Father family: Difference between revisions
Cmloegcmluin (talk | contribs) adding parenthetical "(unchanged intervals)" to eigenmonzo lists |
m Cleanup |
||
| Line 8: | Line 8: | ||
[[Mapping]]: [{{val| 1 0 4 }}, {{val| 0 1 -1 }}] | [[Mapping]]: [{{val| 1 0 4 }}, {{val| 0 1 -1 }}] | ||
Mapping generators: ~2, ~3 | |||
[[POTE generator]]: ~3/2 = 743.986 | [[POTE generator]]: ~3/2 = 743.986 | ||
| Line 19: | Line 21: | ||
[[Badness]]: 0.014884 | [[Badness]]: 0.014884 | ||
== | == Septimal father == | ||
{{see also| Trienstonic clan #Father }} | {{see also| Trienstonic clan #Father }} | ||
| Line 78: | Line 80: | ||
[[Mapping]]: [{{val| 2 0 8 9 }}, {{val| 0 1 -1 -1 }}] | [[Mapping]]: [{{val| 2 0 8 9 }}, {{val| 0 1 -1 -1 }}] | ||
Mapping generators: ~7/5, ~3 | |||
{{Multival|legend=1| 2 -2 -2 -8 -9 1 }} | {{Multival|legend=1| 2 -2 -2 -8 -9 1 }} | ||
| Line 94: | Line 98: | ||
[[Mapping]]: [{{val| 1 0 4 2 }}, {{val| 0 2 -2 1 }}] | [[Mapping]]: [{{val| 1 0 4 2 }}, {{val| 0 2 -2 1 }}] | ||
[[POTE generator]]: ~ | Mapping generators: ~2, ~7/4 | ||
[[POTE generator]]: ~7/4 = 973.296 | |||
{{Multival|legend=1| 2 -2 1 -8 -4 8 }} | {{Multival|legend=1| 2 -2 1 -8 -4 8 }} | ||
| Line 108: | Line 114: | ||
[[Mapping]]: [{{val| 5 8 12 0 }}, {{val| 0 0 0 1 }}] | [[Mapping]]: [{{val| 5 8 12 0 }}, {{val| 0 0 0 1 }}] | ||
Mapping generators: ~9/8, ~7 | |||
{{Multival|legend=1| 0 0 5 0 8 12 }} | {{Multival|legend=1| 0 0 5 0 8 12 }} | ||
[[POTE generator]]: ~ | [[POTE generator]]: ~7/4 = 1017.903 | ||
{{Val list|legend=1| 5, 15ccd }} | {{Val list|legend=1| 5, 15ccd }} | ||
| Line 123: | Line 131: | ||
[[Mapping]]: [{{val| 3 5 7 0 }}, {{val| 0 0 0 1 }}] | [[Mapping]]: [{{val| 3 5 7 0 }}, {{val| 0 0 0 1 }}] | ||
Mapping generators: ~5/4, ~7 | |||
{{Multival|legend=1| 0 0 3 0 5 7 }} | {{Multival|legend=1| 0 0 3 0 5 7 }} | ||
[[POTE generator]]: ~ | [[POTE generator]]: ~7/4 = 1034.013 | ||
{{Val list|legend=1| 3, 6, 15bb }} | {{Val list|legend=1| 3, 6, 15bb }} | ||
| Line 134: | Line 144: | ||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Father]] | [[Category:Father family| ]] <!-- main article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
Revision as of 11:33, 20 October 2021
The father family of temperaments tempers out 16/15, the just diatonic semitone. This equates 4/3 with 5/4, so these are "fourth-thirds", or father, temperaments. In a sense, what father is all about is using semisixths or subfourths and pretending that's 5-limit, and like any temperament which seems to involve pretending, father is at the edge of what can sensibly be called a temperament at all. In other words, it is an exotemperament.
Father
Subgroup: 2.3.5
Comma list: 16/15
Mapping: [⟨1 0 4], ⟨0 1 -1]]
Mapping generators: ~2, ~3
POTE generator: ~3/2 = 743.986
- 5-odd-limit: ~3/2 = [1 1/2 -1/2⟩
- Eigenmonzos (unchanged intervals): 2, 6/5
Badness: 0.014884
Septimal 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
Mother
Subgroup: 2.3.5.7
Comma list: 16/15, 21/20
Mapping: [⟨1 0 4 6], ⟨0 1 -1 -2]]
Wedgie: ⟨⟨ 1 -1 -2 -4 -6 -2 ]]
POTE generator: ~3/2 = 721.569
Badness: 0.024152
Pater
Subgroup: 2.3.5.7
Comma list: 16/15, 126/125
Mapping: [⟨1 0 4 11], ⟨0 1 -1 -5]]
Wedgie: ⟨⟨ 1 -1 -5 -4 -11 -9 ]]
POTE generator: ~3/2 = 753.113
Badness: 0.053001
Walid
Subgroup: 2.3.5.7
Comma list: 16/15, 50/49
Mapping: [⟨2 0 8 9], ⟨0 1 -1 -1]]
Mapping generators: ~7/5, ~3
Wedgie: ⟨⟨ 2 -2 -2 -8 -9 1 ]]
POTE generator: ~3/2 = 749.415
Badness: 0.048978
Baba
Subgroup: 2.3.5.7
Comma list: 16/15, 49/45
Mapping: [⟨1 0 4 2], ⟨0 2 -2 1]]
Mapping generators: ~2, ~7/4
POTE generator: ~7/4 = 973.296
Wedgie: ⟨⟨ 2 -2 1 -8 -4 8 ]]
Badness: 0.044321
Quint
Subgroup: 2.3.5.7
Comma list: 16/15, 27/25
Mapping: [⟨5 8 12 0], ⟨0 0 0 1]]
Mapping generators: ~9/8, ~7
Wedgie: ⟨⟨ 0 0 5 0 8 12 ]]
POTE generator: ~7/4 = 1017.903
Badness: 0.048312
Ternary
Subgroup: 2.3.5.7
Comma list: 10/9, 16/15
Mapping: [⟨3 5 7 0], ⟨0 0 0 1]]
Mapping generators: ~5/4, ~7
Wedgie: ⟨⟨ 0 0 3 0 5 7 ]]
POTE generator: ~7/4 = 1034.013
Badness: 0.028673