4L 2s: Difference between revisions

Line 10:

4L 2s can be seen as a [[Warped diatonic|warped diatonic scale]], where one large step of diatonic (5L 2s) is removed, or as the equal-tempered whole-tone scale ([[6edo]]), but with two "whole tones" that are smaller than the others.

4L 2s can be seen as a [[Warped diatonic|warped diatonic scale]], where one large step of diatonic (5L 2s) is removed, or as the equal-tempered whole-tone scale ([[6edo]]), but with two "whole tones" that are smaller than the others.

Scales with the true MOS pattern are always [[Rothenberg propriety|proper]], because there is only one small step per period. In addition, there are near-MOS patterns, such as LLLsLs, in which the period is the only generic interval that has more than two specific representatives. The near-MOS is only proper if the generator is smaller than 2\10 of an octave (240 ~~cents~~).

Scales with the true MOS pattern are always [[Rothenberg propriety|proper]], because there is only one small step per period. In addition, there are near-MOS patterns, such as LLLsLs, in which the period is the only generic interval that has more than two specific representatives. The near-MOS is only proper if the generator is smaller than 2\10 of an octave (240{{c}}).

== Name==

== Name ==

[[TAMNAMS]] suggests the temperament-agnostic name '''citric''' for this scale.

==Theory==

== Theory ==

=== Low harmonic entropy scales ===

===Low harmonic entropy scales===

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.

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 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.

==~~Modes~~==

== Scale properties ==

== ~~Intervals~~ ==

== Scale tree ==

{{MOS tuning spectrum

| 5/4 = Antikythera

| 13/8 = Golden lemba

| 7/4 = Lemba is around here

| 2/1 = Optimum rank range

| 6/1 = Doublewide is around here

}}

~~==Scale tree==~~

~~{{Scale tree|Comments=5/4: Antikythera;~~

~~13/8: Golden lemba;~~

~~7/4: Lemba is around here;~~

~~2/1: Optimum rank range;~~

~~6/1: Doublewide is around here}}~~

[[Category:6-tone scales]]

@@ Line 10: / Line 10: @@
 {{MOS intro}}
-L 2s can be seen as a [[Warped diatonic|warped diatonic scale]], where one large step of diatonic (5L 2s) is removed, or as the equal-tempered whole-tone scale ([[6edo]]), but with two "whole tones" that are smaller than the others.
+L&nbsp;2s can be seen as a [[Warped diatonic|warped diatonic scale]], where one large step of diatonic (5L&nbsp;2s) is removed, or as the equal-tempered whole-tone scale ([[6edo]]), but with two "whole tones" that are smaller than the others.
-Scales with the true MOS pattern are always [[Rothenberg propriety|proper]], because there is only one small step per period. In addition, there are near-MOS patterns, such as LLLsLs, in which the period is the only generic interval that has more than two specific representatives. The near-MOS is only proper if the generator is smaller than 2\10 of an octave (240 cents).
+Scales with the true MOS pattern are always [[Rothenberg propriety|proper]], because there is only one small step per period. In addition, there are near-MOS patterns, such as LLLsLs, in which the period is the only generic interval that has more than two specific representatives. The near-MOS is only proper if the generator is smaller than 2\10 of an octave (240{{c}}).
-== Name==
+== Name ==
 [[TAMNAMS]] suggests the temperament-agnostic name '''citric''' for this scale.
-==Theory==
+== Theory ==
+=== Low harmonic entropy scales ===
-===Low harmonic entropy scales===
+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.
-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 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.
-==Modes==
+== Scale properties ==
-{{MOS mode degrees}}
+{{TAMNAMS use}}
+{{MOS data}}
-== Intervals ==
+== Scale tree ==
-{{MOS intervals}}
+{{MOS tuning spectrum
+| 5/4 = Antikythera
+| 13/8 = Golden lemba
+| 7/4 = Lemba is around here
+| 2/1 = Optimum rank range
+| 6/1 = Doublewide is around here
+}}
-==Scale tree==
-{{Scale tree|Comments=5/4: Antikythera;
-/8: Golden lemba;
-/4: Lemba is around here;
-/1: Optimum rank range;
-/1: Doublewide is around here}}
 [[Category:6-tone scales]]