Gamelismic clan: Difference between revisions

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The 2.3.7 [[Just_intonation_subgroups|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 three [[Gamelismic family #Gamelan|gamelan temperament]] itself, and for the rank two 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 7/4, or if they do not, the other of the pair must be flattened even more. [[36edo~~|36EDO~~]] is a good tuning for gamelismic itself, though if the full 7-limit is desired, [[72edo~~|72EDO~~]], [[77edo~~|77EDO~~]] or [[118edo~~|118EDO~~]] might be preferred.

The 2.3.7 [[Just_intonation_subgroups|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 three [[Gamelismic family #Gamelan|gamelan temperament]] itself, and for the rank two 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 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.

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'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 15625/15552 and has a generator of 6/5 with a 1/3 octave period.

Full 7-limit temperaments discussed elsewhere are:

* ''[[Blacksmith]]'', {28/27, 49/48} → [[Limmic temperaments #Blacksmith|Limmic temperaments]]

* [[Lemba]], {50/49, 525/512} → [[Jubilismic clan #Lemba|Jubilismic clan]]

* ''[[Mothra]]'', {81/80, 1029/1024} → [[Meantone family #Mothra|Meantone family]]

* [[Valentine]], {126/125, 1029/1024} → [[Starling temperaments #Valentine|Starling temperaments]]

* ''[[Echidnic]]'', {686/675, 1029/1024} → [[Diaschismic family #Echidnic|Diaschismic family]]

* ''[[Trismegistus]]'', {1029/1024, 3125/3072} → [[Magic family #Trismegistus|Magic family]]

* [[Hemithirds]], {1029/1024, 3136/3125} → [[Hemimean clan #Hemithirds|Hemimean clan]]

* ''[[Tritikleismic]]'', {1029/1024, 15625/15552} → [[Kleismic family #Tritikleismic|Kleismic family]]

* ''[[Heinz]]'', {1029/1024, 78732/78125} → [[Sensipent family #Heinz|Sensipent family]]

* ''[[Decades]]'', {1029/1024, 118098/117649} → [[Compton family #Decades|Compton family]]

* ''[[Triwell]]'', {1029/1024, 235298/234375} → [[Semicomma family #Triwell|Semicomma family]]

* ''[[Gamity]]'', {1029/1024, 1071875/1062882} → [[Amity family #Gamity|Amity family]]

The rest are considered below.

No-five subgroup extensions of slendric include [[Chromatic pairs #Radon|radon]], the 2.3.7.11 extension that may be viewed as no-five rodan, and baladic, the 2.3.7.13.17 extension, considered below.

== Slendric ==

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Scales: [[slendric5]], [[slendric6]], [[slendric11]], [[slendric16]]

~~=== Full seven limit extensions ===~~

To the gamelisma itself we need to add the comma which appears next on the modified [[Normal lists #Normal interval list|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 15625/15552 and has a generator of 6/5 with a 1/3 octave period.

Discussed elsewhere are [[blacksmith]], [[lemba]], [[mothra]], [[echidnic]], [[tritikleismic]], [[valentine]], [[trismegistus]], [[hemithirds]], [[gamity]], [[triwell]], [[decades]] and [[heinz]]. The rest are considered below.

~~=== Subgroup extensions ===~~

~~No-five subgroup extensions of slendric include [[Chromatic pairs #Radon|radon]], the 2.3.7.11 extension that may be viewed as no-five rodan, and baladic, the 2.3.7.13.17 extension, considered below.~~

== Rodan ==

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-The 2.3.7 [[Just_intonation_subgroups|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 three [[Gamelismic family #Gamelan|gamelan temperament]] itself, and for the rank two 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 7/4, or if they do not, the other of the pair must be flattened even more. [[36edo|36EDO]] is a good tuning for gamelismic itself, though if the full 7-limit is desired, [[72edo|72EDO]], [[77edo|77EDO]] or [[118edo|118EDO]] might be preferred.
+The 2.3.7 [[Just_intonation_subgroups|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 three [[Gamelismic family #Gamelan|gamelan temperament]] itself, and for the rank two 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 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.
+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'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 15625/15552 and has a generator of 6/5 with a 1/3 octave period.
+Full 7-limit temperaments discussed elsewhere are:
+* ''[[Blacksmith]]'', {28/27, 49/48} → [[Limmic temperaments #Blacksmith|Limmic temperaments]]
+* [[Lemba]], {50/49, 525/512} → [[Jubilismic clan #Lemba|Jubilismic clan]]
+* ''[[Mothra]]'', {81/80, 1029/1024} → [[Meantone family #Mothra|Meantone family]]
+* [[Valentine]], {126/125, 1029/1024} → [[Starling temperaments #Valentine|Starling temperaments]]
+* ''[[Echidnic]]'', {686/675, 1029/1024} → [[Diaschismic family #Echidnic|Diaschismic family]]
+* ''[[Trismegistus]]'', {1029/1024, 3125/3072} → [[Magic family #Trismegistus|Magic family]]
+* [[Hemithirds]], {1029/1024, 3136/3125} → [[Hemimean clan #Hemithirds|Hemimean clan]]
+* ''[[Tritikleismic]]'', {1029/1024, 15625/15552} → [[Kleismic family #Tritikleismic|Kleismic family]]
+* ''[[Heinz]]'', {1029/1024, 78732/78125} → [[Sensipent family #Heinz|Sensipent family]]
+* ''[[Decades]]'', {1029/1024, 118098/117649} → [[Compton family #Decades|Compton family]]
+* ''[[Triwell]]'', {1029/1024, 235298/234375} → [[Semicomma family #Triwell|Semicomma family]]
+* ''[[Gamity]]'', {1029/1024, 1071875/1062882} → [[Amity family #Gamity|Amity family]]
+The rest are considered below.
+No-five subgroup extensions of slendric include [[Chromatic pairs #Radon|radon]], the 2.3.7.11 extension that may be viewed as no-five rodan, and baladic, the 2.3.7.13.17 extension, considered below.
 == Slendric ==
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 Scales: [[slendric5]], [[slendric6]], [[slendric11]], [[slendric16]]
-=== Full seven limit extensions ===
-To the gamelisma itself we need to add the comma which appears next on the modified [[Normal lists #Normal interval list|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 15625/15552 and has a generator of 6/5 with a 1/3 octave period.
-Discussed elsewhere are [[blacksmith]], [[lemba]], [[mothra]], [[echidnic]], [[tritikleismic]], [[valentine]], [[trismegistus]], [[hemithirds]], [[gamity]], [[triwell]], [[decades]] and [[heinz]]. The rest are considered below.
-=== Subgroup extensions ===
-No-five subgroup extensions of slendric include [[Chromatic pairs #Radon|radon]], the 2.3.7.11 extension that may be viewed as no-five rodan, and baladic, the 2.3.7.13.17 extension, considered below.
 == Rodan ==