Aberschismic temperaments: Difference between revisions

Line 46:

: ''For the 5-limit version of this temperament, see [[High badness temperaments #Leapday]].''

Leapday tempers out the leapday comma, {{monzo| 31 -21 1 }}, in the 5-limit, mapping 5/4 to the triple augmented unison (3A1) or equivalently the minor third (m3) + 2 Pyth. commas. This temperament can be described as the 29 & 46 temperament, which tempers out the hemifamity and [[686/675]] (senga). The alternative extension [[Porwell temperaments #Polypyth|polypyth]] (46 & 121) tempers out the same 5-limit comma as the leapday, but with the porwell ([[6144/6125]]) rather than the hemifamity tempered out.

Leapday tempers out the leapday comma, {{monzo| 31 -21 1 }}, in the 5-limit, mapping 5/4 to the triple-augmented unison (3A1) or equivalently the minor third (m3) + 2 Pyth. commas. This temperament can be described as the 29 & 46 temperament, which tempers out the hemifamity and [[686/675]] (senga). The alternative extension [[Porwell temperaments #Polypyth|polypyth]] (46 & 121) tempers out the same 5-limit comma as the leapday, but with the porwell ([[6144/6125]]) rather than the hemifamity tempered out.

[[Subgroup]]: 2.3.5.7

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[[~~Optimal tuning~~]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.263

Optimal tunings:

* [[CTE]]: ~2 = 1\1, ~3/2 = 704.2257

* [[POTE]]: ~2 = 1\1, ~3/2 = 704.263

{{Optimal ET sequence|legend=1| 17c, 29, 46~~, 167d, 213d, 259cdd, 305bcdd~~ }}

[[Badness]]: 0.096123

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Mapping: {{mapping| 1 0 -31 -21 -14 | 0 1 21 15 11 }}

Optimal ~~tuning (~~POTE): ~2 = 1\1, ~3/2 = 704.250

Optimal tunings:

* CTE: ~2 = 1\1, ~3/2 = 704.2625

* POTE: ~2 = 1\1, ~3/2 = 704.250

{{Optimal ET sequence|legend=1| 17c, 29, 46~~, 167de, 213de, 259cdde~~ }}

Badness: 0.038624

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Mapping: {{mapping| 1 0 -31 -21 -14 -9 | 0 1 21 15 11 8 }}

Optimal ~~tuning (~~POTE): ~2 = 1\1, ~3/2 = 704.214

Optimal tunings:

* CTE: ~2 = 1\1, ~3/2 = 704.2924

* POTE: ~2 = 1\1, ~3/2 = 704.214

{{Optimal ET sequence|legend=1| 17c, 29, 46, 121def~~, 167def, 213deff~~ }}

Badness: 0.024732

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Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 | 0 1 21 15 11 8 24 }}

Optimal ~~tuning (~~POTE): ~2 = 1\1, ~3/2 = 704.229

Optimal tunings:

* CTE: ~2 = 1\1, ~3/2 = 704.3098

* POTE: ~2 = 1\1, ~3/2 = 704.229

{{Optimal ET sequence|legend=1| 17cg, 29g, 46, 121defg~~, 167defg, 213deffg~~ }}

Badness: 0.017863

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Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 9 | 0 1 21 15 11 8 24 -3 }}

Optimal ~~tuning (~~POTE): ~2 = 1\1, ~3/2 = 704.135

Optimal tunings:

* CTE: ~2 = 1\1, ~3/2 = 704.2990

* POTE: ~2 = 1\1, ~3/2 = 704.135

{{Optimal ET sequence|legend=1| 17cg, 29g, 46, 75dfgh, 121defgh }}

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Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 9 -5 | 0 1 21 15 11 8 24 -3 6 }}

Optimal ~~tuning (~~POTE): ~2 = 1\1, ~3/2 = 704.141

Optimal tunings:

* CTE: ~2 = 1\1, ~3/2 = 704.3035

* POTE: ~2 = 1\1, ~3/2 = 704.141

{{Optimal ET sequence|legend=1| 17cg, 29g, 46, 75dfgh, 121defgh }}

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Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 -37 | 0 1 21 15 11 8 24 26 }}

Optimal ~~tuning (~~POTE): ~2 = 1\1, ~3/2 = 704.123

Optimal tunings:

* CTE: ~2 = 1\1, ~3/2 = 704.2037

* POTE: ~2 = 1\1, ~3/2 = 704.123

{{Optimal ET sequence|legend=1| 17cgh, 29g, 46h, 75dfg~~, 121defghh~~ }}

Badness: 0.019065

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Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 -37 -5 | 0 1 21 15 11 8 24 26 6 }}

Optimal ~~tuning (~~POTE): ~2 = 1\1, ~3/2 = 704.114

Optimal tunings:

