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| {{Infobox MOS | | {{Infobox MOS}} |
| | Periods = 1
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| | nLargeSteps = 1
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| | nSmallSteps = 12
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| | Equalized = 12
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| | Collapsed = 1
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| | Pattern = Lssssssssssss
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| }} | |
| {{MOS intro}} | | {{MOS intro}} |
| This MOS, also called the Happy tridecatonic scale, has its first harmonic entropy minimum at 1/14edo-3/40edo, where 3:2 is +8 generators (Octacot). However, the absolute harmonic entropy minimum is Nautilus (3:2=-6 generators), and that is not complete until 14 tones.
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| ==Modes== | | This MOS, also called the '''Happy tridecatonic scale''', has its first [[harmonic entropy]] minimum at 1/[[14edo]]-3/[[40edo]], where 3:2 is +8 [[generator]]s (giving [[Octacot]]). However, the absolute harmonic entropy minimum is [[Nautilus]] ({{nowrap|3:2 ← −6 generators}}), and that is not complete until 14 tones. |
| {{MOS modes}} | | |
| | == Scale properties == |
| | {{TAMNAMS use}} |
| | |
| | === Intervals === |
| | {{MOS intervals}} |
| | |
| | === Generator chain === |
| | {{MOS genchain}} |
| | |
| | === Modes === |
| | {{MOS mode degrees}} |
| | |
| | == Scale tree == |
| | {{MOS tuning spectrum |
| | | 10/7 = [[Slithy]] |
| | | 13/8 = Golden [[octacot]] (88.118¢) |
| | | 12/5 = [[Marvolo]] |
| | | 5/2 = [[Nautilus]] |
| | | 13/5 = Unnamed golden tuning |
| | | 3/1 = [[Nuke]] |
| | | 10/3 = [[Valentine]] |
| | | 9/2 = [[Slurpee]] |
| | | 6/1 = ↓[[Unicorn]] |
| | }} |
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| ==Scale tree==
| | {{Todo|improve synopsis|inline=1|text=Rewrite intro with the same information but worded in a way that’s easier to parse.}} |
| {| class="wikitable" | |
| |-
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| | | Cents
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| |-
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| | | 0/1
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| | | | |
| | | 0
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| |-
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| | | 1/17
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| | |
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| | | 70.588
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| |-
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| | |
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| | | 4/67
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| | | 71.641
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| |-
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| | |
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| | | 3/50
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| | | 72
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| |-
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| | |
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| | | 2/33
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| | | 72.727
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| |-
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| | |
| |
| | | 3/49
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| | | 73.469
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| |-
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| | |
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| | | 4/65
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| | | 73.846
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| |-
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| | |
| |
| | | 5/81
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| | | 74.074
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| |-
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| | | 1/16
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| | |
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| | | 75
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| |-
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| | |
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| | | 3/47
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| | | 76.596
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| |-
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| | |
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| | | 2/31
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| | | 77.419
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| |-
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| | |
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| | | 3/46
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| | | 78.261
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| |-
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| | |
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| | | 4/61
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| | | 78.6885
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| |-
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| | |
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| | | 5/76
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| | | 78.947
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| |-
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| | |
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| | | 6/91
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| | | 79.121
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| |-
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| | | 1200/(12+pi)
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| |-
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| | | 1/15
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| | | 80
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| |-
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| | | 1200/(12+e)
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| |-
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| | | 3/44
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| | | 81.818
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| |-
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| | | 1200/(13+phi)
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| |-
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| | | 2/29
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| | | 82.759
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| |-
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| | | 3/43
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| | | 83.721
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| |-
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| | | 4/57
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| | | 84.2105
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| |-
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| | | 1/14
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| | | 85.714
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| |-
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| | | 4/55
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| | | 86.364
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| |-
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| | | 1200/(12+sqrt(3))
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| |-
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| | | 3/41
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| | | 87.805
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| |-
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| | | 1200/(12+phi)
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| |-
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| | | 5/68
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| | | 88.235
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| |-
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| | | 1200/(12+pi/2)
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| |-
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| | | 2/27
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| | | 88.889
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| |-
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| | | 5/67
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| | | 89.552
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| |-
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| | | 3/40
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| | | 90
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| |-
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| | | 4/53
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| | | 90.556
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| |-
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| | | 1/13
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| | | 92.308
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| |}
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| [[Category:13-tone scales]] | | [[Category:13-tone scales]] |