Gamelismic clan
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The [2,3,5]-[[Just intonation subgroups|subgroup]] comma for the gamelismic clan is the gamelisma, 1029/1024, with monzo |-10 1 0 3>. For any member of the clan, and for the gamelismic temperament itself, this means three 8/7 intervals give a fifth, 3/2. In fact, we find that 3/2 = (8/7)^3 * 1029/1024. From this it follows that gamelismic temperaments tend to flatten the both fifth and the 7/4, or if they do not, the other of the pair must be flattened even more.
[[36edo]] is a good tuning for gamelismic itself, though if the full 7-limit is desired, [[72edo]], [[77edo]] or [[118edo]] might be preferred.
7-limit minimax
[|1 0 0 0>, |5/2 3/4 0 -3/4>,
|5/2 -1/4 1 -3/4>, |5/2 -1/4 0 1/4>]
Eigenmonzos: 2, 7/6, 6/5
9-limit minimax
[|1 0 0 0>, |10/7 6/7 0 -3/7>,
|10/7 -1/7 1 -3/7>, |20/7 -2/7 0 1/7>]
Eigenmonzos: 2, 6/5, 9/7
Lattice basis: 8/7 0.5192 5/4 2.3219
Angle(8/7, 5/4) = 90 degrees
Map to lattice: [<0 3 0 -1|, <0 0 1 0|]
Map: [<1 1 0 3|, <0 3 0 -1|, < 0 0 1 0|]
Generators: 2, 5, 7
==Full seven limit children==
To the gamelisma itself we need to add the comma which appears next on the modified [[Normal lists|normal comma list]], which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period.
===Miracle===
7-limit
[[Comma|Commas]]: {1029/1024, 225/224}
[[Minimax tuning]]:
7-limit: [|1 0 0 0>, |25/13 6/13 -6/13 0>,
|25/13 -7/13 7/13 0>, |35/13 -2/13 2/13 0>]
[[Eigenmonzo|Eigenmonzos]]: 2, 6/5
9-limit: [|1 0 0 0>, |25/19 12/19 -6/19 0>,
|50/19 -14/19 7/19 0>, |55/19 -4/19 2/19 0>]
[[Eigenmonzo|Eigenmonzos]]: 2, 10/9
Algebraic generator: Secor59, [[Algebraic number|positive root]] of 15x^6-8x^4-12
11-limit
[[Comma|Commas]]: {1029/1024, 225/224, 243/242}
[[Minimax tuning]]:
[|1 0 0 0 0>, |25/19 12/19 -6/19 0 0>,
|50/19 -14/19 7/19 0 0>, |55/19 -4/19 2/19 0 0>,
|53/19 30/19 -15/19 0 0>]
[[Eigenmonzo|Eigenmonzos]]: 2, 10/9
Algebraic generator: Secor59
Map: [<1 1 3 3 2|, <0 6 -7 -2 15|]
[[edo|Edos]]: [[72edo|72]], [[175edo|175]]
===Rodan===
7-limit
[[Comma|Commas]]: {1029/1024, 245/243}
7+9 limit minimax tuning: [|1 0 0 0>, |5/3 0 1/6 -1/6>,
|25/9 0 17/18 -17/18>, |25/9 0 -1/18 1/18>]
[[Eigenmonzo|Eigenmonzos]]: 2, 7/5
Algebraic generator: [[Algebraic number|larger root]] of 20x^2-36x+15, or (9+sqrt(6))/10.
11-limit
[[Comma|Commas]]: {441/440, 245/243, 385/384}
[[Minimax tuning]]: [|1 0 0 0 0>, |31/19 6/19 0 0 -3/19>,
|49/19 34/19 0 0 -17/19>, |53/19 -2/19 0 0 1/19>,
|62/19 -26/19 0 0 13/19>]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/9
Algebraic generator: [[Algebraic number|positive root]] of x^2+16x-31, or sqrt(95)-8.
13-limit
Commas: {196/195, 245/243, 352/351, 364/363}
13 and 15 limit minimax
[|1 0 0 0 0 0>, |23/14 3/14 0 0 0 -3/28>,
|37/14 17/14 0 0 0 -17/28>, |39/14 -1/14 0 0 0 1/28>,
|45/14 -13/14 0 0 0 13/28>, |23/7 -11/7 0 0 0 11/14>]
Eigenmonzos: 2, 13/9
Algebraic generator: Gatetone, positive root of 4x^6-7x-1. Recurrence converges slowly.
