4L 2s: Difference between revisions

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| Name = citric

}}

~~{{MOS intro}}~~

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 ===

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.

==~~=Low harmonic entropy scales=~~==

== Scale properties ==

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.~~

=== Intervals ===

=== Generator chain ===

==Modes==

=== Modes ===

==Scale tree==

== Scale tree ==

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

{{MOS tuning spectrum

13/8: Golden lemba;

| 5/4 = Antikythera

7/4: Lemba is around here;

| 13/8 = Golden lemba

2/1: Optimum rank range;

| 7/4 = Lemba is around here

6/1: Doublewide is around here}}

| 2/1 = Optimum rank range

| 6/1 = Doublewide is around here

}}

[[Category:6-tone scales]]

@@ Line 8: / Line 8: @@
 | Name = citric
 }}
+{{MOS intro}}
-{{MOS intro}}
+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.
-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.
-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 ===
+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.
-===Low harmonic entropy scales===
+== Scale properties ==
-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.
+{{TAMNAMS use}}
-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.
+=== Intervals ===
+{{MOS intervals}}
+=== Generator chain ===
+{{MOS genchain}}
-==Modes==
+=== Modes ===
 {{MOS mode degrees}}
-==Scale tree==
+== Scale tree ==
-{{Scale tree|Comments=5/4: Antikythera;
+{{MOS tuning spectrum
-/8: Golden lemba;
+| 5/4 = Antikythera
-/4: Lemba is around here;
+| 13/8 = Golden lemba
-/1: Optimum rank range;
+| 7/4 = Lemba is around here
-/1: Doublewide is around here}}
+| 2/1 = Optimum rank range
+| 6/1 = Doublewide is around here
+}}
 [[Category:6-tone scales]]