Trienstonic clan: Difference between revisions
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-opossum (addressed in porcupine family) |
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The '''trienstonic clan''' of temperaments tempers out [[28/27]], the septimal third-tone or trienstonic comma. | The '''trienstonic clan''' of temperaments tempers out [[28/27]], the septimal third-tone or trienstonic comma. | ||
Adding 16/15 to 28/27 leads to father temperament, adding 256/245 gives uncle, adding 50/49 gives octokaidecal and adding 126/125 gives opossum. Other members of the clan discussed elsewhere are [[Dicot family #Sharp| | Adding 16/15 to 28/27 leads to father temperament, adding 256/245 gives uncle, adding 50/49 gives octokaidecal and adding 126/125 gives opossum. Other members of the clan discussed elsewhere are: | ||
* ''[[Sharp (temperament)|Sharp]]'' → [[Dicot family #Sharp|Dicot family]] | |||
* ''[[Blacksmith]]'' → [[Archytas clan #Blacksmith|Archytas clan]] | |||
* ''[[Sharptone]]'' → [[Meantone family #Sharptone|Meantone family]] | |||
* ''[[Opossum]]'' → [[Porcupine family #Opossum|Porcupine family]] | |||
== No-fives trienstonic == | == No-fives trienstonic == | ||
| Line 120: | Line 124: | ||
Badness: 0.030235 | Badness: 0.030235 | ||
== Kangaroo == | == Kangaroo == | ||
Revision as of 11:16, 2 April 2023
The trienstonic clan of temperaments tempers out 28/27, the septimal third-tone or trienstonic comma.
Adding 16/15 to 28/27 leads to father temperament, adding 256/245 gives uncle, adding 50/49 gives octokaidecal and adding 126/125 gives opossum. Other members of the clan discussed elsewhere are:
- Sharp → Dicot family
- Blacksmith → Archytas clan
- Sharptone → Meantone family
- Opossum → Porcupine family
No-fives trienstonic
Subgroup: 2.3.7
Comma list: 28/27
Sval mapping: [⟨1 0 -2], ⟨0 1 3]]
Gencom mapping: [⟨1 0 0 -2], ⟨0 1 0 3]]
POTE generator: ~3/2 = 721.5586
Father
Subgroup: 2.3.5.7
Comma list: 16/15, 28/27
Mapping: [⟨1 0 4 -2], ⟨0 1 -1 3]]
Wedgie: ⟨⟨ 1 -1 3 -4 2 10 ]]
POTE generator: ~3/2 = 742.002
- 7-odd-limit: ~3/2 = [1/2 0 -1/4 1/4⟩
- Eigenmonzos (unchanged intervals): 2, 7/5
- 9-odd-limit: ~3/2 = [1 -2 0 1⟩ = 14/9
- Eigenmonzos (unchanged intervals): 2, 9/7
Badness: 0.021312
Uncle
Subgroup: 2.3.5.7
Comma list: 28/27, 256/245
Mapping: [⟨1 0 12 -2], ⟨0 1 -6 3]]
Wedgie: ⟨⟨ 1 -6 3 -12 2 24 ]]
POTE generator: ~3/2 = 731.177
- 7-odd-limit eigenmonzo subgroup: 2.5/3
- 9-odd-limit eigenmonzo subgroup: 2.9/5
Badness: 0.072653
Wallaby
Subgroup: 2.3.5.7
Comma list: 28/27, 35/32
Mapping: [⟨1 0 7 -2], ⟨0 1 -3 3]]
Wedgie: ⟨⟨ 1 -3 3 -7 2 15 ]]
POTE generator: ~3/2 = 691.351
Badness: 0.058468
Octokaidecal
5-limit (supersharp)
Subgroup: 2.3.5
Comma list: 800/729
Mapping: [⟨2 0 -5], ⟨0 1 3]]
POTE generator: ~3/2 = 729.097
Badness: 0.122848
7-limit
Subgroup: 2.3.5.7
Comma list: 28/27, 50/49
Mapping: [⟨2 0 -5 -4], ⟨0 1 3 3]]
Wedgie: ⟨⟨ 2 6 6 5 4 -2 ]]
POTE generator: ~3/2 = 728.874
- 7-odd-limit eigenmonzo subgroup: 2.5
- 9-odd-limit eigenmonzo subgroup: 2.5
Badness: 0.036747
11-limit
Subgroup: 2.3.5.7.11
Comma list: 28/27, 50/49, 55/54
Mapping: [⟨2 0 -5 -4 7], ⟨0 1 3 3 0]]
POTE generator: ~3/2 = 732.330
Optimal GPV sequence: Template:Val list
Badness: 0.030235
Kangaroo
- For the 5-limit version of this temperament, see High badness temperaments #Kangaroo.
Subgroup: 2.3.5.7
Comma list: 28/27, 1029/1000
Mapping: [⟨1 0 -3 -2], ⟨0 3 10 9]]
Wedgie: ⟨⟨ 3 10 9 9 6 -7 ]]
POTE generator: ~7/5 = 560.328
Badness: 0.077857
11-limit
Subgroup: 2.3.5.7.11
Comma list: 28/27, 77/75, 245/242
Mapping: [⟨1 0 -3 -2 -4], ⟨0 3 10 9 14]]
POTE generator: ~7/5 = 560.155
Optimal GPV sequence: Template:Val list
Badness: 0.043195
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 28/27, 40/39, 66/65, 147/143
Mapping: [⟨1 0 -3 -2 -4 0], ⟨0 3 10 9 14 7]]
POTE generator: ~7/5 = 559.770
Optimal GPV sequence: Template:Val list
Badness: 0.032653
Quindecic
Subgroup: 2.3.5.7.11.13
Comma list: 28/27, 49/48, 55/54, 77/75
Mapping: [⟨15 24 35 42 52 0], ⟨0 0 0 0 0 1]]
POTE generator: ~13/8 = 852.924
Optimal GPV sequence: Template:Val list
Badness: 0.028944