Map: [<1 1 -1 3 6 8|, <0 3 17 -1 -13 -22|]
Generators: 2, 8/7
[[edo|Edos]]: [[87edo|87]], [[128edo|128]]
===Valentine===
7-limit
[[Comma|Commas]]: {1029/1024, 126/125}
[[Minimax tuning]]:
7-limit: [|1 0 0 0>, |5/2 3/4 0 -3/4>,
|17/6 5/12 0 -5/12>, [5/2 -1/4 0 1/4>]
Eigenmonzos: 2, 7/6
9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>,
|47/21 10/21 0 -5/21>, |20/7 -2/7 0 1/7>]
Eigenmonzos: 2, 9/7
Algebraic generator: [[Algebraic number|smaller root]] of x^2-89x+92, or (89-sqrt(7553))/2, at 77.8616 cents.
11-limit
[[Comma|Commas]]: {121/120, 126/125, 176/175}
[[Minimax tuning]]:
[|1 0 0 0 0>, |1 0 0 -9/10 9/10>,
|2 0 0 -1/2 1/2>, |3 0 0 3/10 -3/10>, |3 0 0 -7/10 7/10>]
Eigenmonzos: 2, 11/7
Algebraic generator: [[Algebraic number|positive root]] of 4x^3+15x^2-21, or else Gontrand2, the smallest positive root of 4x^7-8x^6+5.
Map: [<1 1 2 3 3|, <0 9 5 -3 7|]
Generators: 2, 21/20
[[edo|Edos]]: [[77edo|77]], [[108edo|108]], [[185edo|185]]
===Guiron===
7-limit
[[Comma|Commas]]: {1029/1024, 32805/32768}
[[Minimax tuning]]:
7+9 limit: [|1 0 0 0>, |15/8 0 -1/8 0>,
|0 0 1 0>, |65/24 0 1/24 0>]
[[Eigenmonzo|Eigenmonzos]]: 2, 5/4
11-limit:
[[Comma|Commas]]: {385/384, 441/440, 3025/3024}
[[Minimax tuning]]:
[|1 0 0 0 0>, |15/8 0 -1/8 0 0>,
|0 0 1 0 0>, |65/24 0 1/24 0 0>,
|37/6 0 -7/6 0 0>]
[[Eigenmonzo|Eigenmonzos]]: 2, 5/4
Map: [<1 1 7 3 -2|, <0 3 -24 -1 28|]
[[edo|Edos]]: [[118edo|118]], [[159edo|159]]
===Unidec===
7-limit
[[Comma|Commas]]: {1029/1024, 4375/4374}
[[Minimax tuning]]:
7-limit: [|1 0 0 0>, |47/26 0 6/13 -6/13>,
|71/26 0 11/13 -11/13>, |71/26 0 -2/13 2/13>]
[[Eigenmonzo|Eigenmonzos]]: 2, 7/5
9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>,
|57/28 11/7 0 -11/14>, |20/7 -2/7 0 1/7>]
[[Eigenmonzo|Eigenmonzos]]: 2, 9/7
11-limit
[[Comma|Commas]]: {1029/1024, 4375/4374, 441/440}
[[Minimax tuning]]:
[|1 0 0 0 0>, |10/7 6/7 0 -3/7 0>, |57/28 11/7 0 -11/14 0>,
|20/7 -2/7 0 1/7 0>, |99/28 -3/7 0 3/14 0>]
[[Eigenmonzo|Eigenmonzos]]: 2, 9/7
Map: [<2 5 8 5 6|, <0 -6 -11 2 3|]
[[edo|Edos]]: [[118edo|118]], [[190edo|190]]
===Hemithirds===
7-limit
[[Comma|Commas]]: {1029/1024, 3136/3125}
[[Minimax tuning]]:
7-limit: [|1 0 0 0>, |5/2 3/4 0 -3/4>,
|11/5 -1/10 0 1/10>, |5/2 -1/4 0 1/4>]
[[Eigenmonzo|Eigenmonzos]]: 2, 7/6
9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>,
|82/35 -4/35 0 2/35>, |20/7 -2/7 0 1/7>]
[[Eigenmonzo|Eigenmonzos]]: 2, 7/6
11-limit
[[Comma|Commas]]: {385/384, 441/440, 3136/3125}
[[Minimax tuning]]:
[|1 0 0 0 0>, |11/9 0 0 -5/9 5/9>, |64/27 0 0 2/27 -2/27>,
|79/27 0 0 5/27 -5/27>, |79/27 0 0 -22/27 22/27>]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/7
Map: [<1 4 2 2 7|, <0 -15 2 5 -22|]
[[edo|Edos]]: [[118edo|118]], [[149edo|149]]
===Tritikleismic===
7-limit
[[Comma|Commas]]: {1029/1024, 15625/15552}
[[Minimax tunings]]:
7-limit: [|1 0 0 0>, |2 0 6/7 -6/7>,
|8/3 0 5/7 -5/7>, |8/3 0 -2/7 2/7>]
[[Eigenmonzo|Eigenmonzos]]: 2, 7/5
9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>,
|46/21 5/7 0 -5/14>, |20/7 -2/7 0 1/7>]
[[Eigenmonzo|Eigenmonzos]]: 2, 9/7
11-limit
[[Comma|Commas]]: {385/384, 441/440, 4000/3993}
[[Minimax tuning]]:
[|1 0 0 0 0>, |10/7 6/7 0 -3/7 0>, |46/21 5/7 0 -5/14 0>,
|20/7 -2/7 0 1/7 0>, |71/21 3/7 0 -3/14 0>]
[[Eigenmonzo|Eigenmonzos]]: 2, 9/7
[[edo|Edos]]: [[72edo|72]], [[159edo|159]], [[231edo|231]]Original HTML content:
