.3.11=  
[[Tp_tuning#T2 tuning|RMS error]]: 1.149 cents
 
=2.3.11=


==Neuter==  
==Neuter==
Neuter can be thought of as the 2.3.11 version of either [[mohajira]] or [[maqamic]], as well as suhajira (further down on this page) and ringo. Among other things, it is the temperament optimizing the [[neutral tetrad]].
Neuter can be thought of as the 2.3.11 version of either [[Mohajira|mohajira]] or [[maqamic|maqamic]], as well as suhajira (further down on this page) and ringo. Among other things, it is the temperament optimizing the [[neutral_tetrad|neutral tetrad]].


Comma: 243/242
Comma: 243/242


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


Gencom: [2 11/9; 243/242]
Gencom: [2 11/9; 243/242]
Gencom mapping: [&lt;1 1 0 0 2|, &lt;0 2 0 0 5|]
Gencom mapping: [&lt;1 1 0 0 2|, &lt;0 2 0 0 5|]


Map: [&lt;1 1 2|, &lt;0 2 5|]
Map: [&lt;1 1 2|, &lt;0 2 5|]
EDOs: 7, 10, 17, 24, 41, 65, 89, 202, 291, 380
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]]
[[Tp_tuning#T2 tuning|RMS error]]: 0.3021 cents
[[xenharmonic/neutraltet10|Ten note chromatic scale]]
 
[[xenharmonic/neutraltet17|Seventeen note mega chromatic scale]]
[[neutraltet7|Seven note albitonic scale]]


=2.3.5.11=
[[neutraltet10|Ten note chromatic scale]]


==Porkypine==  
[[neutraltet17|Seventeen note mega chromatic scale]]
 
=2.3.5.11=
 
==Porkypine==
Commas: 55/54, 100/99
Commas: 55/54, 100/99


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


Gencom: [2 10/9; 55/54, 100/99]
Gencom: [2 10/9; 55/54, 100/99]
Gencom mapping: [&lt;1 2 3 0 4|, &lt;0 -3 -5 0 -4|]
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|]
Map: [&lt;1 2 3 4|, &lt;0 -3 -5 -4|]
EDOs: 7, 15, 22, 37, 73cd, 95cd, 117bcd
EDOs: 7, 15, 22, 37, 73cd, 95cd, 117bcd
[[Tp tuning#T2%20tuning|RMS error]]: 2.287 cents


==Mohaha==  
[[Tp_tuning#T2 tuning|RMS error]]: 2.287 cents
 
==Mohaha==
Commas: 81/80, 121/120
Commas: 81/80, 121/120


[[Lp tuning|POL2 generator]]: ~11/9 = 348.094
[[Lp_tuning|POL2 generator]]: ~11/9 = 348.094


Gencom: [2 11/9; 81/80 121/120]
Gencom: [2 11/9; 81/80 121/120]
Gencom mapping: [&lt;1 1 0 0 2|, &lt;0 2 8 0 5|]
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|]
Map: [&lt;1 1 0 2|, &lt;0 2 8 5|]
EDOs: 7, 10, 17, 24, 31, 55, 69d, 100d, 131bd
EDOs: 7, 10, 17, 24, 31, 55, 69d, 100d, 131bd
[[Tp tuning#T2%20tuning|RMS error]]: 1.392 cents


===Music===  
[[Tp_tuning#T2 tuning|RMS error]]: 1.392 cents
[[http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3|Mohaha10ping2]] by [[Billy Stiltner]]
 
===Music===
[http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3 Mohaha10ping2] by [[Billy_Stiltner|Billy Stiltner]]


=2.3.7.11=  
=2.3.7.11=


==Ennea==  
==Ennea==
Commas: 41503/41472, 43923/43904
Commas: 41503/41472, 43923/43904


[[Lp tuning|POL2 generator]]: ~99/98 = 17.6258
[[Lp_tuning|POL2 generator]]: ~99/98 = 17.6258


Gencom: [2 99/98; 41503/41472, 43923/43904]
Gencom: [2 99/98; 41503/41472, 43923/43904]
Gencom mapping: [&lt;1 14/9 0 25/9 31/9|, &lt;0 2 0 2 1|]
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|]
Sval map: [&lt;9 0 11 24|, &lt;0 2 2 1|]
EDOs: 54, 63, 68, 72, 135, 342, 477, 525, 613, 681, 749, 817, 2159bcd, 3336bcd, 4153bcd
EDOs: 54, 63, 68, 72, 135, 342, 477, 525, 613, 681, 749, 817, 2159bcd, 3336bcd, 4153bcd
[[Tp tuning#T2%20tuning|RMS error]]: 0.0383 cents


==Supra==  
[[Tp_tuning#T2 tuning|RMS error]]: 0.0383 cents
 
==Supra==
Commas: 64/63, 99/98
Commas: 64/63, 99/98


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


Gencom: [2 3/2; 64/63 99/98]
Gencom: [2 3/2; 64/63 99/98]
Gencom mapping: [&lt;1 1 0 4 7|, &lt;0 1 0 -2 -6|]
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|]
Sval map: [&lt;1 0 6 13|, &lt;0 1 -2 -6|]
EDOs: 5, 12, 17, 39c, 56c
EDOs: 5, 12, 17, 39c, 56c
[[Tp tuning#T2%20tuning|RMS error]]: 1.977 cents


==Skwares==  
[[Tp_tuning#T2 tuning|RMS error]]: 1.977 cents
 
==Skwares==
Commas: 99/98, 243/242
Commas: 99/98, 243/242


[[POTE tuning|POTE generator]]: ~9/7 = 425.244
[[POTE_tuning|POTE generator]]: ~9/7 = 425.244


Gencom: [2 9/7; 99/98 243/242]
Gencom: [2 9/7; 99/98 243/242]
Gencom mapping: [&lt;1 3 0 6 7|, &lt;0 -4 0 -9 -10]]
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|]
Sval map: [&lt;1 3 6 7|, &lt;0 -4 -9 -10|]
EDOs: 14, 17, 31, 48, 79, 127, 206bcd
EDOs: 14, 17, 31, 48, 79, 127, 206bcd
[[Tp tuning#T2%20tuning|RMS error]]: 1.099 cents


==Hemif==  
[[Tp_tuning#T2 tuning|RMS error]]: 1.099 cents
 
==Hemif==
Commas: 243/242, 896/891
Commas: 243/242, 896/891


Line 160: Line 186:


