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| {{Infobox MOS}} | | {{Infobox MOS}} |
| | {{MOS intro|Other Names=p-chromatic}} |
| | 5L 7s represents the chromatic scales of [[Pythagorean tuning|Pythagorean]]/[[schismic]] and [[superpyth]], the former being [[Rothenberg propriety|proper]] but the latter improper until expanded by 5 more notes, producing Superpyth[17]. Such scales are characterized by having a small step ([[diatonic semitone]]) that is smaller than the [[chroma]] ([[chromatic semitone]]), the reverse of [[7L 5s]]. |
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| '''5L 7s''' is the MOS pattern of the [[Pythagorean tuning|Pythagorean]]/[[Schismatic family|schismic]] chromatic scale, and also the [[superpyth]] chromatic scale. In contrast to the [[7L 5s|meantone chromatic scale]], in which the diatonic semitone is larger than the chromatic semitone, here the reverse is true: the diatonic semitone is smaller than the chromatic semitone, so the [[5L 2s|diatonic scale]] subset is actually [[Rothenberg propriety|improper]].
| | The two distinct harmonic entropy minima are, on the one hand, scales very close to Pythagorean tuning or the schismatic temperament, and on the other hand, the simpler and less accurate temperament known as superpyth in which 64/63 is tempered out. |
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| The two distinct harmonic entropy minima with this MOS pattern are, on the one hand, scales very close to Pythagorean such that [[64/63]] is not tempered out, such as the schismatic temperaments known as Helmholtz and Garibaldi, and on the other hand, the much simpler and less accurate scale known as superpyth in which 64/63 is tempered out.
| | == Scale properties == |
| | {{TAMNAMS use}} |
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| The Pythagorean/schismatic version is proper, but the superpyth version is improper (it does not become proper until you add 5 more notes to form the superpyth enharmonic scale, superpyth[17]).
| | === Intervals === |
| | {{MOS intervals}} |
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| == Modes == | | === Generator chain === |
| * 11|0 LsLsLssLsLss
| | {{MOS genchain}} |
| * 10|1 LsLssLsLsLss
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| * 9|2 LsLssLsLssLs
| | === Modes === |
| * 8|3 LssLsLsLssLs
| | {{MOS mode degrees}} |
| * 7|4 LssLsLssLsLs
| | |
| * 6|5 sLsLsLssLsLs
| | === Proposed names === |
| * 5|6 sLsLssLsLsLs
| | The modes are named by [[Eliora]] after Chinese zodiac animals. 5L 7s is the opposite mos to [[7L 5s]], named after a Western concept, Gregorian months, therefore this mos scale has Eastern nomenclature. Furthermore, 12edo (equalized tuning of this MOS) was independently discovered in China. |
| * 4|7 sLsLssLsLssL
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| * 3|8 sLssLsLsLssL
| | {{MOS modes |
| * 2|9 sLssLsLssLsL
| | | Mode Names= |
| * 1|10 ssLsLsLssLsL
| | Rat $ |
| * 0|11 ssLsLssLsLsL
| | Ox $ |
| | Tiger $ |
| | Rabbit $ |
| | Dragon $ |
| | Snake $ |
| | Horse $ |
| | Goat $ |
| | Monkey $ |
| | Rooster $ |
| | Dog $ |
| | Pig $ |
| | }} |
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| == Scales == | | == Scales == |
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| * [[Garibaldi12]] – 94edo tuning | | * [[Garibaldi12]] – 94edo tuning |
| * [[Cotoneum12]] – 217edo tuning | | * [[Cotoneum12]] – 217edo tuning |
| | * [[Edson12]] – 29edo tuning |
| * [[Pepperoni12]] – 271edo tuning | | * [[Pepperoni12]] – 271edo tuning |
| * [[Supra12]] – 56edo tuning | | * [[Supra12]] – 56edo tuning |
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| == Scale tree == | | == Scale tree == |
| Generator ranges:
| | {{MOS tuning spectrum |
| * Chroma-positive generator: 700 cents (7\12) to 720 cents (3\5)
| | | 6/5 = [[Photia]], ↑ [[grackle]] |
| * Chroma-negative generator: 480 cents (2\5) to 500 cents (5\12)
| | | 5/4 = [[Helmholtz (temperament)|Helmholtz]], [[Pythagorean tuning]] (701.955{{c}}) |
| | | | 9/7 = [[Garibaldi]] / [[cassandra]] |
| {| class="wikitable center-all"
| | | 4/3 = Garibaldi / [[andromeda]] |
| ! colspan="6" | Generator
| | | 11/8 = [[Kwai]] |
| ! Cents
| | | 10/7 = [[Undecental]], argent tuning (702.944{{c}}) |
| ! L
| | | 3/2 = [[Edson]] |
| ! s
| | | 13/8 = [[Polypyth]], golden neogothic (704.096{{c}}) |
| ! L/s
| | | 5/3 = [[Leapday]] |
| ! Comments
| | | 12/7 = [[Leapweek]] |
| |-
| | | 7/3 = [[Supra]] |
| | 7\12 || || || || || || 700.000 || 1 || 1 || 1.000 ||
| | | 13/5 = Golden supra (708.054{{c}}) |
| |-
| | | 8/3 = [[Quasisuper]] / [[quasisupra]] |
| | || || || || || 38\65 || 701.539 || 6 || 5 || 1.200 || [[Photia]] / [[pontiac]] / [[grackle]]↑
| | | 3/1 = [[Suprapyth]] |
| |-
| | | 7/2 = [[Superpyth]] |
| | || || || || 31\53 || || 701.887 || 5 || 4 || 1.250 || [[Helmholtz]], [[Pythagorean tuning]] (701.9550¢)
| | | 6/1 = ↓ [[Oceanfront]] / [[ultrapyth]] |
| |-
| | }} |
| | || || || || || 55\94 || 702.128 || 9 || 7 || 1.286 || [[Garibaldi]] / [[cassandra]]
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| |-
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| | || || || 24\41 || || || 702.409 || 4 || 3 || 1.333 || Garibaldi / [[andromeda]]