<html><head><title>Gamelismic clan</title></head><body>The [2,3,5]-<a class="wiki_link" href="/Just%20intonation%20subgroups">subgroup</a> comma for the gamelismic clan is the gamelisma, 1029/1024, with monzo |-10 1 0 3>. For any member of the clan, and for the gamelismic temperament itself, this means three 8/7 intervals give a fifth, 3/2. In fact, we find that 3/2 = (8/7)^3 * 1029/1024. From this it follows that gamelismic temperaments tend to flatten the both fifth and the 7/4, or if they do not, the other of the pair must be flattened even more.<br />
<a class="wiki_link" href="/36edo">36edo</a> is a good tuning for gamelismic itself, though if the full 7-limit is desired, <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/77edo">77edo</a> or <a class="wiki_link" href="/118edo">118edo</a> might be preferred. <br />
<br />
7-limit minimax<br />
[|1 0 0 0>, |5/2 3/4 0 -3/4>, <br />
|5/2 -1/4 1 -3/4>, |5/2 -1/4 0 1/4>]<br />
Eigenmonzos: 2, 7/6, 6/5<br />
<br />
9-limit minimax<br />
[|1 0 0 0>, |10/7 6/7 0 -3/7>, <br />
|10/7 -1/7 1 -3/7>, |20/7 -2/7 0 1/7>]<br />
Eigenmonzos: 2, 6/5, 9/7<br />
<br />
Lattice basis: 8/7 0.5192 5/4 2.3219<br />
Angle(8/7, 5/4) = 90 degrees<br />
Map to lattice: [<0 3 0 -1|, <0 0 1 0|]<br />
<br />
Map: [<1 1 0 3|, <0 3 0 -1|, < 0 0 1 0|]<br />
Generators: 2, 5, 7<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Full seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Full seven limit children</h2>
To the gamelisma itself we need to add the comma which appears next on the modified <a class="wiki_link" href="/Normal%20lists">normal comma list</a>, which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x-Full seven limit children-Miracle"></a><!-- ws:end:WikiTextHeadingRule:2 -->Miracle</h3>
<br />
7-limit<br />
<a class="wiki_link" href="/Comma">Commas</a>: {1029/1024, 225/224}<br />
<br />
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br />
7-limit: [|1 0 0 0>, |25/13 6/13 -6/13 0>, <br />
|25/13 -7/13 7/13 0>, |35/13 -2/13 2/13 0>]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 6/5<br />
<br />
9-limit: [|1 0 0 0>, |25/19 12/19 -6/19 0>, <br />
|50/19 -14/19 7/19 0>, |55/19 -4/19 2/19 0>]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 10/9<br />
<br />
Algebraic generator: Secor59, <a class="wiki_link" href="/Algebraic%20number">positive root</a> of 15x^6-8x^4-12<br />
<br />
11-limit<br />
<a class="wiki_link" href="/Comma">Commas</a>: {1029/1024, 225/224, 243/242}<br />
<br />
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br />
[|1 0 0 0 0>, |25/19 12/19 -6/19 0 0>, <br />
|50/19 -14/19 7/19 0 0>, |55/19 -4/19 2/19 0 0>, <br />
|53/19 30/19 -15/19 0 0>]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 10/9<br />
<br />
Algebraic generator: Secor59<br />
<br />
Map: [<1 1 3 3 2|, <0 6 -7 -2 15|]<br />
<br />
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/175edo">175</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc2"><a name="x-Full seven limit children-Rodan"></a><!-- ws:end:WikiTextHeadingRule:4 -->Rodan</h3>
<br />
7-limit<br />
<a class="wiki_link" href="/Comma">Commas</a>: {1029/1024, 245/243}<br />
<br />
7+9 limit minimax tuning: [|1 0 0 0>, |5/3 0 1/6 -1/6>, <br />
|25/9 0 17/18 -17/18>, |25/9 0 -1/18 1/18>]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/5<br />
<br />
Algebraic generator: <a class="wiki_link" href="/Algebraic%20number">larger root</a> of 20x^2-36x+15, or (9+sqrt(6))/10.<br />
<br />
11-limit<br />
<a class="wiki_link" href="/Comma">Commas</a>: {441/440, 245/243, 385/384}<br />