Gencom: [2 11/9; 243/242 896/891]
Gencom: [2 11/9; 243/242 896/891]
Gencom mapping: [&lt;1 1 0 -1 2|, &lt;0 2 0 13 5|]
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|]
Sval map: [&lt;1 1 -1 2|, &lt;0 2 13 5|]
EDOs: 7, 17, 41, 58, 99d
EDOs: 7, 17, 41, 58, 99d
[[Tp tuning#T2%20tuning|RMS error]]: 0.6108 cents


==Bleu==  
[[Tp_tuning#T2 tuning|RMS error]]: 0.6108 cents
 
==Bleu==
Commas: 99/98, 864/847
Commas: 99/98, 864/847


Line 172: Line 201:


Map: [&lt;1 1 2 3|, &lt;0 5 7 4|]
Map: [&lt;1 1 2 3|, &lt;0 5 7 4|]
EDOs: 9, 17, 43, 60c
EDOs: 9, 17, 43, 60c
RMS error: 1.829 cents
RMS error: 1.829 cents


=2.3.7.11.13=  
=2.3.7.11.13=


==Suhajira==  
==Suhajira==
Commas: 64/63, 78/77, 144/143
Commas: 64/63, 78/77, 144/143


Gencom: [2 11/9; 64/63 78/77 144/143]
Gencom: [2 11/9; 64/63 78/77 144/143]
Gencom map: [&lt;1 1 0 4 2 4|, &lt;0 2 0 -4 5 -1|]
Gencom map: [&lt;1 1 0 4 2 4|, &lt;0 2 0 -4 5 -1|]


[[Tp tuning|POT2 generator]]: ~11/9 = 353.775
[[Tp_tuning|POT2 generator]]: ~11/9 = 353.775


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


==Hemif==  
[[Tp_tuning#T2 tuning|RMS error]]: 1.953 cents
 
==Hemif==
Commas: 144/143, 243/242, 364/363
Commas: 144/143, 243/242, 364/363
Related temperament: [[xenharmonic/Breedsmic temperaments|Hemififths]], namo


[[Tp tuning|POT2 generator]]: ~11/9 = 351.691
Related temperament: [[Breedsmic_temperaments|Hemififths]], namo
 
[[Tp_tuning|POT2 generator]]: ~11/9 = 351.691
 
[[Gencom|Gencom]]: [2 11/9; 144/143 243/242 364/363]


[[Gencom]]: [2 11/9; 144/143 243/242 364/363]
Gencom map: [&lt;1 1 0 -1 2 4|, &lt;0 2 0 13 5 -1|]
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|]
Map: [&lt;1 1 -1 2 4|, &lt;0 2 13 5 -1|]
EDOs: 7, 10, 17, 24, 41, 58
EDOs: 7, 10, 17, 24, 41, 58
[[Tp tuning#T2%20tuning|RMS error]]: 0.7167 cents


==Skwares==  
[[Tp_tuning#T2 tuning|RMS error]]: 0.7167 cents
 
==Skwares==
Commas: 78/77, 99/98, 243/242
Commas: 78/77, 99/98, 243/242


[[Tp tuning|POT2 generator]]: ~9/7 = 424.457
[[Tp_tuning|POT2 generator]]: ~9/7 = 424.457


Map: [&lt;1 3 6 7 9|, &lt;0 -4 -9 -10 -15|]
Map: [&lt;1 3 6 7 9|, &lt;0 -4 -9 -10 -15|]
EDOs: 17, 48e, 65de, 82c, 147ce
EDOs: 17, 48e, 65de, 82c, 147ce
[[Tp tuning#T2%20tuning|RMS error]]: 1.769 cents


==Leapfrog==  
[[Tp_tuning#T2 tuning|RMS error]]: 1.769 cents
 
==Leapfrog==
Commas: 169/168, 352/351, 364/363
Commas: 169/168, 352/351, 364/363


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


Gencom: [2 3/2; 169/169 352/351 364/363]
Gencom: [2 3/2; 169/169 352/351 364/363]
Gencom mapping: [&lt;1 1 0 -6 -3 -1|, &lt;0 1 0 15 11 8|]
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|]
Sval map: [&lt;1 0 -21 -14 -9|, &lt;0 1 15 11 8|]
EDOs: 17, 46, 63
EDOs: 17, 46, 63
[[Tp tuning#T2%20tuning|RMS error]]: 0.7541 cents


==Bleu==  
[[Tp_tuning#T2 tuning|RMS error]]: 0.7541 cents
 
==Bleu==
Group: 2.3.7.11.13
Group: 2.3.7.11.13
Commas: 78/77, 99/98, 144/143
Commas: 78/77, 99/98, 144/143
Sval name: 9&amp;17
Sval name: 9&amp;17


[[Tp tuning|POL2 generator]]: ~13/12 = 139.990
[[Tp_tuning|POL2 generator]]: ~13/12 = 139.990
 
[[Gencom|Gencom]]: [2 13/12; 78/77 99/98 144/143]


[[Gencom]]: [2 13/12; 78/77 99/98 144/143]
Gencom map: [&lt;1 1 0 2 3 3|, &lt;0 5 0 7 4 6|]
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|]
Map: [&lt;1 1 2 3 3|, &lt;0 5 7 4 6|]
EDOs: [[xenharmonic/17edo|17]], [[xenharmonic/43edo|43]], [[xenharmonic/60edo|60c]]
[[Tp tuning#T2%20tuning|RMS error]]: 1.752 cents


==Parapyth (Rank 3)==  
EDOs: [[17edo|17]], [[43edo|43]], [[60edo|60c]]
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.752 cents
 
==Parapyth (Rank 3)==
Commas: 352/351, 364/363
Commas: 352/351, 364/363


[[Lp tuning|POL2 tuning]]: &lt;1200.000 1903.856 (2787.774) 3369.907 4154.482 4442.913|
[[Lp_tuning|POL2 tuning]]: &lt;1200.000 1903.856 (2787.774) 3369.907 4154.482 4442.913|
 
The gencom below gives [[Margo_Schulter|Margo Schulter]]'s favored basis


The gencom below gives [[Margo Schulter]]'s favored basis
Gencom: [2 3/2 28/27; 352/351 364/363]
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|]
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|]
Sval map: [&lt;1 0 0 7 12|, &lt;0 1 0 -4 -7|, &lt;0 0 1 1 1|]
EDOs: 17, 41, 46, 58, 87, 104
EDOs: 17, 41, 46, 58, 87, 104
[[Tp tuning#T2%20tuning|RMS error]]: 0.3789 cents


