7L 4s: Difference between revisions

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== JI approximation ==

7L 4s fails to represent common just intonation intervals and simple temperaments, and ~~its~~ harmonic entropy minimum, ~~insofar as it may be said to have one,~~ is improper ~~(Amity/Hitchcock/Sixix)~~ and is ~~also unconventional to put forward as the most common approach to this scale, because its~~ large ~~and steps are extremely unequal (L>=4, s=1)~~.

7L 4s fails to represent common just intonation intervals and simple temperaments, and it has no clearly discernible harmonic entropy minimum. From a purely computational perspective, 7L 4s's harmonic entropy minimum is [[improper]] and is associated with unusually large step ratios.

However, it is still notable for representing 17:14 with tolerable accuracy for as much as that's worth.

Near the harmonic entropy minimum, the simplest temperament of low-complexity JI supported by 7L 4s is [[amity]] and its variant [[hitchcock]]. However, it is unconventional to put forward this as the most common approach to this scale, because the large and steps are extremely unequal, being at least of 5:1 step ratio in [[39edo]], the smallest patent val supporting either of the two.

A temperament which spans more of the tuning range is [[sixix]], but it is high in just intonation error relative to its step sizes. However, it is still notable for representing 17:14 with tolerable accuracy for as much as that's worth.

== Nomenclature ==

@@ Line 12: / Line 12: @@
 == JI approximation ==
-L 4s fails to represent common just intonation intervals and simple temperaments, and its harmonic entropy minimum, insofar as it may be said to have one, is improper (Amity/Hitchcock/Sixix) and is also unconventional to put forward as the most common approach to this scale, because its large and steps are extremely unequal (L&gt;=4, s=1).
+L 4s fails to represent common just intonation intervals and simple temperaments, and it has no clearly discernible harmonic entropy minimum. From a purely computational perspective, 7L 4s's harmonic entropy minimum is [[improper]] and is associated with unusually large step ratios.
-However, it is still notable for representing 17:14 with tolerable accuracy for as much as that's worth.
+Near the harmonic entropy minimum, the simplest temperament of low-complexity JI supported by 7L 4s is [[amity]] and its variant [[hitchcock]]. However, it is unconventional to put forward this as the most common approach to this scale, because the large and steps are extremely unequal, being at least of 5:1 step ratio in [[39edo]], the smallest patent val supporting either of the two.
+A temperament which spans more of the tuning range is [[sixix]], but it is high in just intonation error relative to its step sizes. However, it is still notable for representing 17:14 with tolerable accuracy for as much as that's worth.
 == Nomenclature ==