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12L 5s: Difference between revisions

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TAMNAMS haven't endorsed a name for this scale; also it's commonly called an enharmonic scale so I add it
Line 6: Line 6:
| Paucitonic = 5
| Paucitonic = 5
| Pattern = LLLsLLsLLLsLLsLLs
| Pattern = LLLsLLsLLLsLLsLLs
| Name = Schismic mega-chromatic
}}
}}


'''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]].
'''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-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).
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).


== Modes ==
== Modes ==
Line 67: Line 66:
| || || 19\46 || || || || 495.652 || 3 || 2 || 1.500 ||  
| || || 19\46 || || || || 495.652 || 3 || 2 || 1.500 ||  
|-
|-
| || || || || || 69\167 || 495.808 || 11 || 7 || 1.571 || [[Leapday]] / [[Polypyth]]
| || || || || || 69\167 || 495.808 || 11 || 7 || 1.571 || [[Leapday]] / [[polypyth]]
|-
|-
| || || || || 50\121 || || 495.868 || 8 || 5 || 1.600 ||  
| || || || || 50\121 || || 495.868 || 8 || 5 || 1.600 ||  
|-
|-
| || || || || || 81\196 || 495.918 || 13 || 8 || 1.625 || Golden neogothic (Generator = 495.9044 cents)
| || || || || || 81\196 || 495.918 || 13 || 8 || 1.625 || Golden neogothic (495.9044¢)
|-
|-
| || || || 31\75 || || || 496.000 || 5 || 3 || 1.667 ||
| || || || 31\75 || || || 496.000 || 5 || 3 || 1.667 ||
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| || || || || 41\99 || || 496.970 || 7 || 3 || 2.333 || [[Undecental]]
| || || || || 41\99 || || 496.970 || 7 || 3 || 2.333 || [[Undecental]]
|-
|-
| || || || || || 70\169 || 497.041 || 12 || 5 || 2.400 || Argent tuning (Generator: 497.0563 cents)
| || || || || || 70\169 || 497.041 || 12 || 5 || 2.400 || Argent tuning (497.0563¢)
|-
|-
| || || || 29\70 || || || 497.143 || 5 || 2 || 2.500 ||
| || || || 29\70 || || || 497.143 || 5 || 2 || 2.500 ||
|-
|-
| || || || || || 75\181 || 497.238 || 13 || 5 || 2.600 || Unnamed golden tuning (Generator: 497.2540 cents)
| || || || || || 75\181 || 497.238 || 13 || 5 || 2.600 || Unnamed golden tuning (497.2540¢)
|-
|-
| || || || || 46\111 || || 497.297 || 8 || 3 || 2.667 ||
| || || || || 46\111 || || 497.297 || 8 || 3 || 2.667 ||
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| || || || || || 63\152 || 497.368 || 11 || 4 || 2.750 || [[Kwai]]
| || || || || || 63\152 || 497.368 || 11 || 4 || 2.750 || [[Kwai]]
|-
|-
| || || 17\41 || || || || 497.561 || 3 || 1 || 3.000 || [[Garibaldi]] / [[Andromeda]]
| || || 17\41 || || || || 497.561 || 3 || 1 || 3.000 || [[Garibaldi]] / [[andromeda]]
|-
|-
| || || || || || 56\135 || 497.778 || 10 || 3 || 3.333 ||
| || || || || || 56\135 || 497.778 || 10 || 3 || 3.333 ||
|-
|-
| || || || || 39\94 || || 497.872 || 7 || 2 || 3.500 || Garibaldi / [[Cassandra]]
| || || || || 39\94 || || 497.872 || 7 || 2 || 3.500 || Garibaldi / [[cassandra]]
|-
|-
| || || || || || 61\147 || 497.959 || 11 || 3 || 3.667 ||
| || || || || || 61\147 || 497.959 || 11 || 3 || 3.667 ||
|-
|-
| || || || 22\53 || || || 498.113 || 4 || 1 || 4.000 || Garibaldi / [[Helenus]] / [[Pythagorean tuning|Pythagorean]]
| || || || 22\53 || || || 498.113 || 4 || 1 || 4.000 || Garibaldi / [[helenus]], [[Pythagorean tuning]] (498.0450¢)
|-
|-
| || || || || || 49\118 || 498.305 || 9 || 2 || 4.500 || [[Pontiac]]
| || || || || || 49\118 || 498.305 || 9 || 2 || 4.500 || [[Pontiac]]
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