=2.3.5.11=
[[Tp_tuning#T2 tuning|RMS error]]: 0.3789 cents


==Larry==  
=2.3.5.11=
 
==Larry==
Commas: 243/242, 4000/3993
Commas: 243/242, 4000/3993
Related temperaments: [[Gravity family#Gravity|gravity]], [[Gravity family#Harry|harry]]
 
Related temperaments: [[Gravity_family#Gravity|gravity]], [[Gravity_family#Harry|harry]]


POTE generator: ~40/27 = 683.166
POTE generator: ~40/27 = 683.166


Gencom: [2 40/27; 243/242 4000/3993]
Gencom: [2 40/27; 243/242 4000/3993]
Gencom mapping: [&lt;1 5 12 0 12|, &lt;0 -6 -17 0 -15|]
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|]
Map: [&lt;1 5 12 12|, &lt;0 -6 -17 -15|]
EDOs: 7, 58, 65, 137, 202
EDOs: 7, 58, 65, 137, 202
[[Tp tuning#T2%20tuning|RMS error]]: 0.3025 cents


=2.9.7.11=
[[Tp_tuning#T2 tuning|RMS error]]: 0.3025 cents


==Machine==  
=2.9.7.11=
 
==Machine==
Commas: 64/63, 99/98
Commas: 64/63, 99/98


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


Gencom: [2 8/7; 64/63 99/98]
Gencom: [2 8/7; 64/63 99/98]
Gencom mapping: [&lt;1 3/2 0 3 4|, &lt;0 1/2 0 -1 -3|]
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|]
[[Smonzos_and_Svals|Sval map]]: [&lt;1 0 6 13|, &lt;0 1 -1 -3|]
 
EDOs: 5, 6, 11, 17, 28
EDOs: 5, 6, 11, 17, 28
[[Tp tuning#T2%20tuning|RMS error]]: 1.977 cents


==Apparatus==  
[[Tp_tuning#T2 tuning|RMS error]]: 1.977 cents
 
==Apparatus==
Commas: 41503/41472, 322102/321489
Commas: 41503/41472, 322102/321489


[[POTE tuning|POTE generator]]: ~77/72 = 115.570
[[POTE_tuning|POTE generator]]: ~77/72 = 115.570


Gencom: [2 77/72; 41503/41472 322102/321489]
Gencom: [2 77/72; 41503/41472 322102/321489]
Gencom mapping: [&lt;1 5/2 0 3 5|, &lt;0 -19/2 0 -2 -16|]
Gencom mapping: [&lt;1 5/2 0 3 5|, &lt;0 -19/2 0 -2 -16|]


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


==Mechanism==  
[[Tp_tuning#T2 tuning|RMS error]]: 0.0673 cents
 
==Mechanism==
Commas: 896/891, 26411/26244
Commas: 896/891, 26411/26244


[[POTE tuning|POTE generator]]: ~9/7 = 438.465
[[POTE_tuning|POTE generator]]: ~9/7 = 438.465


Gencom: [2 9/7; 896/891 26411/26244]
Gencom: [2 9/7; 896/891 26411/26244]
Gencom mapping: [&lt;1 5/2 0 5 2|, &lt;0 -5/2 0 -6 4|]
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|]
[[Smonzos_and_Svals|Sval map]]: [&lt;1 5 5 2|, &lt;0 -5 -6 4|]
 
EDOs: 8, 11, 30, 41, 52
EDOs: 8, 11, 30, 41, 52
[[Tp tuning#T2%20tuning|RMS error]]: 0.4262 cents


=2.9.15.7.11.13=
[[Tp_tuning#T2 tuning|RMS error]]: 0.4262 cents


==Stacks (aka 2magic)==  
=2.9.15.7.11.13=
 
==Stacks (aka 2magic)==
Commas: 100/99, 105/104, 144/143, 196/195
Commas: 100/99, 105/104, 144/143, 196/195


[[Lp tuning|POL2 generator]]: ~9/7 = 438.977
[[Lp_tuning|POL2 generator]]: ~9/7 = 438.977


Gencom: [2 9/7; 100/99 105/104 144/143 196/195]
Gencom: [2 9/7; 100/99 105/104 144/143 196/195]
Gencom mapping: [&lt;1 5/2 5/2 5 2 7|, &lt;0 -5/2 -1/2 -6 4 -9|]
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|]
Sval map: [&lt;1 0 2 -1 6 -2|, &lt;0 5 3 6 -4 9|]
EDOs: 11, 30, 41, 153cdef, 194cdef, 235cdef
EDOs: 11, 30, 41, 153cdef, 194cdef, 235cdef
[[Tp tuning#T2%20tuning|RMS error]]: 1.540 cents


===2.9.15.7.11 stacks===  
[[Tp_tuning#T2 tuning|RMS error]]: 1.540 cents
 
===2.9.15.7.11 stacks===
Commas: 100/99, 225/224, 245/243
Commas: 100/99, 225/224, 245/243


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


Gencom: [2 9/7; 100/99 225/224 245/243]
Gencom: [2 9/7; 100/99 225/224 245/243]
Gencom mapping: [&lt;1 5/2 5/2 5 2|, &lt;0 -5/2 -1/2 -6 4|]
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|]
Sval map: [&lt;1 0 2 -1 6|, &lt;0 5 3 6 -4|]
EDOs: 8, 11, 30, 41, 52, 93, 145, 342bce,
EDOs: 8, 11, 30, 41, 52, 93, 145, 342bce,
[[Tp tuning#T2%20tuning|RMS error]]: 1.226 cents


===2.9.15.7 stacks===  
[[Tp_tuning#T2 tuning|RMS error]]: 1.226 cents
 
===2.9.15.7 stacks===
Commas: 225/224, 245/243
Commas: 225/224, 245/243


[[Lp tuning|POL2 generator]]: ~9/7 = 439.296
[[Lp_tuning|POL2 generator]]: ~9/7 = 439.296


Gencom: [2 9/7; 225/224 245/243]
Gencom: [2 9/7; 225/224 245/243]
Gencom mapping: [&lt;1 5/2 5/2 5|, &lt;0 -5/2 -1/2 -6|]
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 map: [&lt;1 0 2 -1|, &lt;0 5 3 6|]
EDOs: 8, 11, 30, 41, 71, 93, 112c, 134c, 175c
EDOs: 8, 11, 30, 41, 71, 93, 112c, 134c, 175c
[[Tp tuning#T2%20tuning|RMS error]]: 1.074 cents