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| | || || || || || 65\111 || 702.703 || 11 || 8 || 1.375 || [[Kwai]]
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| |-
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| | || || || || 41\70 || || 702.857 || 7 || 5 || 1.400 ||
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| |-
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| | || || || || || 58\99 || 703.030 || 10 || 7 || 1.428 || [[Undecental]]
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| |-
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| | || || 17\29 || || || || 703.448 || 3 || 2 || 1.500 || [[Edson]]
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| |-
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| | || || || || || 61\104 || 703.846 || 11 || 7 || 1.571 ||
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| |-
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| | || || || || 44\75 || || 704.000 || 8 || 5 || 1.600 ||
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| |-
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| | || || || || || 71\121 || 704.132 || 13 || 8 || 1.625 || Golden neogothic (704.0956¢)
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| |-
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| | || || || 27\46 || || || 704.348 || 5 || 3 || 1.667 || [[Leapday]] / [[polypyth]]
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| |-
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| | || || || || || 64\109 || 704.587 || 12 || 7 || 1.714 || [[Leapweek]]
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| |-
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| | || || || || 37\63 || || 704.762 || 7 || 4 || 1.750 ||
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| |-
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| | || || || || || 47\80 || 705.000 || 9 || 5 || 1.800 ||
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| |-
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| | || 10\17 || || || || || 705.882 || 2 || 1 || 2.000 || Basic p-chromatic <br>(Generators smaller than this are proper)
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| |-
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| | || || || || || 43\73 || 706.849 || 9 || 4 || 2.250 ||
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| |-
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| | || || || || 33\56 || || 707.143 || 7 || 3 || 2.333 || [[Supra]]
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| |-
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| | || || || || || 56\95 || 707.368 || 12 || 5 || 2.400 ||
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| |-
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| | || || || 23\39 || || || 707.692 || 5 || 2 || 2.500 ||
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| |-
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| | || || || || || 59\100 || 708.000 || 13 || 5 || 2.600 || Golden supra (708.0539¢)
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| |-
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| | || || || || 36\61 || || 708.197 || 8 || 3 || 2.667 || [[Quasisuper]] / [[quasisupra]]
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| | || || || || || 49\83 || 708.434 || 11 || 4 || 2.750 ||
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| |-
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| | || || 13\22 || || || || 709.091 || 3 || 1 || 3.000 || [[Suprapyth]]
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| |-
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| | || || || || || 42\71 || 709.859 || 10 || 3 || 3.333 ||
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| | || || || || 29\49 || || 710.204 || 7 || 2 || 3.500 || [[Superpyth]]
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| |-
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| | || || || || || 45\76 || 710.526 || 11 || 3 || 3.667 ||
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| |-
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| | || || || 16\27 || || || 711.111 || 4 || 1 || 4.000 ||
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| | || || || || || 35\59 || 711.864 || 9 || 2 || 4.500 ||
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| | || || || || 19\32 || || 712.500 || 5 || 1 || 5.000 ||
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| |-
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| | || || || || || 22\37 || 713.514 || 6 || 1 || 6.000 || [[Oceanfront]]↓ / [[ultrapyth]]↓
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| |-
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| | 3\5 || || || || || || 720.000 || 1 || 0 || → inf ||
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| |}
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| [[Category:12-tone scales]] | | [[Category:12-tone scales]] |
| [[Category:P-chromatic| ]] <!-- main article --> | | [[Category:P-chromatic| ]]<!-- main article --> |
| [[Category:Chromatic scales]] | | [[Category:Chromatic scales]] |