Neutral third scales: Difference between revisions
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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, resulting in the [[Rastmic clan#Neutral|neutral]] temperament and its extensions (described below). | 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 #Mohaha|a meantone system]], sometimes called [[ | 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. | ||
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* 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". | * 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. | * 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 == | == See also == | ||
* [[ | * [[Songs with neutral intervals]] (not a complete list, only a small sampling) | ||
{{Navbox scale gallery}} | |||
[[Category:Lists of scales]] | [[Category:Lists of scales]] | ||
[[Category:Neutral| ]] <!-- main article --> | [[Category:Neutral| ]] <!-- main article --> | ||
[[Category:Rastmic]] | [[Category:Rastmic]] | ||