=2.9.21=  
[[Tp_tuning#T2 tuning|RMS error]]: 1.074 cents
==A-team==  
 
=2.9.21=
 
==A-team==
Commas: 1029/1024
Commas: 1029/1024


[[Lp tuning|POL2 generator]]: ~21/16 = 467.375
[[Lp_tuning|POL2 generator]]: ~21/16 = 467.375


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


Sval map: [&lt;1 2 4|, &lt;0 3 1|]
Sval map: [&lt;1 2 4|, &lt;0 3 1|]
EDOs: 5, 13, 18, 41, 59, 77, 95
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=  
[[Tp_tuning#T2 tuning|RMS error]]: 0.3202 cents
==Historical==  
 
=2.3.7/5.11/5.13/5=
 
==Historical==
Subgroup: 2.3.7/5.11/5.13/5
Subgroup: 2.3.7/5.11/5.13/5
Commas: 364/363, 441/440, 1001/1000
Commas: 364/363, 441/440, 1001/1000


[[Lp tuning|POL2 generator]]: ~21/20 = 83.016
[[Lp_tuning|POL2 generator]]: ~21/20 = 83.016
 
[[Gencom|Gencom]]: [2 21/20; 364/363 441/440 1001/1000]


[[Gencom]]: [2 21/20; 364/363 441/440 1001/1000]
Gencom map: [&lt;1 2 -3/4 -3/4 1/4 5/4|, &lt;0 -6 0 7 2 -9|]
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|]
Sval map: [&lt;1 2 0 1 2|, &lt;0 -6 7 2 -9|]
EDOs: 14, 29, 72, 101, 130, 159
EDOs: 14, 29, 72, 101, 130, 159
[[Tp tuning#T2%20tuning|RMS error]]: 0.2562 cents


=2.3.7.11/5.13=  
[[Tp_tuning#T2 tuning|RMS error]]: 0.2562 cents
==Hypnosis==  
 
=2.3.7.11/5.13=
 
==Hypnosis==
Subgroup: 2.3.7.11/5.13
Subgroup: 2.3.7.11/5.13
Commas: 169/168, 540/539, 729/728
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]
Related temperament: [[Swetismic_temperaments#Hypnos-13-limit|hypnos]], [[Hemifamity_temperaments#Tricot-13-limit|tricot]]
 
[[Gencom|Gencom]]: [2 13/9; 169/168, 540/539, 729/728]
 
Gencom map: [&lt;1 0 -4 -3 4 0|, &lt;0 3 13/2 11 -13/2 7|]
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|]
Sval map: [&lt;1 0 -3 8 0|, &lt;0 3 11 -13 7|]
EDOs: 17, 36, 118e, 125e, 161e, 197e
EDOs: 17, 36, 118e, 125e, 161e, 197e
[[Tp tuning#T2%20tuning|RMS error]]: 0.5379 cents
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.5379 cents


=2.5.7=
=2.5.7=
Line 385: Line 474:
==Didacus==
==Didacus==
Subgroup: 2.5.7
Subgroup: 2.5.7
Commas: 3136/3125
Commas: 3136/3125
Related temperaments: [[Chromatic+pairs#Roulette]]
Related temperaments: [[Chromatic+pairs#Roulette]]


[[Gencom]]: [2 28/25 3136/3125]
[[Gencom|Gencom]]: [2 28/25 3136/3125]
 
Gencom map: [&lt;1 0 2 2|, &lt;0 0 2 5|]
Gencom map: [&lt;1 0 2 2|, &lt;0 0 2 5|]


Sval map: [&lt;1 2 2|, &lt;0 2 5|]
Sval map: [&lt;1 2 2|, &lt;0 2 5|]
EDOs: 6, 19, 25, 31, 37, 99, 130, 161, 353
EDOs: 6, 19, 25, 31, 37, 99, 130, 161, 353
[[Tp tuning#T2%20tuning|RMS error]]: 0.2138 cents</pre></div>
 
