Cloudy clan: Difference between revisions
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* Diamond monotone and tradeoff: ~3/2 = [696.000, 700.000] | * Diamond monotone and tradeoff: ~3/2 = [696.000, 700.000] | ||
Vals: {{Val list| 10, 50 | Vals: {{Val list| 10, 50 }} | ||
Badness: 0.063900 | Badness: 0.063900 | ||
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* Diamond monotone and tradeoff: ~3/2 = [696.000, 700.000] | * Diamond monotone and tradeoff: ~3/2 = [696.000, 700.000] | ||
Vals: {{Val list| 10, 50 | Vals: {{Val list| 10, 50 }} | ||
Badness: 0.036880 | Badness: 0.036880 | ||
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* Diamond monotone and tradeoff: ~3/2 = [696.000, 700.000] | * Diamond monotone and tradeoff: ~3/2 = [696.000, 700.000] | ||
Vals: {{Val list| 10, 50 | Vals: {{Val list| 10, 50 }} | ||
Badness: 0.025064 | Badness: 0.025064 | ||
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Badness: 0.077420 | Badness: 0.077420 | ||
== Quinkee == | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 1029/1000, 6144/6125 | |||
[[Mapping]]: [{{val|5 9 12 14}}, {{val|0 -3 -1 0}}] | |||
[[POTE generator]]: ~5/4 = 393.439 | |||
{{Val list|legend=1| 15, 40, 55, 125cd, 180ccdd }} | |||
[[Badness]]: 0.184222 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 121/120, 176/175, 1029/1000 | |||
Mapping: [{{val|5 9 12 14 18}}, {{val|0 -3 -1 0 -2}}] | |||
POTE generator: ~5/4 = 393.438 | |||
Vals: {{Val list| 15, 40, 55, 125cd, 180ccdde }} | |||
Badness: 0.065192 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 66/65, 105/104, 121/120, 637/625 | |||
Mapping: [{{val|5 9 12 14 18 20}}, {{val|0 -3 -1 0 -2 -4}}] | |||
POTE generator: ~5/4 = 392.798 | |||
Vals: {{Val list| 15, 40, 55 }} | |||
Badness: 0.048440 | |||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
Revision as of 03:29, 9 June 2021
The cloudy clan tempers out the cloudy comma, 16807/16384, thus splitting the octave into 5 equal parts and mapping the harmonic 7 to 4\5.
Temperaments discussed elsewhere are blacksmith, cloudtone, pentacloud and sengasec.
Coblack
Subgroup: 2.3.5.7
Comma list: 126/125, 16807/16384
Mapping: [⟨5 1 7 14], ⟨0 3 2 0]]
Wedgie: ⟨⟨ 15 10 0 -19 -42 -28 ]]
POTE generator: ~21/20 = 73.044
Badness: 0.107282
11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 245/242, 385/384
Mapping: [⟨5 1 7 14 15], ⟨0 3 2 0 1]]
POTE generator: ~21/20 = 73.264
Vals: Template:Val list
Badness: 0.045070
Decic
The decic temperament (10&50) tempers out the cloudy comma, 16807/16384 and the marvel comma, 225/224 in the 7-limit, as well as the linus comma, [11 -10 -10 10⟩. This temperament is supported by 10, 50, and 60 EDOs, and can be extended naturally to the 11-, 13-, and 17-limit by adding 385/384, 105/104, and 170/169 to the comma list in this order.
Subgroup: 2.3.5.7
Comma list: 225/224, 16807/16384
Mapping: [⟨10 0 39 28], ⟨0 1 -1 0]]
Mapping generators: ~15/14, ~3
Wedgie: ⟨⟨ 10 -10 0 -39 -28 28 ]]
POTE generator: ~3/2 = 698.696
- Diamond monotone range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
- Diamond tradeoff range: ~3/2 = [693.129, 702.512]
- Diamond monotone and tradeoff: ~3/2 = [696.000, 700.000]
Badness: 0.089135
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 3087/3025
Mapping: [⟨10 0 39 28 3], ⟨0 1 -1 0 2]]
Mapping generators: ~15/14, ~3
POTE generator: ~3/2 = 696.791
Tuning ranges:
- Diamond monotone range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
- Diamond tradeoff range: ~3/2 = [689.363, 702.512]
- Diamond monotone and tradeoff: ~3/2 = [696.000, 700.000]
Vals: Template:Val list
Badness: 0.063900
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 144/143, 196/195, 2200/2197
Mapping: [⟨10 0 39 28 3 37], ⟨0 1 -1 0 2 0]]
Mapping generators: ~14/13, ~3
POTE generator: ~3/2 = 696.993
Tuning ranges:
- Diamond monotone range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
- Diamond tradeoff range: ~3/2 = [689.363, 702.512]
- Diamond monotone and tradeoff: ~3/2 = [696.000, 700.000]
Vals: Template:Val list
Badness: 0.036880
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 105/104, 144/143, 170/169, 196/195, 221/220
Mapping: [⟨10 0 39 28 3 37 25], ⟨0 1 -1 0 2 0 1]]
Mapping generators: ~14/13, ~3
POTE generator: ~3/2 = 697.085
Tuning ranges:
- Diamond monotone range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
- Diamond tradeoff range: ~3/2 = [689.363, 704.955]
- Diamond monotone and tradeoff: ~3/2 = [696.000, 700.000]
Vals: Template:Val list
Badness: 0.025064
Pentadecal
The pentadecal temperament tempers out the 15-5/3-comma (quintriyo, pentadecatonic minor thirds comma), [-11 -15 15⟩. This temperament can be described as 15&60 temperament, tempering out the cloudy comma, 16807/16384 and the keema, 875/864 in the 7-limit.
Subgroup: 2.3.5
Comma list: 30517578125/29386561536
Mapping: [⟨15 0 11], ⟨0 1 1]]
POTE generator: ~3/2 = 702.652
Badness: 0.692042
7-limit
Subgroup: 2.3.5.7
Comma list: 875/864, 16807/16384
Mapping: [⟨15 0 11 42], ⟨0 1 1 0]]
Mapping generators: ~21/20, ~3
POTE generator: ~3/2 = 700.223
Badness: 0.114833
11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 385/384, 1372/1331
Mapping: [⟨15 0 11 42 52], ⟨0 1 1 0 0]]
Mapping generators: ~21/20, ~3
POTE generator: ~3/2 = 702.733
Vals: Template:Val list
Badness: 0.077420
Quinkee
Subgroup: 2.3.5.7
Comma list: 1029/1000, 6144/6125
Mapping: [⟨5 9 12 14], ⟨0 -3 -1 0]]
POTE generator: ~5/4 = 393.439
Badness: 0.184222
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 1029/1000
Mapping: [⟨5 9 12 14 18], ⟨0 -3 -1 0 -2]]
POTE generator: ~5/4 = 393.438
Vals: Template:Val list
Badness: 0.065192
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 105/104, 121/120, 637/625
Mapping: [⟨5 9 12 14 18 20], ⟨0 -3 -1 0 -2 -4]]
POTE generator: ~5/4 = 392.798
Vals: Template:Val list
Badness: 0.048440