Gamelismic clan: Difference between revisions

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The [[2.3.7 subgroup]] comma for the '''gamelismic clan''' is the gamelisma, [[1029/1024]], with [[monzo]] {{monzo| -10 1 0 3 }}. For any member of the clan, for the rank-3 [[Gamelismic family #~~Gamelan~~|gamelismic temperament]] itself, and for the rank-2 2.3.7 temperament [[slendric]], this means three [[~]][[8/7]] intervals give a fifth, [[3/2]]. In fact, we find that 3/2 = (8/7)<sup>3</sup> × 1029/1024. From this it follows that gamelismic temperaments tend to flatten both the fifth and the harmonic seventh, or if they do not, the other of the pair must be flattened even more. [[36edo]] is a good tuning for slendric, though if the full 7-limit is desired, [[72edo]], [[77edo]] or [[118edo]] might be preferred.

The [[2.3.7 subgroup]] comma for the '''gamelismic clan''' is the gamelisma, [[1029/1024]], with [[monzo]] {{monzo| -10 1 0 3 }}. For any member of the clan, for the rank-3 [[Gamelismic family #Gamelismic|gamelismic temperament]] itself, and for the rank-2 2.3.7 temperament [[slendric]], this means three [[~]][[8/7]] intervals give a fifth, [[3/2]]. In fact, we find that 3/2 = (8/7)<sup>3</sup> × 1029/1024. From this it follows that gamelismic temperaments tend to flatten both the fifth and the harmonic seventh, or if they do not, the other of the pair must be flattened even more. [[36edo]] is a good tuning for slendric, though if the full 7-limit is desired, [[72edo]], [[77edo]] or [[118edo]] might be preferred.

To the gamelisma itself we need to add the comma which appears next on the modified [[Normal lists #Normal interval list|normal comma list]] for the full 7-limit. 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 is the same as ~6/5.

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== Rodan ==

Rodan tempers out 245/243 and can be described as the 41 & 46 temperament. This temperament extends neatly to the 13-limit, though the perfect fifth is sharper than ideal for slendric.

[[Subgroup]]: 2.3.5.7

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Minimax tuning:

* [[11-odd-limit]]: ~8/7 = {{monzo| 4/19 2/19 0 0 -1/19 }}

* 11-odd-limit: ~8/7 = {{monzo| 4/19 2/19 0 0 -1/19 }}

: [{{monzo| 1 0 0 0 0 }}, {{monzo| 31/19 6/19 0 0 -3/19 }}, {{monzo| 49/19 34/19 0 0 -17/19 }}, {{monzo| 53/19 -2/19 0 0 1/19 }}, {{monzo| 62/19 -26/19 0 0 13/19 }}]

: Eigenmonzo (unchanged-interval) basis: 2.11/9

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== Guiron ==

~~{{See also| Schismatic~~ family }}

Guiron tempers out the [[schisma]], and finds the prime 5 at the diminished fourth as does any temperament in the [[schismatic family]]. It can be described as 36 & 41. It is more complex than rodan, but the optimal tuning is closer to optimal slendric.

[[Subgroup]]: 2.3.5.7

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== Mothra ==

Mothra tempers out [[81/80]] and finds the prime 5 at a stack of four fifths as does any temperament in the [[meantone family]]. It also tempers out [[1728/1715]], the orwellisma. Using [[31edo]] with a generator of 6/31 is an excellent tuning choice. Once again something other than a mos should be used as a scale to get the most out of mothra.

Mothra tempers out [[81/80]] and finds the prime 5 at a stack of four fifths as does any temperament in the [[meantone family]]. It also tempers out [[1728/1715]], the orwellisma. It can be described as 26 & 31. Using [[31edo]] with a generator of 6/31 is an excellent tuning choice. Once again something other than a mos should be used as a scale to get the most out of mothra.

Note that mothra is also called '''cynder''' in the 7-limit, which can be a little confusing sometimes.

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; Music:

* [http://micro.soonlabel.com/16-ET/mothra/20141028_mothra16br4.mp3 Prelude for solo piano in mothra16, brat 4 tuning] by [http://chrisvaisvil.com/prelude-for-solo-piano-in-mothra16-brat-4-tuning/ ~~Chris Vaisvil~~]

* [http://micro.soonlabel.com/16-ET/mothra/20141028_mothra16br4.mp3 Prelude for solo piano in mothra16, brat 4 tuning] by [[Chris Vaisvil]] ([http://chrisvaisvil.com/prelude-for-solo-piano-in-mothra16-brat-4-tuning/ blog post])

