3L 4s: Difference between revisions

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 == Tuning ranges ==
+Broadly speaking, the entire tuning range from minisoft to ultrasoft, which implies a generator flatter than 3\10 = 360¢, makes "neutral third" scales, where two generators can be interpreted a 3/2.
 === Ultrasoft ===
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 The sizes of the generator, large step and small step of mosh are as follows in various ultrasoft mosh tunings.
-{| class="wikitable right-2 right-3 right-4 right-5"
+{| class="wikitable right-2 right-3 right-4 right-5 right-6 right-7"
 |-
 !
@@ Line 66: / Line 68: @@
 | [[11/10]], [[12/11]]
 |}
-\10 represents a dividing line between "neutral third scales" on the bottom (eg. [[17edo_neutral_scale|17edo neutral scale]]), and scales generated by submajor and major thirds at the top, with [[10edo|10edo]] standing in between. the neutral third scales, after three more generators, make MOS [[7L_3s|7L 3s]] (dicotonic); the other scales make MOS [[3L_7s|3L 7s]] (sephiroid).
-In dicotonic, 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".
+=== Quasisoft ===
+Quasisoft tunings of mosh have a step ratio between 3/2 and 5/3, implying a generator sharper than 5\17 = 352.94¢ and flatter than 8\27 = 355.56¢.
-In sephirotonic, the generators are major thirds (including some very flat ones), and two generators are definitely sharp of a perfect fifth. L ranges from a "supermajor second" to a "major third" and s is a "semitone" or smaller.
+The large step is a sharper major second in these tunings than in ultrasoft tunings. These tunings could be considered "parapyth mosh" or "archy mosh", in analogy to ultrasoft mosh being meantone mosh.
+{| class="wikitable right-2 right-3 right-4 right-5"
+|-
+!
+! [[17edo]]
+! [[27edo]]
+! [[44edo]]
+|-
+| generator (g)
+| 5\17, 352.94
+| 8\27, 355.56
+| 13\44, 354.55
+|-
+| L (4g - octave)
+| 3\17, 211.76
+| 5\27, 222.22
+| 8\44, 218.18
+|-
+| s (octave - 3g)
+| 2\17, 141.18
+| 3\27, 133.33
+| 5\44, 137.37
+|}
+=== 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.
+{| class="wikitable right-2 right-3 right-4 right-5 right-6"
+|-
+!
+! [[16edo]]
+! [[19edo]]
+! [[22edo]]
+! [[41edo]]
+! JI intervals represented
+|-
+| generator (g)
+| 5\16, 375.00
+| 6\19, 378.95
+| 7\22, 381.82
+| 13\41, 380.49
+| 5/4
+|-
+| L (4g - octave)
+| 4\16, 300.00
+| 5\19, 315.79
+| 6\22, 327.27
+| 11\41, 321.95
+| 6/5
+|-
+| s (octave - 3g)
+| 1\16, 75.00
+| 1\19, 63.16
+| 1\22, 54.54
+| 2\41, 58.54
+| 25/24
+|}
 == Modes ==