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| Name = citric
| Name = citric
}}
}}
{{MOS intro}}


{{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.
[[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.
 
== Scale properties ==
{{TAMNAMS use}}


===Low harmonic entropy scales===
=== Intervals ===
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.
{{MOS intervals}}


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.
=== Generator chain ===
{{MOS genchain}}


==Modes==
=== Modes ===
{{MOS modes}}
{{MOS mode degrees}}
==Scale tree==
{| class="wikitable"
|-
! colspan="11" |Generator
! | Cents
! | Comments
|-
| |1\6
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |200
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |6\34
| |
| |
| |
| |
| |
| |211.76
| style="text-align:center;" |
|-
| |
| |
| |
| |
| | 5\28
| |
| |
| |
| |
| |
| |
| | 214.29
| style="text-align:center;" |Antikythera is around here
|-
| |
| |
| |
| |4\22
| |
| |
| |
| |
| |
| |
| |
| |218.18
| style="text-align:center;" |
|-
| |
| |
| |3\16
| |
| |
| |
| |
| |
| |
| |
| |
| |225
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 227.56
| |
|-
| |
| |
| |
| |
| | 8\42
| |
| |
| |
| |
| |
| |
| |228.57
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |600/(1+phi)
| style="text-align:center;" | Golden lemba
|-
| |
| |
| |
| |
| |
| |13\68
| |
| |
| |
| |
| |
| |229.41
| style="text-align:center;" |
|-
| |
| |
| |
| |5\26
| |
| |
| |
| |
| |
| |
| |
| |230.77
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 232.8
| |
|-
| |
| |
| |
| |
| |7\36
| |
| |
| |
| |
| |
| |
| |233.33
| style="text-align:center;" | Lemba is around here
|-
| |
| |2\10
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |240
| style="text-align:center;" |Boundary of propriety for near-MOS


Optimum rank range (L/s=2/1) for MOS
== Scale tree ==
|-
{{MOS tuning spectrum
| |
| 5/4 = Antikythera
| |
| 13/8 = Golden lemba
| |
| 7/4 = Lemba is around here
| |5\24
| 2/1 = Optimum rank range
| |
| 6/1 = Doublewide is around here
| |
}}
| |
| |
| |
| |
| |
| | 250
| style="text-align:center;" |Decimal is around here
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |251.89
| |
|-
| |
| |
| |
| |
| |8\38
| |
| |
| |
| |
| |
| |
| | 252.63
| |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |253.39
| style="text-align:center;" |<span style="display: block; text-align: center;">L/s = e</span>
|-
| |
| |
| |3\14
| |
| |
| |
| |
| |
| |
| |
| |
| |257.14
| style="text-align:center;" | L/s = 3
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |258.81
| style="text-align:center;" | L/s = pi
|-
| |
| |
| |
| |4\18
| |
| |
| |
| |
| |
| |
| |
| |266.67
| style="text-align:center;" |L/s = 4
|-
| |
| |
| |
| |
| |5\22
| |
| |
| |
| |
| |
| |
| |272.73
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |6\26
| |
| |
| |
| |
| |
| |276.92
| style="text-align:center;" |Doublewide is around here
|-
| |
| |
| |
| |
| |
| |
| | 7\30
| |
| |
| |
| |
| | 280
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |8\34
| |
| |
| |
| |282.35
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |9\38
| |
| |
| | 284.21
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |10\42
| |
| |285.71
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |11\46
| |286.96
| style="text-align:center;" |
|-
| |1\4
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |300
| style="text-align:center;" |
|}


[[Category:6-tone scales]]
[[Category:6-tone scales]]
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