User:Inthar/5L 3s: Difference between revisions

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21edo has the [[Step ratio|soft]] [[oneirotonic]] (5L 3s) MOS with generator 8\21; in addition to the [[naiadic]]s (457.14¢) and extremely sharp fifths (742.85¢) that generate it, it has neutral thirds (instead of major thirds as in [[13edo]] oneirotonic), neogothic minor thirds, and meantone-like diatonic semitones. The oneirofifths (4-step intervals) are more tritone-like than fifth-like, unlike in 13edo, although they do have a consonant, even JI-like quality to them. In terms of JI, it mainly approximates 5:9:11:13 (R-so8-Lon2-Pon4) and 16:23:30 (R-Lon5-Lo8). Importantly, the sharp fifth is now harmonically much more fifth-like than the flat fifth, unlike in [[13edo]] and harder tunings. Rather than squashed tertian triads, it may be preferable to use triads with sharp fifths, quartal harmony, stacks of seconds and thirds, third+sixth and third+seventh chords, and using the JI approximations (subsets of 5:9:11:13 (R-so8-Lon2-Pon4), 9:10:11:13 (R-Lon2-Lon3-Lon5), and 8:15:23 (R-Lon7-Lon5)).

34edo (semisoft) oneirotonic is broadly similar, except the small steps are more 12edo-like and less meantone-like~~, and it is a bit more optimized for the 5:9:11:13 approximation~~.

34edo (semisoft) oneirotonic is broadly similar, except the small steps are more 12edo-like and less meantone-like.

* sus24 non5: J-K-M, L-M-O, M-N-P, O-P-J, Q-J-L

~~Approximate low-complexity JI chords in the JKLMNOPQ = Ultharian mode:~~

* sus24 non5 addmin7: J-Q-K-M, M-L-N-P

* sus24 non5 ~~≈ 5:11:13, 10:11:13~~: J-K-M, L-M-O, M-N-P, O-P-J, Q-J-L

* sus24 non5 addmin7 ~~≈ 5:9:11:13~~: J-Q-K-M, M-L-N-P

* falling fifth addmaj7 ≈ 16:23:30: O-K-N, L-P-K, Q-M-P

* Falling Major Triad ~~≈ 9:11:13~~: Q-K-M, L-N-P

* Falling Major Triad: Q-K-M, L-N-P

* 16:23:29 (in 21edo): J-N-Q

Other chords:

* Quartal Tetrad ~~(≈ 10:11:13:17?)~~: Q-J-L-O, L-M-O-J, O-P-J-M, J-K-M-P, M-N-P-K

* Quartal Tetrad: Q-J-L-O, L-M-O-J, O-P-J-M, J-K-M-P, M-N-P-K

* Quartal Pentad: L-M-O-P-J, O-P-J-K-M, J-K-M-N-P, M-N-P-Q-K

* Falling Minor Triad ~~(≈ 11:13:16?)~~: J-L-N, O-Q-K

* Falling Minor Triad: J-L-N, O-Q-K

* squashed diminished: M-O-Q, P-J-L, K-M-O, N-P-J

Seconds, tritones and sevenths are consonances in addition to thirds and sixths. The naiadic is a semiconsonance. The fifth is fifth-like but is a dissonance.

Use R-mos3-mos5-mos7 sparingly in 21edo oneiro - it just sounds a little too much like a dissonant, unstable 12edo diminished 7th.

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 edo has the [[Step ratio|soft]] [[oneirotonic]] (5L 3s) MOS with generator 8\21; in addition to the [[naiadic]]s (457.14¢) and extremely sharp fifths (742.85¢) that generate it, it has neutral thirds (instead of major thirds as in [[13edo]] oneirotonic), neogothic minor thirds, and meantone-like diatonic semitones. The oneirofifths (4-step intervals) are more tritone-like than fifth-like, unlike in 13edo, although they do have a consonant, even JI-like quality to them. In terms of JI, it mainly approximates 5:9:11:13 (R-so8-Lon2-Pon4) and 16:23:30 (R-Lon5-Lo8). Importantly, the sharp fifth is now harmonically much more fifth-like than the flat fifth, unlike in [[13edo]] and harder tunings. Rather than squashed tertian triads, it may be preferable to use triads with sharp fifths, quartal harmony, stacks of seconds and thirds, third+sixth and third+seventh chords, and using the JI approximations (subsets of 5:9:11:13 (R-so8-Lon2-Pon4), 9:10:11:13 (R-Lon2-Lon3-Lon5), and 8:15:23 (R-Lon7-Lon5)).
-edo (semisoft) oneirotonic is broadly similar, except the small steps are more 12edo-like and less meantone-like, and it is a bit more optimized for the 5:9:11:13 approximation.
+edo (semisoft) oneirotonic is broadly similar, except the small steps are more 12edo-like and less meantone-like.
+* sus24 non5: J-K-M, L-M-O, M-N-P, O-P-J, Q-J-L
-Approximate low-complexity JI chords in the JKLMNOPQ = Ultharian mode:
+* sus24 non5 addmin7: J-Q-K-M, M-L-N-P
-* sus24 non5 ≈ 5:11:13, 10:11:13: J-K-M, L-M-O, M-N-P, O-P-J, Q-J-L
-* sus24 non5 addmin7 ≈ 5:9:11:13: J-Q-K-M, M-L-N-P
 * falling fifth addmaj7 ≈ 16:23:30: O-K-N, L-P-K, Q-M-P
-* Falling Major Triad ≈ 9:11:13: Q-K-M, L-N-P
+* Falling Major Triad: Q-K-M, L-N-P
 * 16:23:29 (in 21edo): J-N-Q
 Other chords:
-* Quartal Tetrad (≈ 10:11:13:17?): Q-J-L-O, L-M-O-J, O-P-J-M, J-K-M-P, M-N-P-K
+* Quartal Tetrad: Q-J-L-O, L-M-O-J, O-P-J-M, J-K-M-P, M-N-P-K
 * Quartal Pentad: L-M-O-P-J, O-P-J-K-M, J-K-M-N-P, M-N-P-Q-K
-* Falling Minor Triad (≈ 11:13:16?): J-L-N, O-Q-K
+* Falling Minor Triad: J-L-N, O-Q-K
 * squashed diminished: M-O-Q, P-J-L, K-M-O, N-P-J
+Seconds, tritones and sevenths are consonances in addition to thirds and sixths. The naiadic is a semiconsonance. The fifth is fifth-like but is a dissonance.
 Use R-mos3-mos5-mos7 sparingly in 21edo oneiro - it just sounds a little too much like a dissonant, unstable 12edo diminished 7th.