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>

Revision as of 00:00, 17 July 2018

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

Semaphore

Comma: 49/48

POL2 generator: ~8/7~7/6 = 250.385

Gencom: [2 8/7; 49/48]

Gencom mapping: [<1 2 0 3|, <0 -2 0 -1|]

Map: [<1 2 3|, <0 -2 -1|]

EDOs: 5, 14, 19, 24, 67c, 91c

RMS error: 2.523 cents

Archy

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

POL2 generator: ~3/2 = 709.321

Gencom: [2 3/2; 64/63]

Gencom mapping: [<1 1 0 4|, <0 1 0 -2|]

Map: [<1 2 2|, <0 -1 2|]

EDOs: 5, 12, 17, 22, 27, 137bc

RMS error: 1.856 cents

Slendric

Comma: 1029/1024

POL2 generator: ~8/7 = 233.688

Gencom: [2 8/7; 1029/1024]

Gencom mapping: [<1 1 0 3|, <0 3 0 -1|]

Map: [<1 1 3|, <0 3 -1|]

EDOs: 5, 21, 26, 31, 36, 77, 113, 190

RMS error: 0.3202 cents

Lee

Comma: 177147/175616

POL2 generator: ~81/56 = 633.525

Map: [<1 0 -3|, <0 3 11|]

EDOs: 17, 36, 89, 125, 161, 358, 519b

RMS error: 0.3519 cents

Skwares

Comma: 19683/19208

POL2 generator: ~9/7 = 425.365 cents

Map: [<1 3 6|, <0 -4 -9|]

EDOs: 14, 17, 31, 48, 79, 189b, 268bc, 347bc

RMS error: 1.149 cents

2.3.11

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.

Comma: 243/242

POL2 generator: ~11/9 = 350.525

Gencom: [2 11/9; 243/242]

Gencom mapping: [<1 1 0 0 2|, <0 2 0 0 5|]

Map: [<1 1 2|, <0 2 5|]

EDOs: 7, 10, 17, 24, 41, 65, 89, 202, 291, 380

RMS error: 0.3021 cents

Seven note albitonic scale

Ten note chromatic scale

Seventeen note mega chromatic scale

2.3.5.11

Porkypine

Commas: 55/54, 100/99

POL2 generator: ~10/9 = 164.078

Gencom: [2 10/9; 55/54, 100/99]

Gencom mapping: [<1 2 3 0 4|, <0 -3 -5 0 -4|]

Map: [<1 2 3 4|, <0 -3 -5 -4|]

EDOs: 7, 15, 22, 37, 73cd, 95cd, 117bcd

RMS error: 2.287 cents

Mohaha

Commas: 81/80, 121/120

POL2 generator: ~11/9 = 348.094

Gencom: [2 11/9; 81/80 121/120]

Gencom mapping: [<1 1 0 0 2|, <0 2 8 0 5|]

Map: [<1 1 0 2|, <0 2 8 5|]

EDOs: 7, 10, 17, 24, 31, 55, 69d, 100d, 131bd

RMS error: 1.392 cents

Music

Mohaha10ping2 by Billy Stiltner

2.3.7.11

Ennea

Commas: 41503/41472, 43923/43904

POL2 generator: ~99/98 = 17.6258

Gencom: [2 99/98; 41503/41472, 43923/43904]

Gencom mapping: [<1 14/9 0 25/9 31/9|, <0 2 0 2 1|]

Sval map: [<9 0 11 24|, <0 2 2 1|]

EDOs: 54, 63, 68, 72, 135, 342, 477, 525, 613, 681, 749, 817, 2159bcd, 3336bcd, 4153bcd

RMS error: 0.0383 cents

Supra

Commas: 64/63, 99/98

POTE generator: ~3/2 = 707.192

Gencom: [2 3/2; 64/63 99/98]

Gencom mapping: [<1 1 0 4 7|, <0 1 0 -2 -6|]

Sval map: [<1 0 6 13|, <0 1 -2 -6|]

EDOs: 5, 12, 17, 39c, 56c

RMS error: 1.977 cents

Skwares

Commas: 99/98, 243/242

POTE generator: ~9/7 = 425.244

Gencom: [2 9/7; 99/98 243/242]

Gencom mapping: [<1 3 0 6 7|, <0 -4 0 -9 -10]]

Sval map: [<1 3 6 7|, <0 -4 -9 -10|]

