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| | nSmallSteps = 4 | | | nSmallSteps = 4 |
| | Equalized = 1 | | | Equalized = 1 |
| | Paucitonic = 0 | | | Collapsed = 0 |
| | Pattern = sLsLsLsL | | | Pattern = LsLsLsLs |
| }} | | }} |
| | {{MOS intro}} |
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| The minimum harmonic entropy scale with this [[MOS]] pattern is [[diminished]][8], basically the familiar [[octatonic scale]] of 12edo. | | The minimum harmonic entropy scale with this mos pattern is [[Diminished]][8], the familiar [[octatonic scale]] of 12edo. |
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| There are 4 different near-MOSes such that multiples of the period are the only generic intervals with more than two specific representatives: LLsLsLss, LLsLssLs, LLssLLss, LLssLsLs. However, none are strictly proper in 12edo. (They are only proper if the generator is larger than 100 cents, which unfortunately is the wrong direction for good diminished tunings.)
| | In addition to the true mos form, LsLsLsLs, there are four near-mos forms – LLsLsLss, LLsLssLs, LLssLLss, and LLssLsLs – in which the period and its multiples are the only intervals with more than two varieties. The near-mos forms are only proper if the dark generator is larger than 1\12 (100{{c}}). |
| | |
| | == Intervals == |
| | {{MOS intervals}} |
| | |
| | == Modes == |
| | {{MOS mode degrees}} |
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| == Scale tree == | | == Scale tree == |
| {| class="wikitable center-all" | | {{MOS tuning spectrum |
| ! colspan="6" rowspan="2" | Generator
| | | 6/5 = [[Fourfives]]↑ |
| ! colspan="2" | Cents
| | | 13/8 = Unnamed golden tuning |
| ! rowspan="2" | L
| | | 2/1 = [[Diminished]] |
| ! rowspan="2" | s
| | | 13/5 = Unnamed golden tuning |
| ! rowspan="2" | L/s
| | | 6/1 = [[Quadritikleismic]]↓ |
| ! rowspan="2" | Comments
| | }} |
| |-
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| ! Chroma-positive
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| ! Chroma-negative
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| | 1\8 || || || || || || 150.000 || 150.000 || 1 || 1 || 1.000 ||
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| | || || || || || 6\44 || 163.636 || 136.364 || 6 || 5 || 1.200 || Fourfives↑
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| | || || || || 5\36 || || 166.667 || 133.333 || 5 || 4 || 1.250 ||
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| | || || || || || 9\64 || 168.750 || 105.000 || 9 || 7 || 1.286 ||
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| | || || || 4\28 || || || 171.429 || 128.571 || 4 || 3 || 1.333 ||
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| |-
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| | || || || || || 11\76 || 173.684 || 126.316 || 11 || 8 || 1.375 ||
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| | || || || || 7\48 || || 175.000 || 125.000 || 7 || 5 || 1.400 ||
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| | || || || || || 10\68 || 176.471 || 123.529 || 10 || 7 || 1.428 ||
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| | || || 3\20 || || || || 180.000 || 60.000 || 3 || 2 || 1.500 || L/s = 3/2
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| | || || || || || 11\72 || 183.333 || 116.667 || 11 || 7 || 1.571 ||
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| | || || || || 8\52 || || 184.615 || 115.385 || 8 || 5 || 1.600 ||
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| | || || || || || 13\84 || 185.714 || 114.286 || 13 || 8 || 1.625 || Golden diminished
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| | || || || 5\32 || || || 187.500 || 112.500 || 5 || 3 || 1.667 ||
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| | || || || || || 12\76 || 189.474 || 110.526 || 12 || 7 || 1.714 ||
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| | || || || || 7\44 || || 190.909 || 109.091 || 7 || 4 || 1.750 ||
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| | || || || || || 9\56 || 192.857 || 107.143 || 9 || 5 || 1.800 ||
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| | || 2\12 || || || || || 200.000 || 100.000 || 2 || 1 || 2.000 || Basic tetrawood<br>Diminished is optimal around here
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| | || || || || || 9\52 || 207.692 || 92.308 || 9 || 4 || 2.250 ||
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| | || || || || 7\40 || || 210.000 || 90.000 || 7 || 3 || 2.333 ||
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| | || || || || || 12\68 || 211.765 || 88.235 || 12 || 5 || 2.400 ||
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| | || || || 5\28 || || || 214.286 || 85.714 || 5 || 2 || 2.500 ||
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| | || || || || || 13\72 || 216.667 || 83.333 || 13 || 5 || 2.600 || Unnamed golden tuning
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| |- | |
| | || || || || 8\44 || || 218.182 || 81.818 || 8 || 3 || 2.667 ||
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| | || || || || || 11\60 || 220.000 || 80.000 || 11 || 4 || 2.750 ||
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| | || || 3\16 || || || || 225.000 || 75.000 || 3 || 1 || 3.000 || L/s = 3/1
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| | || || || || || 10\52 || 230.769 || 69.231 || 10 || 3 || 3.333 ||
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| | || || || || 7\36 || || 233.333 || 66.667 || 7 || 2 || 3.500 ||
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| | || || || || || 11\56 || 235.714 || 64.286 || 11 || 3 || 3.667 ||
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| | || || || 4\20 || || || 240.000 || 60.000 || 4 || 1 || 4.000 ||
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| | || || || || || 9\44 || 245.455 || 54.545 || 9 || 2 || 4.500 ||
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| | || || || || 5\24 || || 250.000 || 50.000 || 5 || 1 || 5.000 ||
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| | || || || || || 6\28 || 257.143 || 42.857 || 6 || 1 || 6.000 || Quadritikleismic↓
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| | 1\4 || || || || || || 300.000 || 0.000 || 1 || 0 || → inf ||
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| |}
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| [[Category:Tetrawood]] <!-- main article --> | | [[Category:Tetrawood| ]] <!-- main article --> |
| | [[Category:8-tone scales]] |