Neutral third scales: Difference between revisions

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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 [[~~Chromatic pairs~~ #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.

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.

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''Any other scales which contain the 7th (350c) and 14th (700c) degrees of ~~10edo~~ are also considered neutral thirds scales.''

''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)

[[Category:Lists of scales]]

[[Category:Neutral| ]]

[[Category:Rastmic]]

@@ Line 3: / Line 3: @@
 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 [[Chromatic pairs #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.
+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.
@@ Line 245: / Line 245: @@
-''Any other scales which contain the 7th (350c) and 14th (700c) degrees of 10edo are also considered neutral thirds scales.''
+''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)
+{{Navbox scale gallery}}
 [[Category:Lists of scales]]
 [[Category:Neutral| ]] <!-- main article -->
 [[Category:Rastmic]]