Miscellaneous 7-limit temperaments: Difference between revisions

Line 14:

[[Comma list]]: 703125/702464

: mapping generators: ~2, ~3, ~75~~/56~~

: mapping generators: ~2, ~3, ~112/75

[[Optimal tuning]] ([[~~POTE~~]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.~~8766~~{{c}}, ~75~~/56~~ = ~~505~~.~~2613~~{{c}}

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.0384{{c}}, ~3/2 = 701.8990{{c}}, ~112/75 = 694.7610{{c}}

: [[error map]]: {{val| +0.038 -0.018 -0.132 +0.083 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8998{{c}}, ~112/75 = 694.7370{{c}}

: error map: {{val| 0.000 -0.055 -0.203 +0.033 }}

{{Optimal ET sequence|legend=1| 12, 19, 31, 81, 90, 102d, 109, 121, 140, 152, 171, 665, 836, 1007, 2185, 3192c }}

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: mapping generators: ~2, ~3, ~5

[[Optimal tuning]] ([[~~POTE~~]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.~~0901~~{{c}}, ~5/4 = 386.~~6931~~{{c}}

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9205{{c}}, ~3/2 = 702.0435{{c}}, ~5/4 = 386.6674{{c}}

: [[error map]]: {{val| -0.079 +0.009 +0.195 -0.029 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0491{{c}}, ~5/4 = 386.6885{{c}}

: error map: {{val| 0.000 +0.094 +0.375 +0.108 }}

{{Optimal ET sequence|legend=1| 31, 87, 118, 152, 239, 270, 571, 723, 841, 993, 1263, 1564c, 1834c, 2104c }}

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Line 123:

: mapping generators: ~15/14, ~3, ~5

[[Optimal tuning]] ([[~~CTE~~]]): ~15/14 = ~~1200~~.0000{{c}}, ~3/2 = 702.~~0437~~{{c}}, ~5/4 = 386.~~5040~~{{c}}

[[Optimal tuning]]s:

* [[WE]]: ~15/14 = 119.9964{{c}}, ~3/2 = 702.0734{{c}}, ~5/4 = 386.5626{{c}}

: [[error map]]: {{val| -0.036 +0.082 +0.177 -0.258 }}

* [[CWE]]: ~15/14 = 120.0000{{c}}, ~3/2 = 702.0700{{c}}, ~5/4 = 386.5404{{c}}

: error map: {{val| 0.000 +0.115 +0.227 -0.215 }}

{{Optimal ET sequence|legend=1| 50, 60, 80, 130, 270, 1270, 1540, 1810, 1940, 2080, 2210c, 2480c }}

@@ Line 14: / Line 14: @@
 [[Comma list]]: 703125/702464
-{{Mapping|legend=1| 1 0 2 1 | 0 1 1 3 | 0 0 -3 -7 }}
+{{Mapping|legend=1| 1 0 2 1 | 0 1 1 3 | 0 0 3 7 }}
-: mapping generators: ~2, ~3, ~75/56
+: mapping generators: ~2, ~3, ~112/75
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.8766{{c}}, ~75/56 = 505.2613{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0384{{c}}, ~3/2 = 701.8990{{c}}, ~112/75 = 694.7610{{c}}
+: [[error map]]: {{val| +0.038 -0.018 -0.132 +0.083 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8998{{c}}, ~112/75 = 694.7370{{c}}
+: error map: {{val| 0.000 -0.055 -0.203 +0.033 }}
 {{Optimal ET sequence|legend=1| 12, 19, 31, 81, 90, 102d, 109, 121, 140, 152, 171, 665, 836, 1007, 2185, 3192c }}
@@ Line 77: / Line 81: @@
 : mapping generators: ~2, ~3, ~5
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.0901{{c}}, ~5/4 = 386.6931{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9205{{c}}, ~3/2 = 702.0435{{c}}, ~5/4 = 386.6674{{c}}
+: [[error map]]: {{val| -0.079 +0.009 +0.195 -0.029 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0491{{c}}, ~5/4 = 386.6885{{c}}
+: error map: {{val| 0.000 +0.094 +0.375 +0.108 }}
 {{Optimal ET sequence|legend=1| 31, 87, 118, 152, 239, 270, 571, 723, 841, 993, 1263, 1564c, 1834c, 2104c }}
@@ Line 115: / Line 123: @@
 : mapping generators: ~15/14, ~3, ~5
-[[Optimal tuning]] ([[CTE]]): ~15/14 = 1200.0000{{c}}, ~3/2 = 702.0437{{c}}, ~5/4 = 386.5040{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~15/14 = 119.9964{{c}}, ~3/2 = 702.0734{{c}}, ~5/4 = 386.5626{{c}}
+: [[error map]]: {{val| -0.036 +0.082 +0.177 -0.258 }}
+* [[CWE]]: ~15/14 = 120.0000{{c}}, ~3/2 = 702.0700{{c}}, ~5/4 = 386.5404{{c}}
+: error map: {{val| 0.000 +0.115 +0.227 -0.215 }}
 {{Optimal ET sequence|legend=1| 50, 60, 80, 130, 270, 1270, 1540, 1810, 1940, 2080, 2210c, 2480c }}