3L 4s: Difference between revisions

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There are two notable harmonic entropy minima:

* [[Neutral third scales]], such as dicot, hemififth, and mohajira, in which the generator is a neutral 3rd (around ~~350¢~~) and two of them make a 3/2 (~~702¢~~).

* [[Neutral third scales]], such as dicot, hemififth, and mohajira, in which the generator is a neutral 3rd (around 350{{c}}) and two of them make a 3/2 (702{{c}}).

* [[Magic]], in which the generator is 5/4 (~~386¢~~) and 5 of them make a 3/1 (~~1902¢~~).

* [[Magic]], in which the generator is 5/4 (386{{c}}) and 5 of them make a 3/1 (1902{{c}}).

== Tuning ranges ==

3\10 represents a dividing line between "neutral third scales" on the bottom (eg. 17edo neutral scale), and scales generated by submajor and major thirds at the top, with 10edo standing in between. The neutral third scales, after three more generators, make MOS [[7L 3s]] (dicoid); the other scales make MOS [[3L 7s]] (sephiroid).

3\10 represents a dividing line between "neutral third scales" on the bottom (eg. 17edo neutral scale), and scales generated by submajor and major thirds at the top, with 10edo standing in between. The neutral third scales, after three more generators, make MOS [[7L 3s]] (dicoid); the other scales make MOS [[3L 7s]] (sephiroid).

In dicoid, the generators are all "neutral thirds," and two of them make an approximation of the "perfect fifth." Additionally, the L of the scale is somewhere around a "whole tone" and the s of the scale is somewhere around a "neutral tone".

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=== Ultrasoft ===

[[Ultrasoft]] mosh tunings have step ratios that are less than 4:3, which implies a generator flatter than 7\24 = ~~350¢~~.

[[Ultrasoft]] mosh tunings have step ratios that are less than 4:3, which implies a generator flatter than {{nowrap|7\24 {{=}} 350{{c}}}}.

Ultrasoft mosh can be considered "meantone mosh". This is because the large step is a "meantone" in these tunings, somewhere between near-10/9 (as in [[38edo]]) and near-9/8 (as in [[24edo]]).

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=== Ultrahard ===

Ultra tunings of mosh have a step ratio greater than 4/1, implying a generator sharper than 5\16 = ~~375¢~~. The generator is thus near a [[5/4]] major third, five of which add up to an approximate [[3/1]]. The 7-note MOS only has two perfect fifths, so extending the chain to bigger MOSes, such as the [[3L 7s]] 10-note MOS, is suggested for getting 5-limit harmony.

Ultra tunings of mosh have a step ratio greater than 4/1, implying a generator sharper than {{nowrap|5\16 {{=}} 375{{c}}}}. The generator is thus near a [[5/4]] major third, five of which add up to an approximate [[3/1]]. The 7-note MOS only has two perfect fifths, so extending the chain to bigger MOSes, such as the [[3L 7s]] 10-note MOS, is suggested for getting 5-limit harmony.

This range is associated with [[magic]] temperament.

@@ Line 30: / Line 30: @@
 There are two notable harmonic entropy minima:
-* [[Neutral third scales]], such as dicot, hemififth, and mohajira, in which the generator is a neutral 3rd (around 350¢) and two of them make a 3/2 (702¢).
+* [[Neutral third scales]], such as dicot, hemififth, and mohajira, in which the generator is a neutral 3rd (around 350{{c}}) and two of them make a 3/2 (702{{c}}).
-* [[Magic]], in which the generator is 5/4 (386¢) and 5 of them make a 3/1 (1902¢).
+* [[Magic]], in which the generator is 5/4 (386{{c}}) and 5 of them make a 3/1 (1902{{c}}).
 == Tuning ranges ==
-\10 represents a dividing line between "neutral third scales" on the bottom (eg. 17edo neutral scale), and scales generated by submajor and major thirds at the top, with 10edo standing in between. The neutral third scales, after three more generators, make MOS [[7L 3s]] (dicoid); the other scales make MOS [[3L 7s]] (sephiroid).
+\10 represents a dividing line between "neutral third scales" on the bottom (eg. 17edo neutral scale), and scales generated by submajor and major thirds at the top, with 10edo standing in between. The neutral third scales, after three more generators, make MOS [[7L&nbsp;3s]] (dicoid); the other scales make MOS [[3L&nbsp;7s]] (sephiroid).
 In dicoid, the generators are all "neutral thirds," and two of them make an approximation of the "perfect fifth." Additionally, the L of the scale is somewhere around a "whole tone" and the s of the scale is somewhere around a "neutral tone".
@@ Line 41: / Line 41: @@
 === Ultrasoft ===
-[[Ultrasoft]] mosh tunings have step ratios that are less than 4:3, which implies a generator flatter than 7\24 = 350¢.
+[[Ultrasoft]] mosh tunings have step ratios that are less than 4:3, which implies a generator flatter than {{nowrap|7\24 {{=}} 350{{c}}}}.
 Ultrasoft mosh can be considered "meantone mosh". This is because the large step is a "meantone" in these tunings, somewhere between near-10/9 (as in [[38edo]]) and near-9/8 (as in [[24edo]]).
@@ Line 150: / Line 150: @@
 === Ultrahard ===
-Ultra tunings of mosh have a step ratio greater than 4/1, implying a generator sharper than 5\16 = 375¢. The generator is thus near a [[5/4]] major third, five of which add up to an approximate [[3/1]]. The 7-note MOS only has two perfect fifths, so extending the chain to bigger MOSes, such as the [[3L 7s]] 10-note MOS, is suggested for getting 5-limit harmony.
+Ultra tunings of mosh have a step ratio greater than 4/1, implying a generator sharper than {{nowrap|5\16 {{=}} 375{{c}}}}. The generator is thus near a [[5/4]] major third, five of which add up to an approximate [[3/1]]. The 7-note MOS only has two perfect fifths, so extending the chain to bigger MOSes, such as the [[3L&nbsp;7s]] 10-note MOS, is suggested for getting 5-limit harmony.
 This range is associated with [[magic]] temperament.