EDOs: 14, 17, 31, 48, 79, 127, 206bcd

RMS error: 1.099 cents

Hemif

Commas: 243/242, 896/891

POTE generator: ~11/9 = 351.535

Gencom: [2 11/9; 243/242 896/891]

Gencom mapping: [<1 1 0 -1 2|, <0 2 0 13 5|]

Sval map: [<1 1 -1 2|, <0 2 13 5|]

EDOs: 7, 17, 41, 58, 99d

RMS error: 0.6108 cents

Bleu

Commas: 99/98, 864/847

POTE generator: ~12/11 = 140.005

Map: [<1 1 2 3|, <0 5 7 4|]

EDOs: 9, 17, 43, 60c

RMS error: 1.829 cents

2.3.7.11.13

Suhajira

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

Gencom: [2 11/9; 64/63 78/77 144/143]

Gencom map: [<1 1 0 4 2 4|, <0 2 0 -4 5 -1|]

POT2 generator: ~11/9 = 353.775

Map: [<1 1 4 2 4|, <0 2 -4 5 -1|]

EDOs: 7, 10, 17, 44d, 61cd, 78cd

RMS error: 1.953 cents

Hemif

Commas: 144/143, 243/242, 364/363

Related temperament: Hemififths, namo

POT2 generator: ~11/9 = 351.691

Gencom: [2 11/9; 144/143 243/242 364/363]

Gencom map: [<1 1 0 -1 2 4|, <0 2 0 13 5 -1|]

Map: [<1 1 -1 2 4|, <0 2 13 5 -1|]

EDOs: 7, 10, 17, 24, 41, 58

RMS error: 0.7167 cents

Skwares

Commas: 78/77, 99/98, 243/242

POT2 generator: ~9/7 = 424.457

Map: [<1 3 6 7 9|, <0 -4 -9 -10 -15|]

EDOs: 17, 48e, 65de, 82c, 147ce

RMS error: 1.769 cents

Leapfrog

Commas: 169/168, 352/351, 364/363

POL2 generator: ~3/2 = 704.745 cents

Gencom: [2 3/2; 169/169 352/351 364/363]

Gencom mapping: [<1 1 0 -6 -3 -1|, <0 1 0 15 11 8|]

Sval map: [<1 0 -21 -14 -9|, <0 1 15 11 8|]

EDOs: 17, 46, 63

RMS error: 0.7541 cents

Bleu

Group: 2.3.7.11.13

Commas: 78/77, 99/98, 144/143

Sval name: 9&17

POL2 generator: ~13/12 = 139.990

Gencom: [2 13/12; 78/77 99/98 144/143]

Gencom map: [<1 1 0 2 3 3|, <0 5 0 7 4 6|]

Map: [<1 1 2 3 3|, <0 5 7 4 6|]

EDOs: 17, 43, 60c

RMS error: 1.752 cents

Parapyth (Rank 3)

Commas: 352/351, 364/363

POL2 tuning: <1200.000 1903.856 (2787.774) 3369.907 4154.482 4442.913|

The gencom below gives Margo Schulter's favored basis

Gencom: [2 3/2 28/27; 352/351 364/363]

Gencom mapping: [<1 1 0 1 4 6|, <0 1 0 3 -1 -4|, <0 0 0 1 1 1|]

Sval map: [<1 0 0 7 12|, <0 1 0 -4 -7|, <0 0 1 1 1|]

EDOs: 17, 41, 46, 58, 87, 104

RMS error: 0.3789 cents

2.3.5.11

Larry

Commas: 243/242, 4000/3993

Related temperaments: gravity, harry

POTE generator: ~40/27 = 683.166

Gencom: [2 40/27; 243/242 4000/3993]

Gencom mapping: [<1 5 12 0 12|, <0 -6 -17 0 -15|]

Map: [<1 5 12 12|, <0 -6 -17 -15|]

EDOs: 7, 58, 65, 137, 202

RMS error: 0.3025 cents

2.9.7.11

Machine

Commas: 64/63, 99/98

POTE generator: ~8/7 = 214.384

Gencom: [2 8/7; 64/63 99/98]

Gencom mapping: [<1 3/2 0 3 4|, <0 1/2 0 -1 -3|]

Sval map: [<1 0 6 13|, <0 1 -1 -3|]

