5L 7s: Difference between revisions

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~~It is the MOS pattern of the~~ [[Pythagorean tuning|Pythagorean]]/[[Schismatic family|schismic]] ~~chromatic scale~~, and ~~also the~~ [[superpyth]] ~~chromatic scale. In contrast to~~ the ~~[[7L 5s|meantone chromatic scale]],~~ in which the diatonic semitone is larger than the chromatic semitone, here the reverse is true: the diatonic semitone is smaller than the chromatic semitone, so the [[5L 2s|diatonic scale]] subset is actually [[Rothenberg propriety|~~improper~~]].

Temperaments that support this scale include [[Pythagorean tuning|Pythagorean]], [[Schismatic family|schismic]] (such as Helmholtz and Garibaldi), and [[superpyth]], with the Pythagorean and schismatic scales in particular being [[Rothenberg propriety|proper]]. Scales of this form are characterized by having a small step (or [[diatonic semitone]]) that is smaller than the [[chroma]] (or [[chromatic semitone]]).

~~The two distinct harmonic entropy minima with~~ this ~~MOS pattern~~ are~~, on the one hand, scales very close to Pythagorean such that~~ [[~~64/63~~]] is ~~not tempered out, such as~~ the ~~schismatic temperaments known as Helmholtz and Garibaldi, and on the other hand, the much simpler and less accurate scale known as superpyth in which 64/63 is tempered out.~~

~~The Pythagorean/schismatic version is proper, but the superpyth version is improper~~ (~~it does not become proper until you add 5 more notes to form the superpyth enharmonic scale, superpyth~~[17]).

== Modes ==

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 {{Infobox MOS}}
 {{MOS intro|Other Names=p-chromatic}}
-It is the MOS pattern of the [[Pythagorean tuning|Pythagorean]]/[[Schismatic family|schismic]] chromatic scale, and also the [[superpyth]] chromatic scale. In contrast to the [[7L 5s|meantone chromatic scale]], in which the diatonic semitone is larger than the chromatic semitone, here the reverse is true: the diatonic semitone is smaller than the chromatic semitone, so the [[5L 2s|diatonic scale]] subset is actually [[Rothenberg propriety|improper]].
+Temperaments that support this scale include [[Pythagorean tuning|Pythagorean]], [[Schismatic family|schismic]] (such as Helmholtz and Garibaldi), and [[superpyth]], with the Pythagorean and schismatic scales in particular being [[Rothenberg propriety|proper]]. Scales of this form are characterized by having a small step (or [[diatonic semitone]]) that is smaller than the [[chroma]] (or [[chromatic semitone]]).
-The two distinct harmonic entropy minima with this MOS pattern are, on the one hand, scales very close to Pythagorean such that [[64/63]] is not tempered out, such as the schismatic temperaments known as Helmholtz and Garibaldi, and on the other hand, the much simpler and less accurate scale known as superpyth in which 64/63 is tempered out.
-The Pythagorean/schismatic version is proper, but the superpyth version is improper (it does not become proper until you add 5 more notes to form the superpyth enharmonic scale, superpyth[17]).
 == Modes ==