<h4>Original HTML content:</h4>
[[Tp_tuning#T2 tuning|RMS error]]: 0.2138 cents
<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:86:&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:86 --&gt;&lt;!-- ws:start:WikiTextTocRule:87: --&gt;&lt;a href="#x2.3.7"&gt;2.3.7&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:87 --&gt;&lt;!-- ws:start:WikiTextTocRule:88: --&gt;&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt;&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&gt;&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt;&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;!-- ws:start:WikiTextTocRule:92: --&gt;&lt;!-- ws:end:WikiTextTocRule:92 --&gt;&lt;!-- ws:start:WikiTextTocRule:93: --&gt; | &lt;a href="#x2.3.11"&gt;2.3.11&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:93 --&gt;&lt;!-- ws:start:WikiTextTocRule:94: --&gt;&lt;!-- ws:end:WikiTextTocRule:94 --&gt;&lt;!-- ws:start:WikiTextTocRule:95: --&gt; | &lt;a href="#x2.3.5.11"&gt;2.3.5.11&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:95 --&gt;&lt;!-- ws:start:WikiTextTocRule:96: --&gt;&lt;!-- ws:end:WikiTextTocRule:96 --&gt;&lt;!-- ws:start:WikiTextTocRule:97: --&gt;&lt;!-- ws:end:WikiTextTocRule:97 --&gt;&lt;!-- ws:start:WikiTextTocRule:98: --&gt;&lt;!-- ws:end:WikiTextTocRule:98 --&gt;&lt;!-- ws:start:WikiTextTocRule:99: --&gt; | &lt;a href="#x2.3.7.11"&gt;2.3.7.11&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:99 --&gt;&lt;!-- ws:start:WikiTextTocRule:100: --&gt;&lt;!-- ws:end:WikiTextTocRule:100 --&gt;&lt;!-- ws:start:WikiTextTocRule:101: --&gt;&lt;!-- ws:end:WikiTextTocRule:101 --&gt;&lt;!-- ws:start:WikiTextTocRule:102: --&gt;&lt;!-- ws:end:WikiTextTocRule:102 --&gt;&lt;!-- ws:start:WikiTextTocRule:103: --&gt;&lt;!-- ws:end:WikiTextTocRule:103 --&gt;&lt;!-- ws:start:WikiTextTocRule:104: --&gt;&lt;!-- ws:end:WikiTextTocRule:104 --&gt;&lt;!-- ws:start:WikiTextTocRule:105: --&gt; | &lt;a href="#x2.3.7.11.13"&gt;2.3.7.11.13&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:105 --&gt;&lt;!-- ws:start:WikiTextTocRule:106: --&gt;&lt;!-- ws:end:WikiTextTocRule:106 --&gt;&lt;!-- ws:start:WikiTextTocRule:107: --&gt;&lt;!-- ws:end:WikiTextTocRule:107 --&gt;&lt;!-- ws:start:WikiTextTocRule:108: --&gt;&lt;!-- ws:end:WikiTextTocRule:108 --&gt;&lt;!-- ws:start:WikiTextTocRule:109: --&gt;&lt;!-- ws:end:WikiTextTocRule:109 --&gt;&lt;!-- ws:start:WikiTextTocRule:110: --&gt;&lt;!-- ws:end:WikiTextTocRule:110 --&gt;&lt;!-- ws:start:WikiTextTocRule:111: --&gt;&lt;!-- ws:end:WikiTextTocRule:111 --&gt;&lt;!-- ws:start:WikiTextTocRule:112: --&gt; | &lt;a href="#x2.3.5.11"&gt;2.3.5.11&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:112 --&gt;&lt;!-- ws:start:WikiTextTocRule:113: --&gt;&lt;!-- ws:end:WikiTextTocRule:113 --&gt;&lt;!-- ws:start:WikiTextTocRule:114: --&gt; | &lt;a href="#x2.9.7.11"&gt;2.9.7.11&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:114 --&gt;&lt;!-- ws:start:WikiTextTocRule:115: --&gt;&lt;!-- ws:end:WikiTextTocRule:115 --&gt;&lt;!-- ws:start:WikiTextTocRule:116: --&gt;&lt;!-- ws:end:WikiTextTocRule:116 --&gt;&lt;!-- ws:start:WikiTextTocRule:117: --&gt;&lt;!-- ws:end:WikiTextTocRule:117 --&gt;&lt;!-- ws:start:WikiTextTocRule:118: --&gt; | &lt;a href="#x2.9.15.7.11.13"&gt;2.9.15.7.11.13&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:118 --&gt;&lt;!-- ws:start:WikiTextTocRule:119: --&gt;&lt;!-- ws:end:WikiTextTocRule:119 --&gt;&lt;!-- ws:start:WikiTextTocRule:120: --&gt;&lt;!-- ws:end:WikiTextTocRule:120 --&gt;&lt;!-- ws:start:WikiTextTocRule:121: --&gt;&lt;!-- ws:end:WikiTextTocRule:121 --&gt;&lt;!-- ws:start:WikiTextTocRule:122: --&gt; | &lt;a href="#x2.9.21"&gt;2.9.21&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:122 --&gt;&lt;!-- ws:start:WikiTextTocRule:123: --&gt;&lt;!-- ws:end:WikiTextTocRule:123 --&gt;&lt;!-- ws:start:WikiTextTocRule:124: --&gt; | &lt;a href="#x2.3.7/5.11/5.13/5"&gt;2.3.7/5.11/5.13/5&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:124 --&gt;&lt;!-- ws:start:WikiTextTocRule:125: --&gt;&lt;!-- ws:end:WikiTextTocRule:125 --&gt;&lt;!-- ws:start:WikiTextTocRule:126: --&gt; | &lt;a href="#x2.3.7.11/5.13"&gt;2.3.7.11/5.13&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:126 --&gt;&lt;!-- ws:start:WikiTextTocRule:127: --&gt;&lt;!-- ws:end:WikiTextTocRule:127 --&gt;&lt;!-- ws:start:WikiTextTocRule:128: --&gt; | &lt;a href="#x2.5.7"&gt;2.5.7&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:128 --&gt;&lt;!-- ws:start:WikiTextTocRule:129: --&gt;&lt;!-- ws:end:WikiTextTocRule:129 --&gt;&lt;!-- ws:start:WikiTextTocRule:130: --&gt;
[[Category:subgroup]]
&lt;!-- ws:end:WikiTextTocRule:130 --&gt;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 &lt;a class="wiki_link" href="/Chromatic%20pairs"&gt;Chromatic pairs&lt;/a&gt;.&lt;br /&gt;
[[Category:temperament]]
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x2.3.7"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;2.3.7&lt;/h1&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x2.3.7-Semaphore"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;&lt;a class="wiki_link" href="/Semaphore%20and%20Godzilla"&gt;Semaphore&lt;/a&gt;&lt;/h2&gt;
Comma: 49/48&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~8/7~7/6 = 250.385&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Gencom"&gt;Gencom&lt;/a&gt;: [2 8/7; 49/48]&lt;br /&gt;
Gencom mapping: [&amp;lt;1 2 0 3|, &amp;lt;0 -2 0 -1|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3|, &amp;lt;0 -2 -1|]&lt;br /&gt;
EDOs: 5, 14, 19, 24, 67c, 91c&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 2.523 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x2.3.7-Archy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Archy&lt;/h2&gt;
Archy can be thought of as &amp;quot;no-5's &lt;a class="wiki_link" href="/dominant"&gt;dominant&lt;/a&gt;&amp;quot; or &amp;quot;no-5's &lt;a class="wiki_link" href="/superpyth"&gt;superpyth&lt;/a&gt;&amp;quot;. The name comes from the fact that it tempers out 64/63, the Archytas comma.&lt;br /&gt;
&lt;br /&gt;
Comma: 64/63&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~3/2 = 709.321&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 3/2; 64/63]&lt;br /&gt;
Gencom mapping: [&amp;lt;1 1 0 4|, &amp;lt;0 1 0 -2|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2|, &amp;lt;0 -1 2|]&lt;br /&gt;
EDOs: 5, 12, 17, 22, 27, 137bc&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.856 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x2.3.7-Slendric"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&lt;a class="wiki_link" href="/Slendric"&gt;Slendric&lt;/a&gt;&lt;/h2&gt;
Comma: 1029/1024&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~8/7 = 233.688&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 8/7; 1029/1024]&lt;br /&gt;
