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 15:31:57 UTC.
- The original revision id was 162296445.
- 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>]
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
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 />
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</body></html>