Gamelismic clan: Difference between revisions

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The [[2.3.7 subgroup|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]] (a.k.a. gamelic), this means three [[~]][[8/7]] intervals give a fifth, [[3/2]]. In fact, we find that {{nowrap| 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.

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 classical 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:~~

* [[Lemba]] (+50/49) → [[Jubilismic clan #Lemba|Jubilismic clan]]

* ''[[Echidnic]]'' (+686/675} → [[Diaschismic family #Echidnic|Diaschismic family]]

* [[Blackwood]] (+28/27) → [[Limmic temperaments #Blackwood|Limmic temperaments]]

* ''[[Trismegistus]]'' (+3125/3072) → [[Magic family #Trismegistus|Magic family]]

* [[Hemithirds]] (+3136/3125) → [[Hemimean clan #Hemithirds|Hemimean clan]]

* ''[[Gamity]]'' (+1071875/1062882) → [[Amity family #Gamity|Amity family]]

* ''[[Tritikleismic]]'' (+15625/15552) → [[Kleismic family #Tritikleismic|Kleismic family]]

* ''[[Heinz]]'' (+78732/78125) → [[Sensipent family #Heinz|Sensipent family]]

* ''[[Triwell]]'' (+235298/234375) → [[Semicomma family #Triwell|Semicomma family]]

* ''[[Gamelstearn]]'' (+118098/117649) → [[Compton family #Gamelstearn|Compton family]]

~~The rest are considered below.~~

No-five subgroup extensions of slendric include radon, a 2.3.7.11 extension that may be viewed as no-five rodan, and baladic, a 2.3.7.13.17 extension, considered below. Dicussed elsewhere is [[No-fives subgroup temperaments #Gigapyth|gigapyth]] in the 2.3.7.85 subgroup.

== Slendric ==

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[[Badness]] (Sintel): 0.158

=== Overview to extensions ===

==== Full 7-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]] 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.

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 classical 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:

* [[Lemba]] (+50/49) → [[Jubilismic clan #Lemba|Jubilismic clan]]

* ''[[Echidnic]]'' (+686/675} → [[Diaschismic family #Echidnic|Diaschismic family]]

* [[Blackwood]] (+28/27) → [[Limmic temperaments #Blackwood|Limmic temperaments]]

* [[Trismegistus]] (+3125/3072) → [[Magic family #Trismegistus|Magic family]]

* [[Hemithirds]] (+3136/3125) → [[Hemimean clan #Hemithirds|Hemimean clan]]

* ''[[Gamity]]'' (+1071875/1062882) → [[Amity family #Gamity|Amity family]]

* ''[[Tritikleismic]]'' (+15625/15552) → [[Kleismic family #Tritikleismic|Kleismic family]]

* ''[[Heinz]]'' (+78732/78125) → [[Sensipent family #Heinz|Sensipent family]]

* ''[[Triwell]]'' (+235298/234375) → [[Semicomma family #Triwell|Semicomma family]]

* ''[[Gamelstearn]]'' (+118098/117649) → [[Compton family #Gamelstearn|Compton family]]

The rest are considered below.

==== Subgroup extensions ====

No-five subgroup extensions of slendric include euslendric, a 2.3.7.13-subgroup extension, radon, a 2.3.7.11-subgroup extension that may be viewed as no-five rodan, and baladic, a weak 2.3.7.13.17-subgroup extension, considered right below. Dicussed elsewhere is [[No-fives subgroup temperaments #Gigapyth|gigapyth]] in the 2.3.7.85 subgroup.

=== Euslendric ===

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== Clyndro ==

~~{{See also| Mavila family }}~~

Clyndro tempers out [[135/128]] and finds the interval class of 5 at a stack of -3 fifths as does any temperament in the [[mavila family]]. It can be described as the {{nowrap| 11 & 16 }} temperament.

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 {{Technical data page}}
 The [[2.3.7 subgroup|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]] (a.k.a. gamelic), this means three [[~]][[8/7]] intervals give a fifth, [[3/2]]. In fact, we find that {{nowrap| 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.
-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 classical 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:
-* [[Lemba]] (+50/49) → [[Jubilismic clan #Lemba|Jubilismic clan]]
-* ''[[Echidnic]]'' (+686/675} → [[Diaschismic family #Echidnic|Diaschismic family]]
-* [[Blackwood]] (+28/27) → [[Limmic temperaments #Blackwood|Limmic temperaments]]
-* ''[[Trismegistus]]'' (+3125/3072) → [[Magic family #Trismegistus|Magic family]]
-* [[Hemithirds]] (+3136/3125) → [[Hemimean clan #Hemithirds|Hemimean clan]]
-* ''[[Gamity]]'' (+1071875/1062882) → [[Amity family #Gamity|Amity family]]
-* ''[[Tritikleismic]]'' (+15625/15552) → [[Kleismic family #Tritikleismic|Kleismic family]]
-* ''[[Heinz]]'' (+78732/78125) → [[Sensipent family #Heinz|Sensipent family]]
-* ''[[Triwell]]'' (+235298/234375) → [[Semicomma family #Triwell|Semicomma family]]
-* ''[[Gamelstearn]]'' (+118098/117649) → [[Compton family #Gamelstearn|Compton family]]
-The rest are considered below.
-No-five subgroup extensions of slendric include radon, a 2.3.7.11 extension that may be viewed as no-five rodan, and baladic, a 2.3.7.13.17 extension, considered below. Dicussed elsewhere is [[No-fives subgroup temperaments #Gigapyth|gigapyth]] in the 2.3.7.85 subgroup.
 == Slendric ==
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 [[Badness]] (Sintel): 0.158
+=== Overview to extensions ===
+==== Full 7-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]] 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.
+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 classical 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:
+* [[Lemba]] (+50/49) → [[Jubilismic clan #Lemba|Jubilismic clan]]
+* ''[[Echidnic]]'' (+686/675} → [[Diaschismic family #Echidnic|Diaschismic family]]
+* [[Blackwood]] (+28/27) → [[Limmic temperaments #Blackwood|Limmic temperaments]]
+* [[Trismegistus]] (+3125/3072) → [[Magic family #Trismegistus|Magic family]]
+* [[Hemithirds]] (+3136/3125) → [[Hemimean clan #Hemithirds|Hemimean clan]]
+* ''[[Gamity]]'' (+1071875/1062882) → [[Amity family #Gamity|Amity family]]
+* ''[[Tritikleismic]]'' (+15625/15552) → [[Kleismic family #Tritikleismic|Kleismic family]]
+* ''[[Heinz]]'' (+78732/78125) → [[Sensipent family #Heinz|Sensipent family]]
+* ''[[Triwell]]'' (+235298/234375) → [[Semicomma family #Triwell|Semicomma family]]
+* ''[[Gamelstearn]]'' (+118098/117649) → [[Compton family #Gamelstearn|Compton family]]
+The rest are considered below.
+==== Subgroup extensions ====
+No-five subgroup extensions of slendric include euslendric, a 2.3.7.13-subgroup extension, radon, a 2.3.7.11-subgroup extension that may be viewed as no-five rodan, and baladic, a weak 2.3.7.13.17-subgroup extension, considered right below. Dicussed elsewhere is [[No-fives subgroup temperaments #Gigapyth|gigapyth]] in the 2.3.7.85 subgroup.
 === Euslendric ===
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 == Clyndro ==
-{{See also| Mavila family }}
 Clyndro tempers out [[135/128]] and finds the interval class of 5 at a stack of -3 fifths as does any temperament in the [[mavila family]]. It can be described as the {{nowrap| 11 & 16 }} temperament.