Gencom mapping: [&amp;lt;1 1 0 3|, &amp;lt;0 3 0 -1|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 3|, &amp;lt;0 3 -1|]&lt;br /&gt;
EDOs: 5, 21, 26, 31, 36, 77, 113, 190&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.3202 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x2.3.7-Lee"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Lee&lt;/h2&gt;
Comma: 177147/175616&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~81/56 = 633.525&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 -3|, &amp;lt;0 3 11|]&lt;br /&gt;
EDOs: 17, 36, 89, 125, 161, 358, 519b&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.3519 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x2.3.7-Skwares"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Skwares&lt;/h2&gt;
Comma: 19683/19208&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~9/7 = 425.365 cents&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 3 6|, &amp;lt;0 -4 -9|]&lt;br /&gt;
EDOs: 14, 17, 31, 48, 79, 189b, 268bc, 347bc&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.149 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="x2.3.11"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;2.3.11&lt;/h1&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="x2.3.11-Neuter"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Neuter&lt;/h2&gt;
Neuter can be thought of as the 2.3.11 version of either &lt;a class="wiki_link" href="/mohajira"&gt;mohajira&lt;/a&gt; or &lt;a class="wiki_link" href="/maqamic"&gt;maqamic&lt;/a&gt;, as well as suhajira (further down on this page) and ringo. Among other things, it is the temperament optimizing the &lt;a class="wiki_link" href="/neutral%20tetrad"&gt;neutral tetrad&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
Comma: 243/242&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~11/9 = 350.525&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 11/9; 243/242]&lt;br /&gt;
Gencom mapping: [&amp;lt;1 1 0 0 2|, &amp;lt;0 2 0 0 5|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 2|, &amp;lt;0 2 5|]&lt;br /&gt;
EDOs: 7, 10, 17, 24, 41, 65, 89, 202, 291, 380&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.3021 cents&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet7"&gt;Seven note albitonic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet10"&gt;Ten note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet17"&gt;Seventeen note mega chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="x2.3.5.11"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;2.3.5.11&lt;/h1&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="x2.3.5.11-Porkypine"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Porkypine&lt;/h2&gt;
Commas: 55/54, 100/99&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~10/9 = 164.078&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 10/9; 55/54, 100/99]&lt;br /&gt;
Gencom mapping: [&amp;lt;1 2 3 0 4|, &amp;lt;0 -3 -5 0 -4|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 4|, &amp;lt;0 -3 -5 -4|]&lt;br /&gt;
EDOs: 7, 15, 22, 37, 73cd, 95cd, 117bcd&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 2.287 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="x2.3.5.11-Mohaha"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Mohaha&lt;/h2&gt;
Commas: 81/80, 121/120&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~11/9 = 348.094&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 11/9; 81/80 121/120]&lt;br /&gt;
Gencom mapping: [&amp;lt;1 1 0 0 2|, &amp;lt;0 2 8 0 5|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 2|, &amp;lt;0 2 8 5|]&lt;br /&gt;
EDOs: 7, 10, 17, 24, 31, 55, 69d, 100d, 131bd&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.392 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc11"&gt;&lt;a name="x2.3.5.11-Mohaha-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Music&lt;/h3&gt;
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3" rel="nofollow"&gt;Mohaha10ping2&lt;/a&gt; by &lt;a class="wiki_link" href="/Billy%20Stiltner"&gt;Billy Stiltner&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="x2.3.7.11"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;2.3.7.11&lt;/h1&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="x2.3.7.11-Ennea"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Ennea&lt;/h2&gt;
Commas: 41503/41472, 43923/43904&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~99/98 = 17.6258&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 99/98; 41503/41472, 43923/43904]&lt;br /&gt;
Gencom mapping: [&amp;lt;1 14/9 0 25/9 31/9|, &amp;lt;0 2 0 2 1|]&lt;br /&gt;
&lt;br /&gt;
Sval map: [&amp;lt;9 0 11 24|, &amp;lt;0 2 2 1|]&lt;br /&gt;
EDOs: 54, 63, 68, 72, 135, 342, 477, 525, 613, 681, 749, 817, 2159bcd, 3336bcd, 4153bcd&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.0383 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="x2.3.7.11-Supra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Supra&lt;/h2&gt;
Commas: 64/63, 99/98&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~3/2 = 707.192&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 3/2; 64/63 99/98]&lt;br /&gt;
Gencom mapping: [&amp;lt;1 1 0 4 7|, &amp;lt;0 1 0 -2 -6|]&lt;br /&gt;
&lt;br /&gt;
Sval map: [&amp;lt;1 0 6 13|, &amp;lt;0 1 -2 -6|]&lt;br /&gt;
EDOs: 5, 12, 17, 39c, 56c&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.977 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="x2.3.7.11-Skwares"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Skwares&lt;/h2&gt;
Commas: 99/98, 243/242&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~9/7 = 425.244&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 9/7; 99/98 243/242]&lt;br /&gt;
Gencom mapping: [&amp;lt;1 3 0 6 7|, &amp;lt;0 -4 0 -9 -10]]&lt;br /&gt;
&lt;br /&gt;
Sval map: [&amp;lt;1 3 6 7|, &amp;lt;0 -4 -9 -10|]&lt;br /&gt;
EDOs: 14, 17, 31, 48, 79, 127, 206bcd&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.099 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="x2.3.7.11-Hemif"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Hemif&lt;/h2&gt;
Commas: 243/242, 896/891&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~11/9 = 351.535&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 11/9; 243/242 896/891]&lt;br /&gt;
Gencom mapping: [&amp;lt;1 1 0 -1 2|, &amp;lt;0 2 0 13 5|]&lt;br /&gt;
&lt;br /&gt;
Sval map: [&amp;lt;1 1 -1 2|, &amp;lt;0 2 13 5|]&lt;br /&gt;
EDOs: 7, 17, 41, 58, 99d&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.6108 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="x2.3.7.11-Bleu"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Bleu&lt;/h2&gt;
Commas: 99/98, 864/847&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~12/11 = 140.005&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 2 3|, &amp;lt;0 5 7 4|]&lt;br /&gt;
