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| {{Infobox MOS | | {{Infobox MOS}} |
| | Periods = 1 | | {{MOS intro|Other Names=p-enharmonic}} |
| | nLargeSteps = 12 | | Temperaments supported by this scale include those under the [[Pythagorean tuning|Pythagorean]] and [[Schismatic family|schismic]] families, characterized by a diesis (the difference between a large step and two small steps) that is smaller than the [[chroma]]. |
| | nSmallSteps = 5
| | |
| | Equalized = 7
| | 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). |
| | Collapsed = 5
| | |
| | Pattern = LLLsLLsLLLsLLsLLs
| | == Scale properties == |
| }} | | {{TAMNAMS use}} |
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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 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]].
| | === Intervals === |
| | {{MOS intervals}} |
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| 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).
| | === Generator chain === |
| | {{MOS genchain}} |
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| 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 === |
| | {{MOS mode degrees}} |
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| == Modes == | | === Proposed tuning-specific names === |
| * 16|0 LLLsLLsLLLsLLsLLs
| | [[Declan Paul Boushy]] has proposed names for these modes corresponding to step ratios [[Subaru scale|3:1]] and [[Tanegashima scale|4:1]]. |
| * 15|1 LLLsLLsLLsLLLsLLs
| | {{todo|add etymology|add Template:MOS modes and annotate each row using Boushy’s names}} |
| * 14|2 LLsLLLsLLsLLLsLLs
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| * 13|3 LLsLLLsLLsLLsLLLs
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| * 12|4 LLsLLsLLLsLLsLLLs
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| * 11|5 LLsLLsLLLsLLsLLsL
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| * 10|6 LLsLLsLLsLLLsLLsL
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| * 9|7 LsLLLsLLsLLLsLLsL
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| * 8|8 LsLLLsLLsLLsLLLsL
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| * 7|9 LsLLsLLLsLLsLLLsL
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| * 6|10 LsLLsLLLsLLsLLsLL
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| * 5|11 LsLLsLLsLLLsLLsLL
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| * 4|12 sLLLsLLsLLLsLLsLL
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| * 3|13 sLLLsLLsLLsLLLsLL
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| * 2|14 sLLsLLLsLLsLLLsLL
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| * 1|15 sLLsLLLsLLsLLsLLL
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| * 0|16 sLLsLLsLLLsLLsLLL
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| == Scales == | | == Scales == |
| | * [[Edson17]] – 29edo tuning |
| | * [[Subaru scale]] – 41edo tuning |
| | * [[Cotoneum17]] – 217edo tuning |
| | * [[Garibaldi17]] – 94edo tuning |
| * [[Pythagorean17]] – Pythagorean tuning | | * [[Pythagorean17]] – Pythagorean tuning |
| | * [[Tanegashima scale]] – 53edo tuning |
| * [[Nestoria17]] – 171edo tuning | | * [[Nestoria17]] – 171edo tuning |
| * [[Cotoneum17]] – 217edo tuning
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| * [[Garibaldi17]] – 94edo tuning
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| == Scale tree == | | == Scale tree == |
| Generator ranges:
| | {{MOS tuning spectrum |
| * Chroma-positive generator: 494.1176 cents (7\17) to 500 cents (5\12)
| | | 4/3 = [[Leapfrog]] |
| * Chroma-negative generator: 700 cents (7\12) to 705.8824 cents (10\17)
| | | 7/5 = [[Leapweek]] |
| | | | 3/2 = [[Leapday]] |
| {| class="wikitable center-all" | | | 11/7 = [[Polypyth]] |
| ! colspan="6" | Generator
| | | 13/8 = Golden neogothic (495.904{{c}}) |
| ! Cents
| | | 7/3 = [[Undecental]] |
| ! L
| | | 12/5 = Argent tuning (497.056{{c}}) |
| ! s
| | | 13/5 = Unnamed golden tuning (497.254{{c}}) |
| ! L/s
| | | 11/4 = [[Kwai]] |
| ! Comments
| | | 3/1 = [[Garibaldi]] / [[andromeda]] |
| |-
| | | 7/2 = Garibaldi / [[cassandra]] |
| | 7\17 || || || || || || 494.118 || 1 || 1 || 1.000 ||
| | | 4/1 = Garibaldi / [[helenus]], Pythagorean tuning (498.045{{c}}) |
| |-
| | | 9/2 = [[Pontiac]] |
| | || || || || || 40\97 || 494.845 || 6 || 5 || 1.200 ||
| | | 5/1 = [[Photia]] |
| |-
| | | 6/1 = ↓ [[Grackle]], ↓↓ [[gracecordial]] |
| | || || || || 33\80 || || 495.000 || 5 || 4 || 1.250 ||
| | }} |
| |-
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| | || || || || || 59\143 || 495.105 || 9 || 7 || 1.286 ||
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| |-
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| | || || || 26\63 || || || 495.238 || 4 || 3 || 1.333 || [[Leapfrog]]
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| |-
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| | || || || || || 71\172 || 495.349 || 11 || 8 || 1.375 ||
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| |-
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| | || || || || 45\109 || || 495.413 || 7 || 5 || 1.400 || [[Leapweek]]
