Misty family: Difference between revisions
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The '''misty family''' tempers out the [[misty comma]], 67108864/66430125 = {{monzo| 26 -12 -3 }}. | The '''misty family''' tempers out the [[misty comma]], 67108864/66430125 = {{monzo| 26 -12 -3 }}. | ||
The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which 7-limit family member we are looking at. | |||
* Adding 3136/3125 (hemimean) leads to septimal misty. | |||
* Adding 225/224 (marvel) leads to fog. | |||
== Misty == | == Misty == | ||
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[[Badness]]: 0.106540 | [[Badness]]: 0.106540 | ||
== Septimal misty == | == Septimal misty == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 128: | Line 125: | ||
== Fog == | == Fog == | ||
The ''fog'' temperament (12&63) tempers out the [[225/224 | The ''fog'' temperament (12&63) tempers out the marvel comma, [[225/224]]. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 159: | Line 156: | ||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Misty]] | [[Category:Misty family| ]] <!-- main article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
Revision as of 10:07, 11 October 2021
The misty family tempers out the misty comma, 67108864/66430125 = [26 -12 -3⟩.
The second comma of the normal comma list defines which 7-limit family member we are looking at.
- Adding 3136/3125 (hemimean) leads to septimal misty.
- Adding 225/224 (marvel) leads to fog.
Misty
Subgroup: 2.3.5
Comma list: 67108864/66430125
Mapping: [⟨3 0 26], ⟨0 1 -4]]
POTE generator: ~3/2 = 703.111
Badness: 0.106540
Septimal misty
Subgroup: 2.3.5.7
Comma list: 3136/3125, 5120/5103
Mapping: [⟨3 0 26 56], ⟨0 1 -4 -10]]
Wedgie: ⟨⟨ 3 -12 -30 -26 -56 -36 ]]
POTE generator: ~3/2 = 703.021
Badness: 0.036802
11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 3136/3125, 4375/4356
Mapping: [⟨3 0 26 56 77], ⟨0 1 -4 -10 -14]]
POTE generator: ~3/2 = 703.210
Vals: Template:Val list
Badness: 0.035932
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 364/363, 625/624
Mapping: [⟨3 0 26 56 77 92], ⟨0 1 -4 -10 -14 -17]]
POTE generator: ~3/2 = 703.303
Vals: Template:Val list
Badness: 0.027820
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 196/195, 352/351, 364/363, 375/374, 595/594
Mapping: [⟨3 0 26 56 77 92 -2], ⟨0 1 -4 -10 -14 -17 3]]
POTE generator: ~3/2 = 703.233
Vals: Template:Val list
Badness: 0.023908
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 196/195, 210/209, 352/351, 364/363, 375/374, 595/594
Mapping: [⟨3 0 26 56 77 92 -2 8], ⟨0 1 -4 -10 -14 -17 3 1]]
POTE generator: ~3/2 = 703.253
Vals: Template:Val list
Badness: 0.019878
Mystic
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 441/440, 896/891, 1001/1000
Mapping: [⟨3 0 26 56 77 -46], ⟨0 1 -4 -10 -14 12]]
POTE generator: ~3/2 = 703.311
Vals: Template:Val list
Badness: 0.036872
Hemimist
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 3136/3125, 5120/5103
Mapping: [⟨3 0 26 56 8], ⟨0 2 -8 -20 1]]
POTE generator: ~11/8 = 551.527
Vals: Template:Val list
Badness: 0.047439
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 676/675, 847/845, 3025/3024
Mapping: [⟨3 0 26 56 8 23], ⟨0 2 -8 -20 1 -5]]
POTE generator: ~11/8 = 551.525
Vals: Template:Val list
Badness: 0.022923
Fog
The fog temperament (12&63) tempers out the marvel comma, 225/224.
Subgroup: 2.3.5.7
Comma list: 225/224, 156250/151263
Mapping: [⟨3 5 6 7], ⟨0 -1 4 6]]
Wedgie: ⟨⟨ 3 -12 -18 -26 -37 -8 ]]
POTE generator: ~3/2 = 704.118
Badness: 0.086866
11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 225/224, 2420/2401
Mapping: [⟨3 5 6 7 8], ⟨0 -1 4 6 10]]
POTE generator: ~3/2 = 704.411
Vals: Template:Val list
Badness: 0.051348