EDOs: 9, 17, 43, 60c&lt;br /&gt;
RMS error: 1.829 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="x2.3.7.11.13"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;2.3.7.11.13&lt;/h1&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="x2.3.7.11.13-Suhajira"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Suhajira&lt;/h2&gt;
Commas: 64/63, 78/77, 144/143&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 11/9; 64/63 78/77 144/143]&lt;br /&gt;
Gencom map: [&amp;lt;1 1 0 4 2 4|, &amp;lt;0 2 0 -4 5 -1|]&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning"&gt;POT2 generator&lt;/a&gt;: ~11/9 = 353.775&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 4 2 4|, &amp;lt;0 2 -4 5 -1|]&lt;br /&gt;
EDOs: 7, 10, 17, 44d, 61cd, 78cd&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.953 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="x2.3.7.11.13-Hemif"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Hemif&lt;/h2&gt;
Commas: 144/143, 243/242, 364/363&lt;br /&gt;
Related temperament: &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Breedsmic%20temperaments"&gt;Hemififths&lt;/a&gt;, namo&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning"&gt;POT2 generator&lt;/a&gt;: ~11/9 = 351.691&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Gencom"&gt;Gencom&lt;/a&gt;: [2 11/9; 144/143 243/242 364/363]&lt;br /&gt;
Gencom map: [&amp;lt;1 1 0 -1 2 4|, &amp;lt;0 2 0 13 5 -1|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 -1 2 4|, &amp;lt;0 2 13 5 -1|]&lt;br /&gt;
EDOs: 7, 10, 17, 24, 41, 58&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.7167 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="x2.3.7.11.13-Skwares"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Skwares&lt;/h2&gt;
Commas: 78/77, 99/98, 243/242&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning"&gt;POT2 generator&lt;/a&gt;: ~9/7 = 424.457&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 3 6 7 9|, &amp;lt;0 -4 -9 -10 -15|]&lt;br /&gt;
EDOs: 17, 48e, 65de, 82c, 147ce&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.769 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="x2.3.7.11.13-Leapfrog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Leapfrog&lt;/h2&gt;
Commas: 169/168, 352/351, 364/363&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~3/2 = 704.745 cents&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 3/2; 169/169 352/351 364/363]&lt;br /&gt;
Gencom mapping: [&amp;lt;1 1 0 -6 -3 -1|, &amp;lt;0 1 0 15 11 8|]&lt;br /&gt;
&lt;br /&gt;
Sval map: [&amp;lt;1 0 -21 -14 -9|, &amp;lt;0 1 15 11 8|]&lt;br /&gt;
EDOs: 17, 46, 63&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.7541 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="x2.3.7.11.13-Bleu"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;Bleu&lt;/h2&gt;
Group: 2.3.7.11.13&lt;br /&gt;
Commas: 78/77, 99/98, 144/143&lt;br /&gt;
Sval name: 9&amp;amp;17&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~13/12 = 139.990&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Gencom"&gt;Gencom&lt;/a&gt;: [2 13/12; 78/77 99/98 144/143]&lt;br /&gt;
Gencom map: [&amp;lt;1 1 0 2 3 3|, &amp;lt;0 5 0 7 4 6|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 2 3 3|, &amp;lt;0 5 7 4 6|]&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/17edo"&gt;17&lt;/a&gt;, &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/43edo"&gt;43&lt;/a&gt;, &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/60edo"&gt;60c&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.752 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="x2.3.7.11.13-Parapyth (Rank 3)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Parapyth (Rank 3)&lt;/h2&gt;
Commas: 352/351, 364/363&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 tuning&lt;/a&gt;: &amp;lt;1200.000 1903.856 (2787.774) 3369.907 4154.482 4442.913|&lt;br /&gt;
&lt;br /&gt;
The gencom below gives &lt;a class="wiki_link" href="/Margo%20Schulter"&gt;Margo Schulter&lt;/a&gt;'s favored basis&lt;br /&gt;
Gencom: [2 3/2 28/27; 352/351 364/363]&lt;br /&gt;
Gencom mapping: [&amp;lt;1 1 0 1 4 6|, &amp;lt;0 1 0 3 -1 -4|, &amp;lt;0 0 0 1 1 1|]&lt;br /&gt;
&lt;br /&gt;
Sval map: [&amp;lt;1 0 0 7 12|, &amp;lt;0 1 0 -4 -7|, &amp;lt;0 0 1 1 1|]&lt;br /&gt;
EDOs: 17, 41, 46, 58, 87, 104&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.3789 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc25"&gt;&lt;a name="x2.3.5.11"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;2.3.5.11&lt;/h1&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="x2.3.5.11-Larry"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;Larry&lt;/h2&gt;
Commas: 243/242, 4000/3993&lt;br /&gt;
Related temperaments: &lt;a class="wiki_link" href="/Gravity%20family#Gravity"&gt;gravity&lt;/a&gt;, &lt;a class="wiki_link" href="/Gravity%20family#Harry"&gt;harry&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~40/27 = 683.166&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 40/27; 243/242 4000/3993]&lt;br /&gt;
Gencom mapping: [&amp;lt;1 5 12 0 12|, &amp;lt;0 -6 -17 0 -15|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 12 12|, &amp;lt;0 -6 -17 -15|]&lt;br /&gt;
EDOs: 7, 58, 65, 137, 202&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.3025 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc27"&gt;&lt;a name="x2.9.7.11"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;2.9.7.11&lt;/h1&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="x2.9.7.11-Machine"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;Machine&lt;/h2&gt;
Commas: 64/63, 99/98&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~8/7 = 214.384&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 8/7; 64/63 99/98]&lt;br /&gt;
Gencom mapping: [&amp;lt;1 3/2 0 3 4|, &amp;lt;0 1/2 0 -1 -3|]&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Smonzos%20and%20Svals"&gt;Sval map&lt;/a&gt;: [&amp;lt;1 0 6 13|, &amp;lt;0 1 -1 -3|]&lt;br /&gt;
EDOs: 5, 6, 11, 17, 28&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.977 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc29"&gt;&lt;a name="x2.9.7.11-Apparatus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;Apparatus&lt;/h2&gt;
Commas: 41503/41472, 322102/321489&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~77/72 = 115.570&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 77/72; 41503/41472 322102/321489]&lt;br /&gt;
Gencom mapping: [&amp;lt;1 5/2 0 3 5|, &amp;lt;0 -19/2 0 -2 -16|]&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Smonzos%20and%20Svals"&gt;Sval map&lt;/a&gt;: [&amp;lt;1 5 3 5|, &amp;lt;0 -19 -2 -16|]&lt;br /&gt;
