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Syntonic–chromatic equivalence continuum: Difference between revisions

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Line 23: Line 23:
| -5
| -5
| -3
| -3
| 7 & 64 ([[Nadir]])
| [[Nadir]]
| [[1162261467/1048576000]]
| [[1162261467/1048576000]]
| {{monzo| -23 19 -3}}
| {{monzo| -23 19 -3}}
|-
|-
| -4
| -4
| -2
| -2
| 7 & 52 ([[Tragicomical]])
| [[Tragicomical]]
| [[14348907/13107200]]
| [[14348907/13107200]]
| {{monzo| -19 15 -2}}
| {{monzo| -19 15 -2}}
Line 35: Line 35:
| -3
| -3
| -1
| -1
| 7 & 33 ([[Deeptone]])
| [[Deeptone]]
| [[177147/163840]]
| [[177147/163840]]
| {{monzo| -15 11 -1}}
| {{monzo| -15 11 -1}}
Line 173: Line 173:
[[Comma list]]: 1125/1024
[[Comma list]]: 1125/1024


[[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -3 2 }}]
{{Mapping|legend=1| 1 2 2 | 0 -3 2 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1/1, ~16/15 = 173.101
[[Optimal tuning]] ([[POTE]]): ~2 = 1/1, ~16/15 = 173.101
Line 190: Line 190:
[[Comma list]]: 10460353203/10240000000
[[Comma list]]: 10460353203/10240000000


[[Mapping]]: [{{val| 7 0 -17 }}, {{val| 0 1 3 }}]
{{Mapping|legend=1| 7 0 -17 | 0 1 3 }}


: mapping generators: ~800/729, ~3
: mapping generators: ~800/729, ~3
Line 209: Line 209:
[[Comma list]]: {{monzo| 14 -22 9 }}
[[Comma list]]: {{monzo| 14 -22 9 }}


[[Mapping]]: [{{val| 1 8 18 }}, {{val| 0 -9 -22 }}]
{{Mapping|legend=1| 1 8 18 | 0 -9 -22 }}


: mapping generators: ~2, ~400/243
: mapping generators: ~2, ~400/243
Line 228: Line 228:
[[Comma list]]: 5000000/4782969
[[Comma list]]: 5000000/4782969


[[Mapping]]: [{{val| 7 0 -6 }}, {{val| 0 1 2 }}]
{{Mapping|legend=1| 7 0 -6 | 0 1 2 }}


[[Optimal tuning]] ([[POTE]]): ~10/9 = 1\7, ~3/2 = 706.288
[[Optimal tuning]] ([[POTE]]): ~10/9 = 1\7, ~3/2 = 706.288
Line 243: Line 243:
[[Comma list]]: 78125/69984
[[Comma list]]: 78125/69984


[[Mapping]]: [{{val| 7 0 5 }}, {{val| 0 1 1 }}]
{{Mapping|legend=1| 7 0 5 | 0 1 1 }}


[[Optimal tuning]] ([[POTE]]): ~125/108 = 1\7, ~3/2 = 706.410
[[Optimal tuning]] ([[POTE]]): ~125/108 = 1\7, ~3/2 = 706.410
Line 252: Line 252:


== Deeptone ==
== Deeptone ==
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 177147/163840
[[Comma list]]: 177147/163840


[[Mapping]]: [{{val| 1 2 7 }}, {{val| 0 -1 -11 }}]
{{Mapping|legend=1| 1 0 -15 | 0 1 11 }}
 
: mapping generators: ~2, ~3


[[Optimal tuning]] ([[POTE]]): 2/1 = 1200.0000, ~4/3 = 511.0100
[[Optimal tuning]] ([[CTE]]): ~2/1 = 1\1, ~3/2 = 689.8791


Recommended ETs: [[33edo]], [[40edo]], [[47edo]], [[54edo]]
{{Optimal ET sequence|legend=1| 7, 33, 40, 47, 54b }}


[[Badness]]:
[[Badness]]: 0.403


== Tragicomical ==
== Tragicomical ==
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 14348907/13107200‎‎
[[Comma list]]: 14348907/13107200‎‎


[[Mapping]]: [{{val| 1 1 -1 }}, {{val| 0 2 15 }}]
{{Mapping|legend=1| 1 1 -1 | 0 2 15 }}


[[Optimal tuning]] ([[POTE]]): 2/1 = 1200.0000, ~3/2 = 345.3878
: mapping generators: ~2, ~2560/2187


Recommended ETs: [[28edo]], [[35edo]], [[38edo]], [[45edo]], [[52edo]], [[59edo]], [[66edo]]
[[Optimal tuning]] ([[CTE]]): 2/1 = 1\1, ~2560/2187 = 345.9462


[[Badness]]:
{{Optimal ET sequence|legend=1| 7, 38c, 45c, 52, 59, 66b }}
 
[[Badness]]: 0.828


== Nadir ==
== Nadir ==
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 1162261467/1048576000
[[Comma list]]: 1162261467/1048576000


[[Mapping]]: [{{val| 1 2 5 }}, {{val| 0 -3 -19 }}]
{{Mapping|legend=1| 1 2 5 | 0 -3 -19 }}
 
: mapping generators: ~2, ~729/640


[[Optimal tuning]] ([[POTE]]): 2/1 = 12000.0000, ~3/2 = 169.3761
[[Optimal tuning]] ([[CTE]]): 2/1 = 1\1, ~729/640 = 168.9826


Recommended ETs: [[28edo]], [[35edo]], [[57edo]], [[64edo]], [[71edo]], [[78edo]]
{{Optimal ET sequence|legend=1| 7, 57c, 64, 71b, 78b, 85b }}


[[Badness]]:
[[Badness]]: 1.47


[[Category:7edo]]
[[Category:7edo]]
[[Category:Equivalence continua]]
[[Category:Equivalence continua]]
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