12L 5s: Difference between revisions

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'''12L 5s''' is the MOS pattern of the [[Pythagorean tuning|Pythagorean]]/[[Schismatic family|schismic]] enharmonic or mega-chromatic scale. In contrast to the [[5L 12s|superpyth enharmonic or mega-chromatic scale]], in which the enharmonic diesis (negative diminished second) is larger than the chromatic semitone, here the reverse is true: the enharmonic diesis is smaller than the chromatic semitone, 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 (494.118 cents) and 5\12 (500 cents).

This MOS separates its small steps by intervals of 3L-2L-3L-2L-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 does not become proper until you add 12 more notes to form the schismic 29-note scale).

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== Scale tree ==

Chroma-positive generator: 494.1176 cents (7\17) to 500 cents (5\12)

Chroma-negative generator: 700 cents (7\12) to 705.8824 cents (10\17)

{| class="wikitable center-all"

! colspan="6" | Generator

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 '''12L 5s''' is the MOS pattern of the [[Pythagorean tuning|Pythagorean]]/[[Schismatic family|schismic]] enharmonic or mega-chromatic scale. In contrast to the [[5L 12s|superpyth enharmonic or mega-chromatic scale]], in which the enharmonic diesis (negative diminished second) is larger than the chromatic semitone, here the reverse is true: the enharmonic diesis is smaller than the chromatic semitone, 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 (494.118 cents) and 5\12 (500 cents).
+This MOS separates its small steps by intervals of 3L-2L-3L-2L-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 does not become proper until you add 12 more notes to form the schismic 29-note scale).
@@ Line 40: / Line 40: @@
 == Scale tree ==
+Chroma-positive generator: 494.1176 cents (7\17) to 500 cents (5\12)
+Chroma-negative generator: 700 cents (7\12) to 705.8824 cents (10\17)
 {| class="wikitable center-all"
 ! colspan="6" | Generator