Father family: Difference between revisions
m Cleanup +1 |
Val list reviewed |
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| Line 8: | Line 8: | ||
Mapping: [{{val| 1 0 4 }}, {{val| 0 1 -1 }}] | Mapping: [{{val| 1 0 4 }}, {{val| 0 1 -1 }}] | ||
{{Val list|legend=1| 1, 2, 3, 5, 8 | {{Val list|legend=1| 1, 2, 3, 5, 8, 13c, 21bcc }} | ||
Badness: 0.0149 | Badness: 0.0149 | ||
| Line 30: | Line 30: | ||
: Eigenmonzo subgroup: 2.9/5 | : Eigenmonzo subgroup: 2.9/5 | ||
{{Val list|legend=1| 5, 8d, 13cd, | {{Val list|legend=1| 2d, 3d, 5, 8d, 13cd, 21bccdd }} | ||
Badness: 0.0213 | Badness: 0.0213 | ||
| Line 43: | Line 43: | ||
Wedgie: {{wedgie| 1 -1 -2 -4 -6 -2 }} | Wedgie: {{wedgie| 1 -1 -2 -4 -6 -2 }} | ||
{{Val list|legend=1| | {{Val list|legend=1| 2, 3, 5 }} | ||
Badness: 0.0242 | Badness: 0.0242 | ||
| Line 56: | Line 56: | ||
Wedgie: {{wedgie| 1 -1 -5 -4 -11 -9 }} | Wedgie: {{wedgie| 1 -1 -5 -4 -11 -9 }} | ||
{{Val list|legend=1| 3, | {{Val list|legend=1| 3, 5d, 8d, 27bbccdd, 35bbbcccddd }} | ||
Badness: 0.0530 | Badness: 0.0530 | ||
| Line 69: | Line 69: | ||
Wedgie: {{wedgie| 2 -2 -2 -8 -9 1 }} | Wedgie: {{wedgie| 2 -2 -2 -8 -9 1 }} | ||
{{Val list|legend=1| 2, 6, | {{Val list|legend=1| 2, 6, 8d }} | ||
Badness: 0.0490 | Badness: 0.0490 | ||
| Line 82: | Line 82: | ||
Wedgie: {{wedgie| 2 -2 1 -8 -4 8 }} | Wedgie: {{wedgie| 2 -2 1 -8 -4 8 }} | ||
{{Val list|legend=1| | {{Val list|legend=1| 5, 11b, 16bc }} | ||
Badness: 0.0443 | Badness: 0.0443 | ||
| Line 95: | Line 95: | ||
Wedgie: {{wedgie| 0 0 5 0 8 12 }} | Wedgie: {{wedgie| 0 0 5 0 8 12 }} | ||
{{Val list|legend=1| 5, | {{Val list|legend=1| 5, 15ccd }} | ||
Badness: 0.0483 | Badness: 0.0483 | ||
| Line 104: | Line 104: | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
{{todo | {{todo|improve readability}} | ||
Revision as of 16:59, 10 February 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.
Father
Comma list: 16/15
POTE generator: ~3/2 = 743.986
Mapping: [⟨1 0 4], ⟨0 1 -1]]
Badness: 0.0149
7-limit
Comma list: 16/15, 28/27
POTE generator: ~3/2 = 742.002
Mapping: [⟨1 0 4 -2], ⟨0 1 -1 3]]
Wedgie: ⟨⟨1 -1 3 -4 2 10]]
Minimax tuning:
- 7-odd-limit
- [[1 0 0 0⟩, [3/2 0 -1/4 1/4⟩, [5/2 0 1/4 -1/4⟩, [5/2 0 -3/4 3/4⟩]
- Eigenmonzo subgroup: 2.7/5
- 9-odd-limit
- Eigenmonzo subgroup: 2.9/5
Badness: 0.0213
Mother
Comma list: 16/15, 21/20
POTE generator: ~3/2 = 721.569
Mapping: [⟨1 0 4 6], ⟨0 1 -1 -2]]
Wedgie: ⟨⟨1 -1 -2 -4 -6 -2]]
Badness: 0.0242
Pater
Comma list: 16/15, 126/125
POTE generator: ~3/2 = 753.113
Mapping: [⟨1 0 4 11], ⟨0 1 -1 -5]]
Wedgie: ⟨⟨1 -1 -5 -4 -11 -9]]
Badness: 0.0530
Walid
Comma list: 16/15, 50/49
POTE generator: ~3/2 = 749.415
Mapping: [⟨2 0 8 9], ⟨0 1 -1 -1]]
Wedgie: ⟨⟨2 -2 -2 -8 -9 1]]
Badness: 0.0490
Baba
Comma list: 16/15, 49/45
POTE generator: ~8/7 = 226.704
Mapping: [⟨1 0 4 2], ⟨0 2 -2 1]]
Wedgie: ⟨⟨2 -2 1 -8 -4 8]]
Badness: 0.0443
Quint
Comma list: 16/15, 27/25
POTE generator: ~8/7 = 182.097
Mapping: [⟨5 8 12 0], ⟨0 0 0 -1]]
Wedgie: ⟨⟨0 0 5 0 8 12]]
Badness: 0.0483