5L 7s: Difference between revisions

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

'''5L 7s''' is the MOS pattern of the [[Pythagorean tuning|Pythagorean]]/[[Garibaldi temperament|Helmholtz/Garibaldi]] chromatic scale, and also the [[superpyth]] chromatic scale. In contrast to the [[7L 5s|meantone chromatic scale]], in which diatonic semitones are larger than chromatic semitones, here the reverse is true: diatonic semitones are smaller than chromatic semitones, so the [[5L 2s|diatonic scale]] subset is actually [[Rothenberg propriety|improper]].

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 doesn't become proper until you add 5 more notes to form the superpyth "enharmonic" scale, superpyth[17]).

== Scales ==

* [[Garibaldi12]]

* [[Archy12]]

== Scale tree ==

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-This is the MOS pattern of the [[Pythagorean tuning|Pythagorean]]/[[Garibaldi temperament|Helmholtz/Garibaldi]] chromatic scale, and also the [[superpyth]] chromatic scale. In contrast to the [[7L 5s|meantone chromatic scale]], in which diatonic semitones are larger than chromatic semitones, here the reverse is true: diatonic semitones are smaller than chromatic semitones, so the [[5L 2s|diatonic scale]] subset is actually [[Rothenberg propriety|improper]].
+'''5L 7s''' is the MOS pattern of the [[Pythagorean tuning|Pythagorean]]/[[Garibaldi temperament|Helmholtz/Garibaldi]] chromatic scale, and also the [[superpyth]] chromatic scale. In contrast to the [[7L 5s|meantone chromatic scale]], in which diatonic semitones are larger than chromatic semitones, here the reverse is true: diatonic semitones are smaller than chromatic semitones, so the [[5L 2s|diatonic scale]] subset is actually [[Rothenberg propriety|improper]].
 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 doesn't become proper until you add 5 more notes to form the superpyth "enharmonic" scale, superpyth[17]).
+== Scales ==
+* [[Garibaldi12]]
+* [[Archy12]]
 == Scale tree ==