EDOs: 10, 21, 31, 52, 83, 135, 353, 488, 623&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.0673 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc30"&gt;&lt;a name="x2.9.7.11-Mechanism"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;Mechanism&lt;/h2&gt;
Commas: 896/891, 26411/26244&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~9/7 = 438.465&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 9/7; 896/891 26411/26244]&lt;br /&gt;
Gencom mapping: [&amp;lt;1 5/2 0 5 2|, &amp;lt;0 -5/2 0 -6 4|]&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Smonzos%20and%20Svals"&gt;Sval map&lt;/a&gt;: [&amp;lt;1 5 5 2|, &amp;lt;0 -5 -6 4|]&lt;br /&gt;
EDOs: 8, 11, 30, 41, 52&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.4262 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc31"&gt;&lt;a name="x2.9.15.7.11.13"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;2.9.15.7.11.13&lt;/h1&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc32"&gt;&lt;a name="x2.9.15.7.11.13-Stacks (aka 2magic)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;Stacks (aka 2magic)&lt;/h2&gt;
Commas: 100/99, 105/104, 144/143, 196/195&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~9/7 = 438.977&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 9/7; 100/99 105/104 144/143 196/195]&lt;br /&gt;
Gencom mapping: [&amp;lt;1 5/2 5/2 5 2 7|, &amp;lt;0 -5/2 -1/2 -6 4 -9|]&lt;br /&gt;
&lt;br /&gt;
Sval map: [&amp;lt;1 0 2 -1 6 -2|, &amp;lt;0 5 3 6 -4 9|]&lt;br /&gt;
EDOs: 11, 30, 41, 153cdef, 194cdef, 235cdef&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.540 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc33"&gt;&lt;a name="x2.9.15.7.11.13-Stacks (aka 2magic)-2.9.15.7.11 stacks"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;2.9.15.7.11 stacks&lt;/h3&gt;
Commas: 100/99, 225/224, 245/243&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~9/7 = 438.607&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 9/7; 100/99 225/224 245/243]&lt;br /&gt;
Gencom mapping: [&amp;lt;1 5/2 5/2 5 2|, &amp;lt;0 -5/2 -1/2 -6 4|]&lt;br /&gt;
&lt;br /&gt;
Sval map: [&amp;lt;1 0 2 -1 6|, &amp;lt;0 5 3 6 -4|]&lt;br /&gt;
EDOs: 8, 11, 30, 41, 52, 93, 145, 342bce,&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.226 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc34"&gt;&lt;a name="x2.9.15.7.11.13-Stacks (aka 2magic)-2.9.15.7 stacks"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;2.9.15.7 stacks&lt;/h3&gt;
Commas: 225/224, 245/243&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~9/7 = 439.296&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 9/7; 225/224 245/243]&lt;br /&gt;
Gencom mapping: [&amp;lt;1 5/2 5/2 5|, &amp;lt;0 -5/2 -1/2 -6|]&lt;br /&gt;
&lt;br /&gt;
Sval map: [&amp;lt;1 0 2 -1|, &amp;lt;0 5 3 6|]&lt;br /&gt;
EDOs: 8, 11, 30, 41, 71, 93, 112c, 134c, 175c&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 1.074 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc35"&gt;&lt;a name="x2.9.21"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;2.9.21&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:72:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc36"&gt;&lt;a name="x2.9.21-A-team"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:72 --&gt;A-team&lt;/h2&gt;
Commas: 1029/1024&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~21/16 = 467.375&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 21/16; 1029/1024]&lt;br /&gt;
Gencom mapping: [&amp;lt;1 1 0 3|, &amp;lt;0 3/2 0 -1/2|]&lt;br /&gt;
&lt;br /&gt;
Sval map: [&amp;lt;1 2 4|, &amp;lt;0 3 1|]&lt;br /&gt;
EDOs: 5, 13, 18, 41, 59, 77, 95&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.3202 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:74:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc37"&gt;&lt;a name="x2.3.7/5.11/5.13/5"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:74 --&gt;2.3.7/5.11/5.13/5&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:76:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc38"&gt;&lt;a name="x2.3.7/5.11/5.13/5-Historical"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:76 --&gt;Historical&lt;/h2&gt;
Subgroup: 2.3.7/5.11/5.13/5&lt;br /&gt;
Commas: 364/363, 441/440, 1001/1000&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~21/20 = 83.016&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Gencom"&gt;Gencom&lt;/a&gt;: [2 21/20; 364/363 441/440 1001/1000]&lt;br /&gt;
Gencom map: [&amp;lt;1 2 -3/4 -3/4 1/4 5/4|, &amp;lt;0 -6 0 7 2 -9|]&lt;br /&gt;
&lt;br /&gt;
Sval map: [&amp;lt;1 2 0 1 2|, &amp;lt;0 -6 7 2 -9|]&lt;br /&gt;
EDOs: 14, 29, 72, 101, 130, 159&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.2562 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:78:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc39"&gt;&lt;a name="x2.3.7.11/5.13"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:78 --&gt;2.3.7.11/5.13&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:80:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc40"&gt;&lt;a name="x2.3.7.11/5.13-Hypnosis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:80 --&gt;Hypnosis&lt;/h2&gt;
Subgroup: 2.3.7.11/5.13&lt;br /&gt;
Commas: 169/168, 540/539, 729/728&lt;br /&gt;
Related temperament: &lt;a class="wiki_link" href="/Swetismic%20temperaments#Hypnos-13-limit"&gt;hypnos&lt;/a&gt;, &lt;a class="wiki_link" href="/Hemifamity%20temperaments#Tricot-13-limit"&gt;tricot&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Gencom"&gt;Gencom&lt;/a&gt;: [2 13/9; 169/168, 540/539, 729/728]&lt;br /&gt;
Gencom map: [&amp;lt;1 0 -4 -3 4 0|, &amp;lt;0 3 13/2 11 -13/2 7|]&lt;br /&gt;
&lt;br /&gt;
Sval map: [&amp;lt;1 0 -3 8 0|, &amp;lt;0 3 11 -13 7|]&lt;br /&gt;
EDOs: 17, 36, 118e, 125e, 161e, 197e&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.5379 cents&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:82:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc41"&gt;&lt;a name="x2.5.7"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:82 --&gt;2.5.7&lt;/h1&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:84:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc42"&gt;&lt;a name="x2.5.7-Didacus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:84 --&gt;Didacus&lt;/h2&gt;
Subgroup: 2.5.7&lt;br /&gt;
Commas: 3136/3125&lt;br /&gt;
Related temperaments: [[Chromatic+pairs#Roulette]]&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Gencom"&gt;Gencom&lt;/a&gt;: [2 28/25 3136/3125]&lt;br /&gt;
Gencom map: [&amp;lt;1 0 2 2|, &amp;lt;0 0 2 5|]&lt;br /&gt;
&lt;br /&gt;
Sval map: [&amp;lt;1 2 2|, &amp;lt;0 2 5|]&lt;br /&gt;
EDOs: 6, 19, 25, 31, 37, 99, 130, 161, 353&lt;br /&gt;
&lt;a class="wiki_link" href="/Tp%20tuning#T2%20tuning"&gt;RMS error&lt;/a&gt;: 0.2138 cents&lt;/body&gt;&lt;/html&gt;</pre></div>