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Hemimean family: Difference between revisions

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Line 9: Line 9:
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 3136/3125 (hemimean)
[[Comma list]]: 3136/3125


{{Mapping|legend=1| 1 0 0 -3 | 0 1 0 0 | 0 0 2 5 }}
{{Mapping|legend=1| 1 0 0 -3 | 0 1 0 0 | 0 0 2 5 }}
Line 21: Line 21:
: Angle (28/25, 3/2) = 90 degrees
: Angle (28/25, 3/2) = 90 degrees


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9550, ~28/25 = 193.6499
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000¢, ~3/2 = 701.955¢, ~28/25 = 193.650¢
* [[CWE]]: ~2 = 1200.000¢, ~3/2 = 702.112¢, ~28/25 = 193.717¢


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 111: Line 113:
: Angle (28/25, 16/15) = 93.2696
: Angle (28/25, 16/15) = 93.2696


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.7205, ~28/25 = 193.5545
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000¢, ~3/2 = 701.720¢, ~28/25 = 193.554¢
* [[CWE]]: ~2 = 1200.000¢, ~3/2 = 701.714¢, ~28/25 = 193.552¢


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 133: Line 137:
Mapping: {{mapping| 1 0 0 -3 -9 15 | 0 1 0 0 2 -2 | 0 0 2 5 8 -7 }}
Mapping: {{mapping| 1 0 0 -3 -9 15 | 0 1 0 0 2 -2 | 0 0 2 5 8 -7 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.8219, ~28/25 = 193.5816
Optimal tunings:
* CTE: ~2 = 1200.000¢, ~3/2 = 701.822¢, ~28/25 = 193.582¢
* CWE: ~2 = 1200.000¢, ~3/2 = 701.835¢, ~28/25 = 193.596¢


{{Optimal ET sequence|legend=1| 31, 43, 56, 74, 87, 118, 130, 217, 248, 347e, 378, 465, 595e }}
{{Optimal ET sequence|legend=0| 31, 43, 56, 74, 87, 118, 130, 217, 248, 347e, 378, 465, 595e }}


Badness (Sintel): 1.034
Badness (Sintel): 1.034
Line 146: Line 152:
Mapping: {{mapping| 1 0 0 -3 -9 -4 | 0 1 0 0 2 -1 | 0 0 2 5 8 8 }}
Mapping: {{mapping| 1 0 0 -3 -9 -4 | 0 1 0 0 2 -1 | 0 0 2 5 8 8 }}


Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.5667, ~28/25 = 193.2493
Optimal tunings:
* CTE: ~2 = 1200.000¢, ~3/2 = 702.567¢, ~28/25 = 193.249¢
* CWE: ~2 = 1200.000¢, ~3/2 = 702.634¢, ~28/25 = 193.293¢


{{Optimal ET sequence|legend=1| 12f, 19e, 31, 56, 68e, 87, 118, 186ef, 205d }}
{{Optimal ET sequence|legend=0| 12f, 19e, 31, 56, 68e, 87, 118, 186ef, 205d }}


Badness (Sintel): 1.183
Badness (Sintel): 1.183
Line 161: Line 169:
: Mapping generators: ~2, ~3, ~56/25
: Mapping generators: ~2, ~3, ~56/25


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.1636, ~28/25 = 193.8645
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000¢, ~3/2 = 701.164¢, ~28/25 = 193.865¢
* [[CWE]]: ~2 = 1200.000¢, ~3/2 = 701.723¢, ~28/25 = 193.995¢


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 181: Line 191:
: Mapping generators: ~2, ~3, ~18/11
: Mapping generators: ~2, ~3, ~18/11


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.2875, ~18/11 = 854.3132
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000¢, ~3/2 = 702.288¢, ~18/11 = 854.313¢
* [[CWE]]: ~2 = 1200.000¢, ~3/2 = 702.407¢, ~18/11 = 854.350¢


{{Optimal ET sequence|legend=1| 24d, 31, 80, 87, 111, 118, 198, 316, 514c, 545c }}
{{Optimal ET sequence|legend=1| 24d, 31, 80, 87, 111, 118, 198, 316, 514c, 545c }}
Line 218: Line 230:


[[Badness]] (Sintel): 1.550
[[Badness]] (Sintel): 1.550
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Comma list: 289/288, 561/560, 1001/1000, 1632/1625
Mapping: {{Mapping| 2 0 0 -6 -3 15 5 | 0 1 0 0 -2 2 1 | 0 0 2 5 7 -6 0 }}
Optimal tunings:
* CTE: ~17/12 = 600.000¢, ~3/2 = 702.108¢, ~28/25 = 193.723¢
* CWE: ~17/12 = 600.000¢, ~3/2 = 702.269¢, ~28/25 = 193.776¢
{{Optimal ET sequence|legend=0| 12, 50, 68, 80, 118, 130, 198 }}
[[Badness]] (Sintel): 1.743


[[Category:Temperament families]]
[[Category:Temperament families]]
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