Undim family: Difference between revisions
Created page with "The '''undim family''' tempers out {{monzo| 41 -20 -4 }}, equating the Pythagorean comma with a stack of four schismas, making it a member of the schismic-Pythagorea..." |
+13-limit undim (pretty obvious extension) |
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| Line 12: | Line 12: | ||
Mapping generators: ~1215/1024, ~3 | Mapping generators: ~1215/1024, ~3 | ||
[[POTE generator]]: ~3/2 = 702. | [[POTE generator]]: ~3/2 = 702.6054 | ||
{{Val list|legend=1| 12, 104, 116, 128, 140, 152, 620, 772, 924c, 1076bc, 1228bc }} | {{Val list|legend=1| 12, …, 104, 116, 128, 140, 152, 620, 772, 924c, 1076bc, 1228bc }} | ||
[[Badness]]: 0.241703 | [[Badness]]: 0.241703 | ||
| Line 27: | Line 27: | ||
{{Multival|legend=1| 4 -20 -44 -41 -81 -46 }} | {{Multival|legend=1| 4 -20 -44 -41 -81 -46 }} | ||
[[POTE generator]]: ~3/2 = 702. | [[POTE generator]]: ~3/2 = 702.7362 | ||
{{Val list|legend=1| | {{Val list|legend=1| 140, 152, 292 }} | ||
[[Badness]]: 0.062754 | [[Badness]]: 0.062754 | ||
| Line 40: | Line 40: | ||
Mapping: [{{val| 4 0 41 81 128 }}, {{val| 0 1 -5 -11 -18 }}] | Mapping: [{{val| 4 0 41 81 128 }}, {{val| 0 1 -5 -11 -18 }}] | ||
POTE generator: ~3/2 = 702. | POTE generator: ~3/2 = 702.6886 | ||
Vals: {{Val list| | Vals: {{Val list| 140, 152, 292, 444d, 596d }} | ||
Badness: 0.034837 | Badness: 0.034837 | ||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 352/351, 625/624, 847/845, 1375/1372 | |||
Mapping: [{{val| 4 0 41 81 128 148 }}, {{val| 0 1 -5 -11 -18 -21 }}] | |||
POTE generator: ~3/2 = 702.7363 | |||
Vals: {{Val list| 140, 152f, 292 }} | |||
Badness: 0.0282 | |||
== Unlit == | == Unlit == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
Comma list: 4375/4374, 2199023255552/2179240250625 | [[Comma list]]: 4375/4374, 2199023255552/2179240250625 | ||
Mapping: [{{val| 4 0 41 -160 }}, {{val| 0 1 -5 27 }} | [[Mapping]]: [{{val| 4 0 41 -160 }}, {{val| 0 1 -5 27 }} | ||
POTE generator: ~3/2 = 702.5764 | [[POTE generator]]: ~3/2 = 702.5764 | ||
{{Val list|legend=1| 152, 316, 468, 620, 1088bcd, 1708bccdd }} | {{Val list|legend=1| 152, 316, 468, 620, 1088bcd, 1708bccdd }} | ||
Badness: 0.268 | [[Badness]]: 0.268 | ||
=== 11-limit === | === 11-limit === | ||
| Line 88: | Line 101: | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
Comma list: 6144/6125, 31470387200/31381059609 | [[Comma list]]: 6144/6125, 31470387200/31381059609 | ||
Mapping: [{{val| 8 0 82 -79 }}, {{val| 0 1 -5 8 }} | [[Mapping]]: [{{val| 8 0 82 -79 }}, {{val| 0 1 -5 8 }} | ||
Mapping generators: ~7168/6561, ~3 | Mapping generators: ~7168/6561, ~3 | ||
POTE | [[POTE generator]]: ~3/2 = 702.5090 | ||
{{Val list|legend=1| 152, 328, 480, 1592bccddd }} | {{Val list|legend=1| 152, 328, 480, 1592bccddd }} | ||
| Line 107: | Line 120: | ||
Mapping: [{{val| 8 0 82 -79 15 }}, {{val| 0 1 -5 8 1 }} | Mapping: [{{val| 8 0 82 -79 15 }}, {{val| 0 1 -5 8 1 }} | ||
POTE | POTE generator: ~3/2 = 702.5090 | ||
Vals: {{Val list| 152, 328, 480, 1112bccddee, 1592bccdddeee }} | Vals: {{Val list| 152, 328, 480, 1112bccddee, 1592bccdddeee }} | ||
| Line 120: | Line 133: | ||
Mapping: [{{val| 8 0 82 -79 15 -186 }}, {{val| 0 1 -5 8 1 17 }} | Mapping: [{{val| 8 0 82 -79 15 -186 }}, {{val| 0 1 -5 8 1 17 }} | ||
POTE | POTE generator: ~3/2 = 702.4773 | ||
Vals: {{Val list| 152f, 328, 480f, 808cdeff }} | Vals: {{Val list| 152f, 328, 480f, 808cdeff }} | ||