EDOs: 5, 6, 11, 17, 28

RMS error: 1.977 cents

Apparatus

Commas: 41503/41472, 322102/321489

POTE generator: ~77/72 = 115.570

Gencom: [2 77/72; 41503/41472 322102/321489]

Gencom mapping: [<1 5/2 0 3 5|, <0 -19/2 0 -2 -16|]

Sval map: [<1 5 3 5|, <0 -19 -2 -16|]

EDOs: 10, 21, 31, 52, 83, 135, 353, 488, 623

RMS error: 0.0673 cents

Mechanism

Commas: 896/891, 26411/26244

POTE generator: ~9/7 = 438.465

Gencom: [2 9/7; 896/891 26411/26244]

Gencom mapping: [<1 5/2 0 5 2|, <0 -5/2 0 -6 4|]

Sval map: [<1 5 5 2|, <0 -5 -6 4|]

EDOs: 8, 11, 30, 41, 52

RMS error: 0.4262 cents

2.9.15.7.11.13

Stacks (aka 2magic)

Commas: 100/99, 105/104, 144/143, 196/195

POL2 generator: ~9/7 = 438.977

Gencom: [2 9/7; 100/99 105/104 144/143 196/195]

Gencom mapping: [<1 5/2 5/2 5 2 7|, <0 -5/2 -1/2 -6 4 -9|]

Sval map: [<1 0 2 -1 6 -2|, <0 5 3 6 -4 9|]

EDOs: 11, 30, 41, 153cdef, 194cdef, 235cdef

RMS error: 1.540 cents

2.9.15.7.11 stacks

Commas: 100/99, 225/224, 245/243

POL2 generator: ~9/7 = 438.607

Gencom: [2 9/7; 100/99 225/224 245/243]

Gencom mapping: [<1 5/2 5/2 5 2|, <0 -5/2 -1/2 -6 4|]

Sval map: [<1 0 2 -1 6|, <0 5 3 6 -4|]

EDOs: 8, 11, 30, 41, 52, 93, 145, 342bce,

RMS error: 1.226 cents

2.9.15.7 stacks

Commas: 225/224, 245/243

POL2 generator: ~9/7 = 439.296

Gencom: [2 9/7; 225/224 245/243]

Gencom mapping: [<1 5/2 5/2 5|, <0 -5/2 -1/2 -6|]

Sval map: [<1 0 2 -1|, <0 5 3 6|]

EDOs: 8, 11, 30, 41, 71, 93, 112c, 134c, 175c

RMS error: 1.074 cents

2.9.21

A-team

Commas: 1029/1024

POL2 generator: ~21/16 = 467.375

Gencom: [2 21/16; 1029/1024]

Gencom mapping: [<1 1 0 3|, <0 3/2 0 -1/2|]

Sval map: [<1 2 4|, <0 3 1|]

EDOs: 5, 13, 18, 41, 59, 77, 95

RMS error: 0.3202 cents

2.3.7/5.11/5.13/5

Historical

Subgroup: 2.3.7/5.11/5.13/5

Commas: 364/363, 441/440, 1001/1000

POL2 generator: ~21/20 = 83.016

Gencom: [2 21/20; 364/363 441/440 1001/1000]

Gencom map: [<1 2 -3/4 -3/4 1/4 5/4|, <0 -6 0 7 2 -9|]

Sval map: [<1 2 0 1 2|, <0 -6 7 2 -9|]

EDOs: 14, 29, 72, 101, 130, 159

RMS error: 0.2562 cents

2.3.7.11/5.13

Hypnosis

Subgroup: 2.3.7.11/5.13

Commas: 169/168, 540/539, 729/728

Related temperament: hypnos, tricot

Gencom: [2 13/9; 169/168, 540/539, 729/728]

Gencom map: [<1 0 -4 -3 4 0|, <0 3 13/2 11 -13/2 7|]

Sval map: [<1 0 -3 8 0|, <0 3 11 -13 7|]

EDOs: 17, 36, 118e, 125e, 161e, 197e

RMS error: 0.5379 cents

2.5.7

Didacus

Subgroup: 2.5.7

Commas: 3136/3125

Related temperaments: Chromatic+pairs#Roulette

Gencom: [2 28/25 3136/3125]

Gencom map: [<1 0 2 2|, <0 0 2 5|]

Sval map: [<1 2 2|, <0 2 5|]

EDOs: 6, 19, 25, 31, 37, 99, 130, 161, 353

RMS error: 0.2138 cents

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