<br />
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>: [|1 0 0 0 0>, |31/19 6/19 0 0 -3/19>, <br />
|49/19 34/19 0 0 -17/19>, |53/19 -2/19 0 0 1/19>, <br />
|62/19 -26/19 0 0 13/19>]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/9<br />
<br />
Algebraic generator: <a class="wiki_link" href="/Algebraic%20number">positive root</a> of x^2+16x-31, or sqrt(95)-8.<br />
<br />
<br />
<br />
13-limit<br />
Commas: {196/195, 245/243, 352/351, 364/363}<br />
<br />
13 and 15 limit minimax<br />
[|1 0 0 0 0 0>, |23/14 3/14 0 0 0 -3/28>, <br />
|37/14 17/14 0 0 0 -17/28>, |39/14 -1/14 0 0 0 1/28>, <br />
|45/14 -13/14 0 0 0 13/28>, |23/7 -11/7 0 0 0 11/14>]<br />
Eigenmonzos: 2, 13/9<br />
<br />
Algebraic generator: Gatetone, positive root of 4x^6-7x-1. Recurrence converges slowly.<br />
<br />
Map: [<1 1 -1 3 6 8|, <0 3 17 -1 -13 -22|]<br />
Generators: 2, 8/7<br />
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/128edo">128</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h3> --><h3 id="toc3"><a name="x-Full seven limit children-Valentine"></a><!-- ws:end:WikiTextHeadingRule:6 -->Valentine</h3>
<br />
7-limit<br />
<a class="wiki_link" href="/Comma">Commas</a>: {1029/1024, 126/125}<br />
<br />
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br />
7-limit: [|1 0 0 0>, |5/2 3/4 0 -3/4>, <br />
|17/6 5/12 0 -5/12>, [5/2 -1/4 0 1/4>]<br />
Eigenmonzos: 2, 7/6<br />
<br />
9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>, <br />
|47/21 10/21 0 -5/21>, |20/7 -2/7 0 1/7>]<br />
Eigenmonzos: 2, 9/7<br />
<br />
Algebraic generator: <a class="wiki_link" href="/Algebraic%20number">smaller root</a> of x^2-89x+92, or (89-sqrt(7553))/2, at 77.8616 cents.<br />
<br />
11-limit<br />
<a class="wiki_link" href="/Comma">Commas</a>: {121/120, 126/125, 176/175}<br />
<br />
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br />
[|1 0 0 0 0>, |1 0 0 -9/10 9/10>, <br />
|2 0 0 -1/2 1/2>, |3 0 0 3/10 -3/10>, |3 0 0 -7/10 7/10>]<br />
Eigenmonzos: 2, 11/7<br />
<br />
Algebraic generator: <a class="wiki_link" href="/Algebraic%20number">positive root</a> of 4x^3+15x^2-21, or else Gontrand2, the smallest positive root of 4x^7-8x^6+5.<br />
<br />
Map: [<1 1 2 3 3|, <0 9 5 -3 7|]<br />
Generators: 2, 21/20<br />
<br />
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/77edo">77</a>, <a class="wiki_link" href="/108edo">108</a>, <a class="wiki_link" href="/185edo">185</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:<h3> --><h3 id="toc4"><a name="x-Full seven limit children-Guiron"></a><!-- ws:end:WikiTextHeadingRule:8 -->Guiron</h3>
<br />
7-limit<br />
<a class="wiki_link" href="/Comma">Commas</a>: {1029/1024, 32805/32768}<br />
<br />
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br />
7+9 limit: [|1 0 0 0>, |15/8 0 -1/8 0>, <br />
|0 0 1 0>, |65/24 0 1/24 0>]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 5/4<br />
<br />
11-limit:<br />
<a class="wiki_link" href="/Comma">Commas</a>: {385/384, 441/440, 3025/3024}<br />
<br />
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br />
[|1 0 0 0 0>, |15/8 0 -1/8 0 0>, <br />
|0 0 1 0 0>, |65/24 0 1/24 0 0>, <br />
|37/6 0 -7/6 0 0>]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 5/4<br />
<br />
Map: [<1 1 7 3 -2|, <0 3 -24 -1 28|]<br />
<br />
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/118edo">118</a>, <a class="wiki_link" href="/159edo">159</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:<h3> --><h3 id="toc5"><a name="x-Full seven limit children-Unidec"></a><!-- ws:end:WikiTextHeadingRule:10 -->Unidec</h3>
