Father family: Difference between revisions
Val list reviewed |
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= Father = | = Father = | ||
Period: 1\1 | |||
Optimal ([[POTE]]) generator: ~3/2 = 743.986 | |||
EDO generators: [[5edo|3\5]], [[8edo|5\8]], [[13edo|8\13]] | |||
Scales (Scala files): | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Comma list: 16/15 | Comma list: 16/15 | ||
Mapping: [{{val| 1 0 4 }}, {{val| 0 1 -1 }}] | Mapping: [{{val| 1 0 4 }}, {{val| 0 1 -1 }}] | ||
| Line 11: | Line 22: | ||
Badness: 0.0149 | Badness: 0.0149 | ||
</div></div> | |||
= 7-limit = | = 7-limit = | ||
{{see also| Trienstonic clan #Father }} | {{see also| Trienstonic clan #Father }} | ||
Period: 1\1 | |||
Optimal ([[POTE]]) generator: ~3/2 = 742.002 | |||
EDO generators: [[5edo|3\5]], [[8edo|5\8]], [[13edo|8\13]] | |||
Scales (Scala files): | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Comma list: 16/15, 28/27 | Comma list: 16/15, 28/27 | ||
Mapping: [{{val| 1 0 4 -2 }}, {{val| 0 1 -1 3 }}] | Mapping: [{{val| 1 0 4 -2 }}, {{val| 0 1 -1 3 }}] | ||
| Line 33: | Line 56: | ||
Badness: 0.0213 | Badness: 0.0213 | ||
</div></div> | |||
= Mother = | = Mother = | ||
Period: 1\1 | |||
Optimal ([[POTE]]) generator: ~3/2 = 721.569 | |||
EDO generators: [[5edo|3\5]] | |||
Scales (Scala files): | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Comma list: 16/15, 21/20 | Comma list: 16/15, 21/20 | ||
Mapping: [{{val| 1 0 4 6 }}, {{val| 0 1 -1 -2 }}] | Mapping: [{{val| 1 0 4 6 }}, {{val| 0 1 -1 -2 }}] | ||
| Line 46: | Line 82: | ||
Badness: 0.0242 | Badness: 0.0242 | ||
</div></div> | |||
= Pater = | = Pater = | ||
Period: 1\1 | |||
Optimal ([[POTE]]) generator: ~3/2 = 753.113 | |||
EDO generators: [[8edo|5\8]] | |||
Scales (Scala files): | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Comma list: 16/15, 126/125 | Comma list: 16/15, 126/125 | ||
Mapping: [{{val| 1 0 4 11 }}, {{val| 0 1 -1 -5 }}] | Mapping: [{{val| 1 0 4 11 }}, {{val| 0 1 -1 -5 }}] | ||
| Line 59: | Line 108: | ||
Badness: 0.0530 | Badness: 0.0530 | ||
</div></div> | |||
= Walid = | = Walid = | ||
Period: 1\1 | |||
Optimal ([[POTE]]) generator: ~3/2 = 749.415 | |||
EDO generators: [[6edo|4\6]], [[8edo|5\8]] | |||
Scales (Scala files): | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Comma list: 16/15, 50/49 | Comma list: 16/15, 50/49 | ||
Mapping: [{{val| 2 0 8 9 }}, {{val| 0 1 -1 -1 }}] | Mapping: [{{val| 2 0 8 9 }}, {{val| 0 1 -1 -1 }}] | ||
| Line 72: | Line 134: | ||
Badness: 0.0490 | Badness: 0.0490 | ||
</div></div> | |||
= Baba = | = Baba = | ||
Period: 1\1 | |||
Optimal ([[POTE]]) generator: ~8/7 = 226.704 | |||
EDO generators: [[5edo|1\5]], [[11edo|2\11]], [[16edo|3\16]] | |||
Scales (Scala files): | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Comma list: 16/15, 49/45 | Comma list: 16/15, 49/45 | ||
| Line 85: | Line 162: | ||
Badness: 0.0443 | Badness: 0.0443 | ||
</div></div> | |||
= Quint = | = Quint = | ||
Period: 1\5 | |||
Optimal ([[POTE]]) generator: ~8/7 = 182.097 | |||
EDO generators: [[15edo|3\15]] | |||
Scales (Scala files): | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Comma list: 16/15, 27/25 | Comma list: 16/15, 27/25 | ||
Mapping: [{{val| 5 8 12 0 }}, {{val| 0 0 0 -1 }}] | Mapping: [{{val| 5 8 12 0 }}, {{val| 0 0 0 -1 }}] | ||
| Line 98: | Line 188: | ||
Badness: 0.0483 | Badness: 0.0483 | ||
</div></div> | |||
[[Category:Theory]] | [[Category:Theory]] | ||
Revision as of 19:11, 12 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
Period: 1\1
Optimal (POTE) generator: ~3/2 = 743.986
EDO generators: 3\5, 5\8, 8\13
Scales (Scala files):
7-limit
Period: 1\1
Optimal (POTE) generator: ~3/2 = 742.002
EDO generators: 3\5, 5\8, 8\13
Scales (Scala files):
Comma list: 16/15, 28/27
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
Period: 1\1
Optimal (POTE) generator: ~3/2 = 721.569
EDO generators: 3\5
Scales (Scala files):
Comma list: 16/15, 21/20
Mapping: [⟨1 0 4 6], ⟨0 1 -1 -2]]
Wedgie: ⟨⟨1 -1 -2 -4 -6 -2]]
Badness: 0.0242
Pater
Period: 1\1
Optimal (POTE) generator: ~3/2 = 753.113
EDO generators: 5\8
Scales (Scala files):
Comma list: 16/15, 126/125
Mapping: [⟨1 0 4 11], ⟨0 1 -1 -5]]
Wedgie: ⟨⟨1 -1 -5 -4 -11 -9]]
Badness: 0.0530
Walid
Period: 1\1
Optimal (POTE) generator: ~3/2 = 749.415
Scales (Scala files):
Comma list: 16/15, 50/49
Mapping: [⟨2 0 8 9], ⟨0 1 -1 -1]]
Wedgie: ⟨⟨2 -2 -2 -8 -9 1]]
Badness: 0.0490
Baba
Period: 1\1
Optimal (POTE) generator: ~8/7 = 226.704
EDO generators: 1\5, 2\11, 3\16
Scales (Scala files):
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
Period: 1\5
Optimal (POTE) generator: ~8/7 = 182.097
EDO generators: 3\15
Scales (Scala files):
Comma list: 16/15, 27/25
Mapping: [⟨5 8 12 0], ⟨0 0 0 -1]]
Wedgie: ⟨⟨0 0 5 0 8 12]]
Badness: 0.0483