Xenharmonic Wiki

Undim family: Difference between revisions

← Older editNewer edit →
VisualWikitext
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,172 edits
"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Update keys
Line 4: Line 4:


== Undim ==
== Undim ==
Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: {{monzo| 41 -20 -4 }} = 2199023255552/2179240250625
[[Comma list]]: {{monzo| 41 -20 -4 }} = 2199023255552/2179240250625


[[Mapping]]: [{{val| 4 0 41 }}, {{val| 0 1 -5 }}]
{{Mapping|legend=1| 4 0 41 | 0 1 -5 }}


Mapping generators: ~1215/1024, ~3
: mapping generators: ~1215/1024, ~3


[[POTE generator]]: ~3/2 = 702.6054
[[Optimal tuning]] ([[POTE]]): ~1215/1024 = 1\4, ~3/2 = 702.6054


{{Optimal ET sequence|legend=1| 12, …, 104, 116, 128, 140, 152, 620, 772, 924c, 1076bc, 1228bc }}
{{Optimal ET sequence|legend=1| 12, …, 104, 116, 128, 140, 152, 620, 772, 924c, 1076bc, 1228bc }}
Line 19: Line 19:


== Septimal undim ==
== Septimal undim ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 5120/5103, 390625/388962
[[Comma list]]: 5120/5103, 390625/388962


[[Mapping]]: [{{val| 4 0 41 81 }}, {{val| 0 1 -5 -11 }}]
{{Mapping|legend=1| 4 0 41 81 | 0 1 -5 -11 }}


{{Multival|legend=1| 4 -20 -44 -41 -81 -46 }}
{{Multival|legend=1| 4 -20 -44 -41 -81 -46 }}


[[POTE generator]]: ~3/2 = 702.7362
[[Optimal tuning]] ([[POTE]]): ~25/21 = 1\4, ~3/2 = 702.7362


{{Optimal ET sequence|legend=1| 140, 152, 292 }}
{{Optimal ET sequence|legend=1| 140, 152, 292 }}
Line 38: Line 38:
Comma list: 1375/1372, 5120/5103, 5632/5625
Comma list: 1375/1372, 5120/5103, 5632/5625


Mapping: [{{val| 4 0 41 81 128 }}, {{val| 0 1 -5 -11 -18 }}]
Mapping: {{mapping| 4 0 41 81 128 | 0 1 -5 -11 -18 }}


POTE generator: ~3/2 = 702.6886
Optimal tuning (POTE): ~25/21 = 1\4, ~3/2 = 702.6886


{{Optimal ET sequence|legend=1| 140, 152, 292, 444d, 596d }}
{{Optimal ET sequence|legend=1| 140, 152, 292, 444d, 596d }}
Line 51: Line 51:
Comma list: 352/351, 625/624, 847/845, 1375/1372
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 }}]
Mapping: {{mapping| 4 0 41 81 128 148 | 0 1 -5 -11 -18 -21 }}


POTE generator: ~3/2 = 702.7363
Optimal tuning (POTE): ~25/21 = 1\4, ~3/2 = 702.7363


{{Optimal ET sequence|legend=1| 140, 152f, 292 }}
{{Optimal ET sequence|legend=1| 140, 152f, 292 }}
Line 60: Line 60:


== 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|legend=1| 4 0 41 -160 | 0 1 -5 27 }}


[[POTE generator]]: ~3/2 = 702.5764
[[Optimal tuning]] ([[POTE]]): ~1215/1024 = 1\4, ~3/2 = 702.5764


{{Optimal ET sequence|legend=1| 152, 316, 468, 620, 1088bcd, 1708bccdd }}
{{Optimal ET sequence|legend=1| 152, 316, 468, 620, 1088bcd, 1708bccdd }}
Line 77: Line 77:
Comma list: 3025/3024, 4375/4374, 5767168/5740875
Comma list: 3025/3024, 4375/4374, 5767168/5740875


Mapping: [{{val| 4 0 41 -160 -113 }}, {{val| 0 1 -5 27 20 }}
Mapping: {{mapping| 4 0 41 -160 -113 | 0 1 -5 27 20 }}


POTE generator: ~3/2 = 702.5826
Optimal tuning (POTE): ~1215/1024 = 1\4, ~3/2 = 702.5826


{{Optimal ET sequence|legend=1| 152, 468, 620 }}
{{Optimal ET sequence|legend=1| 152, 468, 620 }}
Line 90: Line 90:
Comma list: 1716/1715, 2080/2079, 3025/3024, 1835008/1828125
Comma list: 1716/1715, 2080/2079, 3025/3024, 1835008/1828125


Mapping: [{{val| 4 0 41 -160 -113 -334 }}, {{val| 0 1 -5 27 20 55 }}
Mapping: {{mapping| 4 0 41 -160 -113 -334 | 0 1 -5 27 20 55 }}


POTE generator: ~3/2 = 702.5741
Optimal tuning (POTE): ~1215/1024 = 1\4, ~3/2 = 702.5741


{{Optimal ET sequence|legend=1| 152f, 316, 468, 620f, 1088bcdf }}
{{Optimal ET sequence|legend=1| 152f, 316, 468, 620f, 1088bcdf }}
Line 99: Line 99:


== Twilight ==
== Twilight ==
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|legend=1| 8 0 82 -79 | 0 1 -5 8 }}


Mapping generators: ~7168/6561, ~3
: mapping generators: ~7168/6561, ~3


[[POTE generator]]: ~3/2 = 702.5090
[[Optimal tuning]] ([[POTE]]): ~7168/6561 = 1\8, ~3/2 = 702.5090


{{Optimal ET sequence|legend=1| 152, 328, 480, 1592bccddd }}
{{Optimal ET sequence|legend=1| 152, 328, 480, 1592bccddd }}
Line 118: Line 118:
Comma list: 6144/6125, 9801/9800, 19712/19683
Comma list: 6144/6125, 9801/9800, 19712/19683


Mapping: [{{val| 8 0 82 -79 15 }}, {{val| 0 1 -5 8 1 }}
Mapping: {{mapping| 8 0 82 -79 15 | 0 1 -5 8 1 }}


POTE generator: ~3/2 = 702.5090
Optimal tuning (POTE): ~12/11 = 1\8, ~3/2 = 702.5090


{{Optimal ET sequence|legend=1| 152, 328, 480, 1112bccddee, 1592bccdddeee }}
{{Optimal ET sequence|legend=1| 152, 328, 480, 1112bccddee, 1592bccdddeee }}
Line 131: Line 131:
Comma list: 1716/1715, 2080/2079, 3584/3575, 14641/14625
Comma list: 1716/1715, 2080/2079, 3584/3575, 14641/14625


Mapping: [{{val| 8 0 82 -79 15 -186 }}, {{val| 0 1 -5 8 1 17 }}
Mapping: {{mapping| 8 0 82 -79 15 -186 | 0 1 -5 8 1 17 }}


POTE generator: ~3/2 = 702.4773
Optimal tuning (POTE): ~12/11 = 1\8, ~3/2 = 702.4773


{{Optimal ET sequence|legend=1| 152f, 328, 480f, 808cdeff }}
{{Optimal ET sequence|legend=1| 152f, 328, 480f, 808cdeff }}
Line 141: Line 141:
[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Undim family| ]] <!-- main article -->
[[Category:Undim family| ]] <!-- main article -->
[[Category:Undim| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Undim_family"