=== Cynder ===

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-The [[2.3.7 subgroup]] comma for the '''gamelismic clan''' is the gamelisma, [[1029/1024]], with [[monzo]] {{monzo| -10 1 0 3 }}. For any member of the clan, for the rank-3 [[Gamelismic family #Gamelan|gamelismic temperament]] itself, and for the rank-2 2.3.7 temperament [[slendric]], this means three [[~]][[8/7]] intervals give a fifth, [[3/2]]. In fact, we find that 3/2 = (8/7)<sup>3</sup> × 1029/1024. From this it follows that gamelismic temperaments tend to flatten both the fifth and the harmonic seventh, or if they do not, the other of the pair must be flattened even more. [[36edo]] is a good tuning for slendric, though if the full 7-limit is desired, [[72edo]], [[77edo]] or [[118edo]] might be preferred.
+The [[2.3.7 subgroup]] comma for the '''gamelismic clan''' is the gamelisma, [[1029/1024]], with [[monzo]] {{monzo| -10 1 0 3 }}. For any member of the clan, for the rank-3 [[Gamelismic family #Gamelismic|gamelismic temperament]] itself, and for the rank-2 2.3.7 temperament [[slendric]], this means three [[~]][[8/7]] intervals give a fifth, [[3/2]]. In fact, we find that 3/2 = (8/7)<sup>3</sup> × 1029/1024. From this it follows that gamelismic temperaments tend to flatten both the fifth and the harmonic seventh, or if they do not, the other of the pair must be flattened even more. [[36edo]] is a good tuning for slendric, though if the full 7-limit is desired, [[72edo]], [[77edo]] or [[118edo]] might be preferred.
 To the gamelisma itself we need to add the comma which appears next on the modified [[Normal lists #Normal interval list|normal comma list]] for the full 7-limit. 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 is the same as ~6/5.
@@ Line 73: / Line 73: @@
 == Rodan ==
 {{Main| Rodan }}
+Rodan tempers out 245/243 and can be described as the 41 & 46 temperament. This temperament extends neatly to the 13-limit, though the perfect fifth is sharper than ideal for slendric.
 [[Subgroup]]: 2.3.5.7
@@ Line 105: / Line 107: @@
 Minimax tuning:
-* [[11-odd-limit]]: ~8/7 = {{monzo| 4/19 2/19 0 0 -1/19 }}
+* 11-odd-limit: ~8/7 = {{monzo| 4/19 2/19 0 0 -1/19 }}
 : [{{monzo| 1 0 0 0 0 }}, {{monzo| 31/19 6/19 0 0 -3/19 }}, {{monzo| 49/19 34/19 0 0 -17/19 }}, {{monzo| 53/19 -2/19 0 0 1/19 }}, {{monzo| 62/19 -26/19 0 0 13/19 }}]
 : Eigenmonzo (unchanged-interval) basis: 2.11/9
@@ Line 217: / Line 219: @@
 == Guiron ==
-{{See also| Schismatic family }}
+Guiron tempers out the [[schisma]], and finds the prime 5 at the diminished fourth as does any temperament in the [[schismatic family]]. It can be described as 36 & 41. It is more complex than rodan, but the optimal tuning is closer to optimal slendric.
 [[Subgroup]]: 2.3.5.7
@@ Line 276: / Line 278: @@
 == Mothra ==
-Mothra tempers out [[81/80]] and finds the prime 5 at a stack of four fifths as does any temperament in the [[meantone family]]. It also tempers out [[1728/1715]], the orwellisma. Using [[31edo]] with a generator of 6/31 is an excellent tuning choice. Once again something other than a mos should be used as a scale to get the most out of mothra.
+Mothra tempers out [[81/80]] and finds the prime 5 at a stack of four fifths as does any temperament in the [[meantone family]]. It also tempers out [[1728/1715]], the orwellisma. It can be described as 26 & 31. Using [[31edo]] with a generator of 6/31 is an excellent tuning choice. Once again something other than a mos should be used as a scale to get the most out of mothra.
 Note that mothra is also called '''cynder''' in the 7-limit, which can be a little confusing sometimes.
@@ Line 330: / Line 332: @@
 ; Music:
-* [http://micro.soonlabel.com/16-ET/mothra/20141028_mothra16br4.mp3 Prelude for solo piano in mothra16, brat 4 tuning] by [http://chrisvaisvil.com/prelude-for-solo-piano-in-mothra16-brat-4-tuning/ Chris Vaisvil]
+* [http://micro.soonlabel.com/16-ET/mothra/20141028_mothra16br4.mp3 Prelude for solo piano in mothra16, brat 4 tuning] by [[Chris Vaisvil]] ([http://chrisvaisvil.com/prelude-for-solo-piano-in-mothra16-brat-4-tuning/ blog post])
 === Cynder ===