Aberschismic temperaments: Difference between revisions

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== Leapday ==

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

~~: ''Not to be confused with calendar-based temperaments modes such as those in [[293edo]], [[400edo]], [[353edo]] or [[Irvic scale|Irvian mode]].''~~

[[Leapday]] tempers out {{monzo|31 -21 1}} (trisayo) in the 5-limit. This temperament can be described as 29&46 temperament, which tempers out the hemifamity and 686/675 (senga). ~~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 {{monzo|31 -21 1}} (trisayo) in the 5-limit. 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

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 686/675, 5120/5103

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[[POTE ~~generator~~]]: ~3/2 = 704.263

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

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Mapping: [{{val| 1 0 -31 -21 -14 }}, {{val| 0 1 21 15 11 }}]

POTE ~~generator~~: ~3/2 = 704.250

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

Optimal GPV sequence: {{Val list| 17c, 29, 46, 167de, 213de, 259cdde }}

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Mapping: [{{val| 1 0 -31 -21 -14 -9 }}, {{val| 0 1 21 15 11 8 }}]

POTE ~~generator~~: ~3/2 = 704.214

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

Optimal GPV sequence: {{Val list| 17c, 29, 46, 121def, 167def, 213deff }}

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Mapping: [{{val| 1 0 -31 -21 -14 -9 -34 }}, {{val| 0 1 21 15 11 8 24 }}]

POTE ~~generator~~: ~3/2 = 704.229

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

Optimal GPV sequence: {{Val list| 17cg, 29g, 46, 121defg, 167defg, 213deffg }}

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Mapping: [{{val| 1 0 -31 -21 -14 -9 -34 9 }}, {{val| 0 1 21 15 11 8 24 -3 }}]

POTE ~~generator~~: ~3/2 = 704.135

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

Optimal GPV sequence: {{Val list| 17cg, 29g, 46, 75dfgh, 121defgh }}

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

POTE ~~generator~~: ~3/2 = 704.141

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

Optimal GPV sequence: {{Val list| 17cg, 29g, 46, 75dfgh, 121defgh }}

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Mapping: [{{val| 1 0 -31 -21 -14 -9 -34 -37 }}, {{val| 0 1 21 15 11 8 24 26 }}]

POTE ~~generator~~: ~3/2 = 704.123

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

Optimal GPV sequence: {{Val list| 17cgh, 29g, 46h, 75dfg, 121defghh }}

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

POTE ~~generator~~: ~3/2 = 704.114

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

Optimal GPV sequence: {{Val list| 17cgh, 29g, 46h, 75dfg, 121defghh }}

@@ Line 36: / Line 36: @@
 == Leapday ==
+{{Main| Leapday }}
 : ''For the 5-limit version of this temperament, see [[High badness temperaments #Leapday]].''
-: ''Not to be confused with calendar-based temperaments modes such as those in [[293edo]], [[400edo]], [[353edo]] or [[Irvic scale|Irvian mode]].''
-[[Leapday]] tempers out {{monzo|31 -21 1}} (trisayo) in the 5-limit. This temperament can be described as 29&amp;46 temperament, which tempers out the hemifamity and 686/675 (senga). 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 {{monzo|31 -21 1}} (trisayo) in the 5-limit. 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
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 686/675, 5120/5103
@@ Line 49: / Line 49: @@
 {{Multival|legend=1| 1 21 15 31 21 -24 }}
-[[POTE generator]]: ~3/2 = 704.263
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.263
 {{Val list|legend=1| 17c, 29, 46, 167d, 213d, 259cdd, 305bcdd }}
@@ Line 62: / Line 62: @@
 Mapping: [{{val| 1 0 -31 -21 -14 }}, {{val| 0 1 21 15 11 }}]
-POTE generator: ~3/2 = 704.250
+Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.250
 Optimal GPV sequence: {{Val list| 17c, 29, 46, 167de, 213de, 259cdde }}
@@ Line 75: / Line 75: @@
 Mapping: [{{val| 1 0 -31 -21 -14 -9 }}, {{val| 0 1 21 15 11 8 }}]
-POTE generator: ~3/2 = 704.214
+Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.214
 Optimal GPV sequence: {{Val list| 17c, 29, 46, 121def, 167def, 213deff }}
@@ Line 88: / Line 88: @@
 Mapping: [{{val| 1 0 -31 -21 -14 -9 -34 }}, {{val| 0 1 21 15 11 8 24 }}]
-POTE generator: ~3/2 = 704.229
+Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.229
 Optimal GPV sequence: {{Val list| 17cg, 29g, 46, 121defg, 167defg, 213deffg }}
@@ Line 101: / Line 101: @@
 Mapping: [{{val| 1 0 -31 -21 -14 -9 -34 9 }}, {{val| 0 1 21 15 11 8 24 -3 }}]
-POTE generator: ~3/2 = 704.135
+Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.135
 Optimal GPV sequence: {{Val list| 17cg, 29g, 46, 75dfgh, 121defgh }}
@@ Line 114: / Line 114: @@
 Mapping: [{{val| 1 0 -31 -21 -14 -9 -34 9 -5 }}, {{val| 0 1 21 15 11 8 24 -3 6 }}]
-POTE generator: ~3/2 = 704.141
+Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.141
 Optimal GPV sequence: {{Val list| 17cg, 29g, 46, 75dfgh, 121defgh }}
@@ Line 127: / Line 127: @@
 Mapping: [{{val| 1 0 -31 -21 -14 -9 -34 -37 }}, {{val| 0 1 21 15 11 8 24 26 }}]
-POTE generator: ~3/2 = 704.123
+Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.123
 Optimal GPV sequence: {{Val list| 17cgh, 29g, 46h, 75dfg, 121defghh }}
@@ Line 140: / Line 140: @@
 Mapping: [{{val| 1 0 -31 -21 -14 -9 -34 -37 -5 }}, {{val| 0 1 21 15 11 8 24 26 6 }}]
-POTE generator: ~3/2 = 704.114
+Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.114
 Optimal GPV sequence: {{Val list| 17cgh, 29g, 46h, 75dfg, 121defghh }}