12L 5s: Difference between revisions

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'''12L 5s''' is the MOS pattern of the [[Pythagorean tuning|Pythagorean]]/[[~~Garibaldi temperament~~|~~Helmholtz/Garibaldi~~]] mega-chromatic scale. In contrast to the [[5L 12s|superpyth mega-chromatic scale]], in which mega-chromatic semitones (negative diminished seconds) are larger than chromatic semitones, here the reverse is true: mega-chromatic semitones are smaller than chromatic semitones, so the [[5L 7s|diatonic scale]] subset is actually [[Rothenberg propriety|proper]].

'''12L 5s''' is the MOS pattern of the [[Pythagorean tuning|Pythagorean]]/[[Schismatic family|schismic]] mega-chromatic scale. In contrast to the [[5L 12s|superpyth mega-chromatic scale]], in which mega-chromatic semitones (negative diminished seconds) are larger than chromatic semitones, here the reverse is true: mega-chromatic semitones are smaller than chromatic semitones, so the [[5L 7s|diatonic scale]] subset is actually [[Rothenberg propriety|proper]].

This MOS separates its small steps by intervals of 3L-2L-2L-3L-2L. Its major third of -4 generators approximates an interval between [[24/19]] and [[32/25]], thus its generator is a perfect fourth between 7\17 (494.~~412~~ cents) and 5\12 (500 cents).

This MOS separates its small steps by intervals of 3L-2L-2L-3L-2L. Its major third of -4 generators approximates an interval between [[24/19]] and [[32/25]], thus its generator is a perfect fourth between 7\17 (494.118 cents) and 5\12 (500 cents).

The leapday/leapweek version is proper, but the Pythagorean/schismic version is improper (it doesn't become proper until you add 12 more notes to form the schismic 29-note scale).

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! Comments

|-

| 7\17 || || || || || || 494.~~412~~ || 1 || 1 || 1.000 ||

| 7\17 || || || || || || 494.118 || 1 || 1 || 1.000 ||

|-

| || || || || || 40\97 || 494.845 || 6 || 5 || 1.200 ||

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| || || || || || 61\147 || 497.959 || 11 || 3 || 3.667 ||

|-

| || || || 22\53 || || || 498.113 || 4 || 1 || 4.000 || Garibaldi / [[Helenus]] / [[Pythagorean]]

| || || || 22\53 || || || 498.113 || 4 || 1 || 4.000 || Garibaldi / [[Helenus]] / [[Pythagorean tuning|Pythagorean]]

|-

| || || || || || 49\118 || 498.305 || 9 || 2 || 4.500 || [[Pontiac]]

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 }}
-'''12L 5s''' is the MOS pattern of the [[Pythagorean tuning|Pythagorean]]/[[Garibaldi temperament|Helmholtz/Garibaldi]] mega-chromatic scale. In contrast to the [[5L 12s|superpyth mega-chromatic scale]], in which mega-chromatic semitones (negative diminished seconds) are larger than chromatic semitones, here the reverse is true: mega-chromatic semitones are smaller than chromatic semitones, so the [[5L 7s|diatonic scale]] subset is actually [[Rothenberg propriety|proper]].
+'''12L 5s''' is the MOS pattern of the [[Pythagorean tuning|Pythagorean]]/[[Schismatic family|schismic]] mega-chromatic scale. In contrast to the [[5L 12s|superpyth mega-chromatic scale]], in which mega-chromatic semitones (negative diminished seconds) are larger than chromatic semitones, here the reverse is true: mega-chromatic semitones are smaller than chromatic semitones, so the [[5L 7s|diatonic scale]] subset is actually [[Rothenberg propriety|proper]].
-This MOS separates its small steps by intervals of 3L-2L-2L-3L-2L. Its major third of -4 generators approximates an interval between [[24/19]] and [[32/25]], thus its generator is a perfect fourth between 7\17 (494.412 cents) and 5\12 (500 cents).
+This MOS separates its small steps by intervals of 3L-2L-2L-3L-2L. Its major third of -4 generators approximates an interval between [[24/19]] and [[32/25]], thus its generator is a perfect fourth between 7\17 (494.118 cents) and 5\12 (500 cents).
 The leapday/leapweek version is proper, but the Pythagorean/schismic version is improper (it doesn't become proper until you add 12 more notes to form the schismic 29-note scale).
@@ Line 49: / Line 49: @@
 ! Comments
 |-
-| 7\17 || || || || || || 494.412 || 1 || 1 || 1.000 ||
+| 7\17 || || || || || || 494.118 || 1 || 1 || 1.000 ||
 |-
 | || || || || || 40\97 || 494.845 || 6 || 5 || 1.200 ||
@@ Line 105: / Line 105: @@
 | || || || || || 61\147 || 497.959 || 11 || 3 || 3.667 ||
 |-
-| || || || 22\53 || || || 498.113 || 4 || 1 || 4.000 || Garibaldi / [[Helenus]] / [[Pythagorean]]
+| || || || 22\53 || || || 498.113 || 4 || 1 || 4.000 || Garibaldi / [[Helenus]] / [[Pythagorean tuning|Pythagorean]]
 |-
 | || || || || || 49\118 || 498.305 || 9 || 2 || 4.500 || [[Pontiac]]