Gamelismic clan
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2010-09-13 22:56:56 UTC.
- The original revision id was 162404219.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
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.
==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
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>]
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>]
11-limit
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>]
Edos: 72, 175
===Rodan===
7-limit
Commas {1029/1024, 245/243}
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>]
11-limit
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>]
Edos: 87, 128
===Valentine===
7-limit
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>]
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>]
11-limit
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>]
Edos: 77, 108, 185
===Guiron===
7-limit
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>]
11-limit:
Commas: {385/384, 441/440, 3025/3024}
Minimax tuning:
[|1 0 0 0 0>, |10/7 6/7 0 -3/7 0>, |20/7 -2/7 1 -6/7 0>,
|20/7 -2/7 0 1/7 0>, |19/7 10/7 -1 2/7 0>]
Edos: 118, 159
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 />
<!-- 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 />
Commas {1029/1024, 225/224}<br />
<br />
Minimax tuning:<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 />
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 />
<br />
11-limit<br />
Commas {1029/1024, 225/224, 243/242}<br />
<br />
Minimax tuning:<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 />
<br />
Edos: 72, 175<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 />
Commas {1029/1024, 245/243}<br />
<br />
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 />
<br />
11-limit<br />
Commas {441/440, 245/243, 385/384}<br />
<br />
Minimax tuning: [|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 />
<br />
Edos: 87, 128<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 />
Commas: {1029/1024, 126/125}<br />
<br />
Minimax tuning:<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 />
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 />
<br />
11-limit<br />
Commas: {121/120, 126/125, 176/175}<br />
<br />
Minimax tuning:<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 />
<br />
Edos: 77, 108, 185<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 />
Commas: {1029/1024, 32805/32768}<br />
<br />
Minimax tuning:<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 />
<br />
11-limit:<br />
Commas: {385/384, 441/440, 3025/3024}<br />
<br />
Minimax tuning:<br />
[|1 0 0 0 0>, |10/7 6/7 0 -3/7 0>, |20/7 -2/7 1 -6/7 0>, <br />
|20/7 -2/7 0 1/7 0>, |19/7 10/7 -1 2/7 0>]<br />
<br />
Edos: 118, 159</body></html>