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| |-
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| | || || || || || 64\155 || 495.484 || 10 || 7 || 1.428 ||
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| |-
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| | || || 19\46 || || || || 495.652 || 3 || 2 || 1.500 ||
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| |-
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| | || || || || || 69\167 || 495.808 || 11 || 7 || 1.571 || [[Leapday]] / [[polypyth]]
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| |-
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| | || || || || 50\121 || || 495.868 || 8 || 5 || 1.600 ||
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| |-
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| | || || || || || 81\196 || 495.918 || 13 || 8 || 1.625 || Golden neogothic (495.9044¢)
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| |-
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| | || || || 31\75 || || || 496.000 || 5 || 3 || 1.667 ||
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| |-
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| | || || || || || 74\179 || 496.089 || 12 || 7 || 1.714 ||
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| |-
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| | || || || || 43\104 || || 496.154 || 7 || 4 || 1.750 ||
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| |-
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| | || || || || || 55\133 || 496.241 || 9 || 5 || 1.800 ||
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| |-
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| | || 12\29 || || || || || 496.552 || 2 || 1 || 2.000 || Basic 12L 5s <br>(Generators smaller than this are proper)
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| |-
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| | || || || || || 53\128 || 496.875 || 9 || 4 || 2.250 ||
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| |-
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| | || || || || 41\99 || || 496.970 || 7 || 3 || 2.333 || [[Undecental]]
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| |-
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| | || || || || || 70\169 || 497.041 || 12 || 5 || 2.400 || Argent tuning (497.0563¢)
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| |-
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| | || || || 29\70 || || || 497.143 || 5 || 2 || 2.500 ||
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| |-
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| | || || || || || 75\181 || 497.238 || 13 || 5 || 2.600 || Unnamed golden tuning (497.2540¢)
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| |-
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| | || || || || 46\111 || || 497.297 || 8 || 3 || 2.667 ||
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| |-
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| | || || || || || 63\152 || 497.368 || 11 || 4 || 2.750 || [[Kwai]]
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| |-
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| | || || 17\41 || || || || 497.561 || 3 || 1 || 3.000 || [[Garibaldi]] / [[andromeda]]
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| |-
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| | || || || || || 56\135 || 497.778 || 10 || 3 || 3.333 ||
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| |-
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| | || || || || 39\94 || || 497.872 || 7 || 2 || 3.500 || Garibaldi / [[cassandra]]
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| |-
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| | || || || || || 61\147 || 497.959 || 11 || 3 || 3.667 ||
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| |-
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| | || || || 22\53 || || || 498.113 || 4 || 1 || 4.000 || Garibaldi / [[helenus]], [[Pythagorean tuning]] (498.0450¢)
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| |-
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| | || || || || || 49\118 || 498.305 || 9 || 2 || 4.500 || [[Pontiac]]
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| |-
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| | || || || || 27\65 || || 498.462 || 5 || 1 || 5.000 || [[Photia]]
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| |-
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| | || || || || || 32\77 || 498.701 || 6 || 1 || 6.000 || [[Grackle]]↓
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| |-
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| | 5\12 || || || || || || 500.000 || 1 || 0 || → inf ||
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| |}
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| [[Category:17-tone scales]] | | [[Category:17-tone scales]] |
| [[Category:Mega chromatic scales]] | | [[Category:Mega chromatic scales]] |