3L 4s: Difference between revisions

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== Theory ==

Mosh can be thought of as a midpoint between two diatonic scales which are two cyclic orders away from each other. For example, ~~LsLsLss~~ is the midpoint between ~~LsLLLsL~~ and ~~LLLsLLs~~. You can prove this by simple addition.

Mosh can be thought of as a midpoint between two diatonic scales which are two cyclic orders away from each other. For example, sLsLsLs is the midpoint between the Ionian (major, LLsLLLs) and Phrygian (sLLLsLL) modes. You can prove this by simple addition:

<pre>

2 1 2 2 2 1 2 (~~LsLLLsL~~)

2 2 1 2 2 2 1 (LLsLLLs)

+ 2 2 2 1 2 2 1 (~~LLLsLLs~~)

+ 1 2 2 2 1 2 2 (sLLLsLL)

= 4 3 4 3 4 3 3 (~~LsLsLss~~)

= 3 4 3 4 3 4 3 (sLsLsLs)

</pre>

The rest of the equivalencies are listed in [[#Proposed names]].

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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{{c}}) and two of them make a 3/2 (702{{c}}).

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

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

* [[Magic]], in which the generator is 5/4 (386{{c}}) and five of them make a 3/1 (1902{{c}}), though the step ratios in this range are very hard to the point of being lopsided.

== Tuning ranges ==

@@ Line 57: / Line 57: @@
 == Theory ==
-Mosh can be thought of as a midpoint between two diatonic scales which are two cyclic orders away from each other. For example, LsLsLss is the midpoint between LsLLLsL and LLLsLLs. You can prove this by simple addition.
+Mosh can be thought of as a midpoint between two diatonic scales which are two cyclic orders away from each other. For example, sLsLsLs is the midpoint between the Ionian (major, LLsLLLs) and Phrygian (sLLLsLL) modes. You can prove this by simple addition:
 <pre>
-1 2 2 2 1 2 (LsLLLsL)
+2 1 2 2 2 1 (LLsLLLs)
-+ 2 2 2 1 2 2 1 (LLLsLLs)
++ 1 2 2 2 1 2 2 (sLLLsLL)
-= 4 3 4 3 4 3 3 (LsLsLss)
+= 3 4 3 4 3 4 3 (sLsLsLs)
 </pre>
 The rest of the equivalencies are listed in [[#Proposed names]].
@@ Line 69: / Line 69: @@
 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{{c}}) and two of them make a 3/2 (702{{c}}).
+* [[Neutral third scales]], such as dicot, hemififth, and mohajira, in which the generator is a neutral third (around 350{{c}}) and two of them make a 3/2 (702{{c}}).
-* [[Magic]], in which the generator is 5/4 (386{{c}}) and 5 of them make a 3/1 (1902{{c}}).
+* [[Magic]], in which the generator is 5/4 (386{{c}}) and five of them make a 3/1 (1902{{c}}), though the step ratios in this range are very hard to the point of being lopsided.
 == Tuning ranges ==