4L 2s: Difference between revisions

Line 9:

}}

~~'''4L 2s''' is a hexatonic [[~~MOS ~~scale]]. It~~ resembles ~~the~~ [[5L 2s~~|diatonic scale~~]] but ~~has~~ one step removed.

This MOS resembles [[5L 2s]], but with one large step removed.

There are three scales with this [[MOSScales|MOS]] pattern that are significant minima of harmonic entropy.

There are three scales with this [[MOSScales|MOS]] pattern that are significant minima of harmonic entropy. The first is [[antikythera]], or no-3's [[Diaschismic_family|srutal/pajara]], which is srutal/pajara without any intervals containing 3 in their prime factorization, so it becomes a 2.5.9 or 2.5.7.9 subgroup temperament. This means that the generator is twice that of srutal/pajara (210-220 cents rather than 105-110), since odd numbers of generators are only needed for intervals with 3. So this is a basically "whole tone" scale, but made uneven so some 2-step intervals are 5/4 and others are 9/7.

The first is [[antikythera]], or no-3's [[Diaschismic_family|srutal/pajara]], which is srutal/pajara without any intervals containing 3 in their prime factorization, so it becomes a 2.5.9 or 2.5.7.9 subgroup temperament. This means that the generator is twice that of srutal/pajara (210-220 cents rather than 105-110), since odd numbers of generators are only needed for intervals with 3. So this is a basically "whole tone" scale, but made uneven so some 2-step intervals are 5/4 and others are 9/7.

The second is [[Dicot_family|decimal]], in which two generators make a 4/3, and the third is [[Jubilismic_clan|Doublewide]], in which the generator is 7/6 so the period minus the generator is 6/5.

@@ Line 9: / Line 9: @@
 }}
-'''4L 2s''' is a hexatonic [[MOS scale]]. It resembles the [[5L 2s|diatonic scale]] but has one step removed.
+{{MOS intro}}
+This MOS resembles [[5L 2s]], but with one large step removed.
-There are three scales with this [[MOSScales|MOS]] pattern that are significant minima of harmonic entropy.
+There are three scales with this [[MOSScales|MOS]] pattern that are significant minima of harmonic entropy. The first is [[antikythera]], or no-3's [[Diaschismic_family|srutal/pajara]], which is srutal/pajara without any intervals containing 3 in their prime factorization, so it becomes a 2.5.9 or 2.5.7.9 subgroup temperament. This means that the generator is twice that of srutal/pajara (210-220 cents rather than 105-110), since odd numbers of generators are only needed for intervals with 3. So this is a basically "whole tone" scale, but made uneven so some 2-step intervals are 5/4 and others are 9/7.
-The first is [[antikythera]], or no-3's [[Diaschismic_family|srutal/pajara]], which is srutal/pajara without any intervals containing 3 in their prime factorization, so it becomes a 2.5.9 or 2.5.7.9 subgroup temperament. This means that the generator is twice that of srutal/pajara (210-220 cents rather than 105-110), since odd numbers of generators are only needed for intervals with 3. So this is a basically "whole tone" scale, but made uneven so some 2-step intervals are 5/4 and others are 9/7.
 The second is [[Dicot_family|decimal]], in which two generators make a 4/3, and the third is [[Jubilismic_clan|Doublewide]], in which the generator is 7/6 so the period minus the generator is 6/5.