4L 2s: Difference between revisions

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There are three scales with this [[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{{c}} 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.

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

== Scale properties ==

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== Scale tree ==

{{MOS tuning spectrum

| 5/4 = Antikythera

| 5/4 = [[Antikythera]]

| 13/8 = Golden lemba

| 9/7 = [[Wizard]]

| 7/4 = Lemba ~~is around here~~

| 13/8 = Golden [[lemba]]

| 2/1 = ~~Optimum rank range~~

| 5/3 = Lemba

| 6/1 = Doublewide ~~is around here~~

| 12/5 = [[Sruti]]

| 6/1 = [[Doublewide]]

}}

[[Category:6-tone scales]]

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 There are three scales with this [[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{{c}} 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.
+The second is [[Dicot_family#Decimal|decimal]], in which two generators make a 4/3, and the third is [[Jubilismic_clan#Doublewide|doublewide]], in which the generator is 7/6 so the period minus the generator is 6/5.
 == Scale properties ==
@@ Line 37: / Line 37: @@
 == Scale tree ==
 {{MOS tuning spectrum
-| 5/4 = Antikythera
+| 5/4 = [[Antikythera]]
-| 13/8 = Golden lemba
+| 9/7 = [[Wizard]]
-| 7/4 = Lemba is around here
+| 13/8 = Golden [[lemba]]
-| 2/1 = Optimum rank range
+| 5/3 = Lemba
-| 6/1 = Doublewide is around here
+| 12/5 = [[Sruti]]
+| 6/1 = [[Doublewide]]
 }}
 [[Category:6-tone scales]]