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'''Neutral third scales''' are characterized by the division of the 3/2 "perfect fifth" into two equal "neutral thirds". It usually refers to a [[MOS]] or [[MODMOS]] generated by a neutral third (usually from 342.9c in [[7edo]] to 360c in [[10edo]]).
'''Neutral third scales''' are characterized by the division of the 3/2 "perfect fifth" into two equal "neutral thirds". It usually refers to a [[MOS]] or [[MODMOS]] generated by a neutral third (usually from 342.9c in [[7edo]] to 360c in [[10edo]]).


One possible temperament interpretation is that the neutral third generator can be taken to represent either 11/9 or 27/22. This means the comma 243/242 is tempered out.
One possible temperament interpretation is that the neutral third generator can be taken to represent either 11/9 or 27/22. This means the comma [[243/242]] is tempered out, resulting in the [[Rastmic clan#Neutral|neutral]] temperament and its ''extensions'' (described below).


If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it [[Meantone_family#Mohajira|a meantone system]], sometimes called [[Chromatic_pairs#Mohaha|"mohaha"]]. If 7 is also mapped a particular way it is called [[Mohajira|mohajira]]. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of [[maqamic|maqamic temperament]]. But neither of these adjustments to the farther-out intervals affects its basic nature as a "neutral thirds" scale, which equally subdivides the 3/2 into two equal parts.
If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it [[Meantone family #Mohaha|a meantone system]], sometimes called [[Rastmic clan #Mohaha|mohaha]]. If 7 is also mapped a particular way it is called [[mohajira]]. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of [[neutrominant]] temperament. But neither of these adjustments to the farther-out intervals affects its basic nature as a "neutral thirds" scale, which equally subdivides the 3/2 into two equal parts.


Any temperament tempering out 243/242 lends itself to neutral thirds; this becomes more significant when fifths are of low complexity, such as hemififths or the rank three temperament jove, but also includes miracle, harry and so forth. Nor does a scale need to be a MOS to qualify as a neutral thirds scale; that name could reasonably be given to [[Graph-theoretic properties of scales#Oktone|Oktone]], for example.
Any temperament tempering out 243/242 lends itself to neutral thirds; this becomes more significant when fifths are of low complexity, such as hemififths or the rank three temperament jove, but also includes miracle, harry and so forth. Nor does a scale need to be a MOS to qualify as a neutral thirds scale; that name could reasonably be given to [[Graph-theoretic properties of scales #Oktone|Oktone]], for example.


==Interval chains==
== Interval chains ==
 
=== Basic 2.3.11 neutral thirds scale ===
===Basic 2.3.11 neutral thirds scale===


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===2.3.5.11 mohaha===
=== 2.3.5.11 mohaha ===


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===2.3.7.11 maqamic===
=== 2.3.7.11 suhajira ===


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==MOSes==
== MOSes ==
Neutral third scales are associated with the [[MOSScales|MOS patterns]] [[3L_4s|3L 4s]] and [[7L_3s|7L 3s]].
Neutral third scales are associated with the [[MOS scales|MOS patterns]]: [[3L 4s]] and [[7L 3s]].


In the 3L4s MOS, the large step is a 9/8 and the small step is a 12/11 neutral second. In the 7L3s MOS, the 12/11 is now the large step and the small step is a 33/32 quarter tone.
In the 3L4s MOS, the large step is a 9/8 and the small step is a 12/11 neutral second. In the 7L3s MOS, the 12/11 is now the large step and the small step is a 33/32 quarter tone.


==Munits==
== Munits ==
Though they differ in the specifics of their temperaments, all neutral third scales have certain [[Munit|munit]]s in common.
Though they differ in the specifics of their temperaments, all neutral third scales have certain [[munit]]s in common.
 
* 4/3 Lss, 4/3 sLs: Rather than being divided into two large steps and one small step as in the diatonic scale, 4/3 can always be divided into one large step and two small steps. The large step is 9/8, and the two small steps are "neutral seconds" representing the sub-munit "32/27 ss".
* 11/8 LsL: In contrast, two large steps and a small step make a much less consonant and more colorful interval, 11/8.
 
== Lumatone mapping ==
''See: [[Lumatone mapping for neutral thirds scales]]''.
 
== Neutral thirds scales by EDO ==
Not an exhaustive list.
 
 
=== 7edo ===
 
 
1 1 1 1 1 1 1
 
7edo
 
 
=== 10edo ===
 
 
2 1 2 1 2 1 1
 
Neutral Hypolydian
 
 
2 1 2 1 1 2 1
 
Neutral Hypodorian
 
 
2 1 1 2 1 2 1
 
Neutral Lydian
 
 
1 2 1 2 1 2 1
 
Neutral Dorian
 
 
1 2 1 2 1 1 2
 
Neutral Hypophrygian
 
 
''Any other scales which contain the 3rd (360c) and 6th (720c) degrees of 10edo are also considered neutral thirds scales.''
 
 
=== 17edo ===
''See also: [[17edo neutral scale]]''
 
 
3 2 3 2 3 2 2
 
Neutral Hypolydian
 
 
3 2 3 2 2 3 2
 
Neutral Hypodorian
 
 
3 2 2 3 2 3 2
 
Neutral Lydian
 
 
2 3 2 3 2 3 2
 
Neutral Dorian, Misaelides 2nd Byzantine mode, Maqam Sikah Baladi
 
 
2 3 2 3 2 2 3
 
Neutral Hypophrygian
 
 
''Any other scales which contain the 5th (~353c) and 10th (~706c) degrees of 10edo are also considered neutral thirds scales.''
 
 
=== 24edo ===
''See also: [[24edo scales]]''
 
 
4 3 4 3 4 3 3
 
Neutral Hypolydian
 
 
4 3 4 3 3 4 3
 
Neutral Hypodorian
 
 
4 3 3 4 3 4 3
 
Neutral Lydian
 
 
3 4 3 4 3 4 3
 
Neutral Dorian, Misaelides 2nd Byzantine mode, Maqam Sikah Baladi
 
 
3 4 3 4 3 3 4
 
Neutral Hypophrygian
 
 
''Any other scales which contain the 7th (350c) and 14th (700c) degrees of 24edo are also considered neutral thirds scales.''
 
== See also ==
* [[Songs with neutral intervals]] (not a complete list, only a small sampling)
 


<ul><li>4/3 Lss, 4/3 sLs: Rather than being divided into two large steps and one small step as in the diatonic scale, 4/3 can always be divided into one large step and two small steps. The large step is 9/8, and the two small steps are "neutral seconds" representing the sub-munit "32/27 ss".</li><li>11/8 LsL: In contrast, two large steps and a small step make a much less consonant and more colorful interval, 11/8.</li></ul>
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