<br />
7-limit<br />
<a class="wiki_link" href="/Comma">Commas</a>: {1029/1024, 4375/4374}<br />
<br />
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br />
7-limit: [|1 0 0 0>, |47/26 0 6/13 -6/13>, <br />
|71/26 0 11/13 -11/13>, |71/26 0 -2/13 2/13>]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/5<br />
<br />
9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>, <br />
|57/28 11/7 0 -11/14>, |20/7 -2/7 0 1/7>]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 9/7<br />
<br />
11-limit<br />
<a class="wiki_link" href="/Comma">Commas</a>: {1029/1024, 4375/4374, 441/440}<br />
<br />
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br />
[|1 0 0 0 0>, |10/7 6/7 0 -3/7 0>, |57/28 11/7 0 -11/14 0>,<br />
|20/7 -2/7 0 1/7 0>, |99/28 -3/7 0 3/14 0>]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 9/7<br />
<br />
Map: [<2 5 8 5 6|, <0 -6 -11 2 3|]<br />
<br />
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/118edo">118</a>, <a class="wiki_link" href="/190edo">190</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:<h3> --><h3 id="toc6"><a name="x-Full seven limit children-Hemithirds"></a><!-- ws:end:WikiTextHeadingRule:12 -->Hemithirds</h3>
<br />
7-limit<br />
<a class="wiki_link" href="/Comma">Commas</a>: {1029/1024, 3136/3125}<br />
<br />
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br />
7-limit: [|1 0 0 0>, |5/2 3/4 0 -3/4>, <br />
|11/5 -1/10 0 1/10>, |5/2 -1/4 0 1/4>]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/6<br />
<br />
9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>, <br />
|82/35 -4/35 0 2/35>, |20/7 -2/7 0 1/7>]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/6<br />
<br />
11-limit<br />
<a class="wiki_link" href="/Comma">Commas</a>: {385/384, 441/440, 3136/3125}<br />
<br />
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br />
[|1 0 0 0 0>, |11/9 0 0 -5/9 5/9>, |64/27 0 0 2/27 -2/27>,<br />
|79/27 0 0 5/27 -5/27>, |79/27 0 0 -22/27 22/27>]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/7<br />
<br />
Map: [<1 4 2 2 7|, <0 -15 2 5 -22|]<br />
<br />
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/118edo">118</a>, <a class="wiki_link" href="/149edo">149</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:<h3> --><h3 id="toc7"><a name="x-Full seven limit children-Tritikleismic"></a><!-- ws:end:WikiTextHeadingRule:14 -->Tritikleismic</h3>
<br />
7-limit<br />
<a class="wiki_link" href="/Comma">Commas</a>: {1029/1024, 15625/15552}<br />
<br />
<a class="wiki_link" href="/Minimax%20tunings">Minimax tunings</a>:<br />
7-limit: [|1 0 0 0>, |2 0 6/7 -6/7>, <br />
|8/3 0 5/7 -5/7>, |8/3 0 -2/7 2/7>]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/5<br />
<br />
9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>, <br />
|46/21 5/7 0 -5/14>, |20/7 -2/7 0 1/7>]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 9/7<br />
<br />
11-limit<br />
<a class="wiki_link" href="/Comma">Commas</a>: {385/384, 441/440, 4000/3993}<br />
<br />
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br />
[|1 0 0 0 0>, |10/7 6/7 0 -3/7 0>, |46/21 5/7 0 -5/14 0>, <br />
|20/7 -2/7 0 1/7 0>, |71/21 3/7 0 -3/14 0>]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 9/7<br />
<br />
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/231edo">231</a></body></html>