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| {{Infobox MOS}} | | {{Infobox MOS}} |
| {{MOS intro|Other Names=p-chromatic}} | | {{MOS intro|Other Names=p-chromatic}} |
| Temperaments that support this scale include [[Pythagorean tuning|Pythagorean]], [[Schismatic family|schismic]] (such as Helmholtz and Garibaldi), and [[superpyth]], with the Pythagorean and schismatic scales in particular being [[Rothenberg propriety|proper]]. Scales of this form are characterized by having a small step (or [[diatonic semitone]]) that is smaller than the [[chroma]] (or [[chromatic semitone]]).
| | 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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| == Modes == | | 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. |
| 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. | | |
| * 11|0 LsLsLssLsLss - Rat
| | == Scale properties == |
| * 10|1 LsLssLsLsLss - Ox
| | {{TAMNAMS use}} |
| * 9|2 LsLssLsLssLs - Tiger
| | |
| * 8|3 LssLsLsLssLs - Rabbit
| | === Intervals === |
| * 7|4 LssLsLssLsLs - Dragon
| | {{MOS intervals}} |
| * 6|5 sLsLsLssLsLs - Snake
| | |
| * 5|6 sLsLssLsLsLs - Horse
| | === Generator chain === |
| * 4|7 sLsLssLsLssL - Goat
| | {{MOS genchain}} |
| * 3|8 sLssLsLsLssL - Monkey
| | |
| * 2|9 sLssLsLssLsL - Rooster
| | === Modes === |
| * 1|10 ssLsLsLssLsL - Dog
| | {{MOS mode degrees}} |
| * 0|11 ssLsLssLsLsL - Pig
| | |
| | === Proposed names === |
| | 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. |
| | |
| | {{MOS modes |
| | | Mode Names= |
| | Rat $ |
| | Ox $ |
| | Tiger $ |
| | Rabbit $ |
| | Dragon $ |
| | Snake $ |
| | Horse $ |
| | Goat $ |
| | Monkey $ |
| | Rooster $ |
| | Dog $ |
| | Pig $ |
| | }} |
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| == Scales == | | == Scales == |
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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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| |-
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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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| | || || || 27\46 || || || 704.348 || 5 || 3 || 1.667 || [[Leapday]] / [[polypyth]]
| |
| |-
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| | || || || || || 64\109 || 704.587 || 12 || 7 || 1.714 || [[Leapweek]]
| |
| |-
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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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| | || || || || || 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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| |-
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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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| |-
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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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| |-
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| | || || || || || 35\59 || 711.864 || 9 || 2 || 4.500 ||
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| |-
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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]] |