User:Overthink/Neutral scale theory: Difference between revisions

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Neutral scales are generated by a neutral third of around 350 cents, which exists in 17edo, 24edo, and many other tunings. The generator can be taken to represent [[11/9]], and two generators reach [[3/2]], tempering out the comma [[243/242]]. This generator leads to [[MOS]]es of size 4, 7, 10, 17, etc. Here we will mainly be considering the 7-note [[3L 4s]] and 10-note [[7L 3s]] MOSes.

''Note: Similar theory can be used in the 2.3.13 temperament tempering out 512/507.''

== 3L 4s (mosh) ==

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This scale is in the [[2.3.11 subgroup]], with the fundamental otonal consonance being [[8:9:11:12]] (or one of its different voicings), which in our scale is P1-M2-M4-M5. A different construction, Root-2nd-4th-5th, is now needed. The utonal inverse of 8:9:11:12 is 1/(8:9:11:12) = [[66:72:88:99]], or P1-m2-m4-M5. The otonal 8:9:11:12 chord occurs on F and A, and the utonal 1/(8:9:11:12) chord occurs on E and G. Neither chord occurs on C, B, or D, with a P1-M2-m4-M5 cent chord on C, and a P1-m2-m4-m5 chord on B and D. We need names for these chords, and once again we can borrow from diatonic:

''~~Note~~: This is not the best construction. Chords are better constructed as a chain of three fourths (4/3 or 11/8) or fifths (3/2 or 16/11).''

''Rewrite: This is not the best construction. Chords are better constructed as a chain of three fourths (4/3 or 11/8) or fifths (3/2 or 16/11).''

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@@ Line 1: / Line 1: @@
 Neutral scales are generated by a neutral third of around 350 cents, which exists in 17edo, 24edo, and many other tunings. The generator can be taken to represent [[11/9]], and two generators reach [[3/2]], tempering out the comma [[243/242]]. This generator leads to [[MOS]]es of size 4, 7, 10, 17, etc. Here we will mainly be considering the 7-note [[3L 4s]] and 10-note [[7L 3s]] MOSes.
+''Note: Similar theory can be used in the 2.3.13 temperament tempering out 512/507.''
 == 3L 4s (mosh) ==
@@ Line 75: / Line 77: @@
 This scale is in the [[2.3.11 subgroup]], with the fundamental otonal consonance being [[8:9:11:12]] (or one of its different voicings), which in our scale is P1-M2-M4-M5. A different construction, Root-2nd-4th-5th, is now needed. The utonal inverse of 8:9:11:12 is 1/(8:9:11:12) = [[66:72:88:99]], or P1-m2-m4-M5. The otonal 8:9:11:12 chord occurs on F and A, and the utonal 1/(8:9:11:12) chord occurs on E and G. Neither chord occurs on C, B, or D, with a P1-M2-m4-M5 cent chord on C, and a P1-m2-m4-m5 chord on B and D. We need names for these chords, and once again we can borrow from diatonic:
-''Note: This is not the best construction. Chords are better constructed as a chain of three fourths (4/3 or 11/8) or fifths (3/2 or 16/11).''
+''Rewrite: This is not the best construction. Chords are better constructed as a chain of three fourths (4/3 or 11/8) or fifths (3/2 or 16/11).''
 {| class="wikitable"