* CTE: ~2 = 1\1, ~3/2 = 704.2082

* POTE: ~2 = 1\1, ~3/2 = 704.114

{{Optimal ET sequence|legend=1| 17cgh, 29g, 46h, 75dfg~~, 121defghh~~ }}

Badness: 0.016067

@@ Line 46: / Line 46: @@
 : ''For the 5-limit version of this temperament, see [[High badness temperaments #Leapday]].''
-Leapday tempers out the leapday comma, {{monzo| 31 -21 1 }}, in the 5-limit, mapping 5/4 to the triple augmented unison (3A1) or equivalently the minor third (m3) + 2 Pyth. commas. This temperament can be described as the 29 &amp; 46 temperament, which tempers out the hemifamity and [[686/675]] (senga). The alternative extension [[Porwell temperaments #Polypyth|polypyth]] (46 &amp; 121) tempers out the same 5-limit comma as the leapday, but with the porwell ([[6144/6125]]) rather than the hemifamity tempered out.
+Leapday tempers out the leapday comma, {{monzo| 31 -21 1 }}, in the 5-limit, mapping 5/4 to the triple-augmented unison (3A1) or equivalently the minor third (m3) + 2 Pyth. commas. This temperament can be described as the 29 &amp; 46 temperament, which tempers out the hemifamity and [[686/675]] (senga). The alternative extension [[Porwell temperaments #Polypyth|polypyth]] (46 &amp; 121) tempers out the same 5-limit comma as the leapday, but with the porwell ([[6144/6125]]) rather than the hemifamity tempered out.
 [[Subgroup]]: 2.3.5.7
@@ Line 56: / Line 56: @@
 {{Multival|legend=1| 1 21 15 31 21 -24 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.263
+Optimal tunings:
+* [[CTE]]: ~2 = 1\1, ~3/2 = 704.2257
+* [[POTE]]: ~2 = 1\1, ~3/2 = 704.263
-{{Optimal ET sequence|legend=1| 17c, 29, 46, 167d, 213d, 259cdd, 305bcdd }}
+{{Optimal ET sequence|legend=1| 17c, 29, 46 }}
 [[Badness]]: 0.096123
@@ Line 69: / Line 71: @@
 Mapping: {{mapping| 1 0 -31 -21 -14 | 0 1 21 15 11 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.250
+Optimal tunings:
+* CTE: ~2 = 1\1, ~3/2 = 704.2625
+* POTE: ~2 = 1\1, ~3/2 = 704.250
-{{Optimal ET sequence|legend=1| 17c, 29, 46, 167de, 213de, 259cdde }}
+{{Optimal ET sequence|legend=1| 17c, 29, 46 }}
 Badness: 0.038624
@@ Line 82: / Line 86: @@
 Mapping: {{mapping| 1 0 -31 -21 -14 -9 | 0 1 21 15 11 8 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.214
+Optimal tunings:
+* CTE: ~2 = 1\1, ~3/2 = 704.2924
+* POTE: ~2 = 1\1, ~3/2 = 704.214
-{{Optimal ET sequence|legend=1| 17c, 29, 46, 121def, 167def, 213deff }}
+{{Optimal ET sequence|legend=1| 17c, 29, 46, 121def }}
 Badness: 0.024732
@@ Line 95: / Line 101: @@
 Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 | 0 1 21 15 11 8 24 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.229
+Optimal tunings:
+* CTE: ~2 = 1\1, ~3/2 = 704.3098
+* POTE: ~2 = 1\1, ~3/2 = 704.229
-{{Optimal ET sequence|legend=1| 17cg, 29g, 46, 121defg, 167defg, 213deffg }}
+{{Optimal ET sequence|legend=1| 17cg, 29g, 46, 121defg }}
 Badness: 0.017863
@@ Line 108: / Line 116: @@
 Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 9 | 0 1 21 15 11 8 24 -3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.135
+Optimal tunings:
+* CTE: ~2 = 1\1, ~3/2 = 704.2990
+* POTE: ~2 = 1\1, ~3/2 = 704.135
 {{Optimal ET sequence|legend=1| 17cg, 29g, 46, 75dfgh, 121defgh }}
@@ Line 121: / Line 131: @@
 Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 9 -5 | 0 1 21 15 11 8 24 -3 6 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.141
+Optimal tunings:
+* CTE: ~2 = 1\1, ~3/2 = 704.3035
+* POTE: ~2 = 1\1, ~3/2 = 704.141
 {{Optimal ET sequence|legend=1| 17cg, 29g, 46, 75dfgh, 121defgh }}
@@ Line 134: / Line 146: @@
 Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 -37 | 0 1 21 15 11 8 24 26 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.123
+Optimal tunings:
+* CTE: ~2 = 1\1, ~3/2 = 704.2037
+* POTE: ~2 = 1\1, ~3/2 = 704.123
-{{Optimal ET sequence|legend=1| 17cgh, 29g, 46h, 75dfg, 121defghh }}
+{{Optimal ET sequence|legend=1| 17cgh, 29g, 46h, 75dfg }}
 Badness: 0.019065
@@ Line 147: / Line 161: @@
 Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 -37 -5 | 0 1 21 15 11 8 24 26 6 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.114
+Optimal tunings:
+* CTE: ~2 = 1\1, ~3/2 = 704.2082
+* POTE: ~2 = 1\1, ~3/2 = 704.114
-{{Optimal ET sequence|legend=1| 17cgh, 29g, 46h, 75dfg, 121defghh }}
+{{Optimal ET sequence|legend=1| 17cgh, 29g, 46h, 75dfg }}
 Badness: 0.016067