Quince clan: Difference between revisions

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[[Comma list]]: 823543/819200

: mapping generators: ~2, ~343/320

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== Countermiracle ==

The countermiracle temperament tempers out the porwell comma ([[6144/6125]]), the trimyna comma ([[50421/50000]]) and the quince comma ([[823543/819200]]). It can be described as the {{nowrap| 31 & ~~145~~ }} temperament, and finds the [[3/2|perfect fifth]] -25 generators away (normalized for 2.5.7) as opposed to miracle's +6 generators. It has the [[ploidacot]] signature of 22-sheared 25-cot.

The countermiracle temperament tempers out the porwell comma ([[6144/6125]]), the trimyna comma ([[50421/50000]]) and the quince comma ([[823543/819200]]). It can be described as the {{nowrap| 31 & 176 }} temperament, and finds the [[3/2|perfect fifth]] -25 generators away (normalized for 2.5.7) as opposed to miracle's +6 generators. It has the [[ploidacot]] signature of 22-sheared 25-cot (or omega-heptaseph).

Like miracle, it is naturally an 11-limit temperament with the generator representing [[77/72]], but here the generator does not represent [[15/14]] or [[16/15]].

Like miracle, it is naturally an [[11-limit]] temperament with the generator representing [[77/72]], but here the generator does not represent [[15/14]] or [[16/15]]. [[176edo]] makes for a recommendable tuning for both the 7- and 11-limit.

Countermiracle extends less naturally to the 13- and 17-limit, with countermiraculous (31 & 145), countermanna (145 & 176), and counterbenediction (176 & 207) being possible candidates, each favoring a tuning range shown by the [[temperament merging|equal-temperament joins]].

Countermiracle extends less naturally to the [[13-limit|13-]] and [[17-limit]], with countermiraculous (31 & 145), countermanna (145 & 176), and counterbenediction (176 & 207) being possible candidates, each favoring a tuning range shown by the [[temperament merging|equal-temperament joins]].

[[Subgroup]]: 2.3.5.7

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Comma list: 441/440, 3388/3375, 6144/6125

~~Mapping:~~ {{~~mapping~~| 1 -21 -4 1 -39 | 0 25 7 2 47 }}

Optimal tunings:

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Comma list: 196/195, 352/351, 1001/1000, 6144/6125

~~Mapping:~~ {{~~mapping~~| 1 -21 -4 1 -39 29 | 0 25 7 2 47 -28 }}

Optimal tunings:

Line 95:

Comma list: 196/195, 256/255, 352/351, 1001/1000, 1225/1224

~~Mapping:~~ {{~~mapping~~| 1 -21 -4 1 -39 29 33 | 0 25 7 2 47 -28 -32 }}

{{Mapping|legend=0| 1 -21 -4 1 -39 29 33 | 0 25 7 2 47 -28 -32 }}

Optimal tunings:

Line 110:

Comma list: 351/350, 441/440, 3146/3125, 3584/3575

~~Mapping:~~ {{~~mapping~~| 1 -21 -4 1 -39 29 57 | 0 25 7 2 47 -59 }}

Optimal tunings:

Line 125:

Comma list: 351/350, 441/440, 561/560, 1632/1625, 3146/3125

~~Mapping:~~ {{~~mapping~~| 1 -21 -4 1 -39 29 57 61 | 0 25 7 2 47 -59 -63 }}

{{Mapping|legend=0| 1 -21 -4 1 -39 29 57 61 | 0 25 7 2 47 -59 -63 }}

Optimal tunings:

Line 140:

Comma list: 364/363, 441/440, 3388/3375, 6144/6125

~~Mapping:~~ {{~~mapping~~| 1 -21 -4 1 -39 -102 | 0 25 7 2 47 117 }}

Optimal tunings:

Line 155:

Comma list: 364/363, 441/440, 595/594, 1632/1625, 3388/3375

~~Mapping:~~ {{~~mapping~~| 1 -21 -4 1 -39 -102 -98 | 0 25 7 2 47 117 113 }}

{{Mapping|legend=0| 1 -21 -4 1 -39 -102 -98 | 0 25 7 2 47 117 113 }}

Optimal tunings:

Line 173:

Comma list: 343/338, 640/637

~~Subgroup-val mapping:~~ {{~~mapping~~| 1 3 3 4 | 0 -7 -2 -3 }}

~~Gencom mapping:~~ {{~~mapping~~| 1 0 3 3 0 4 | 0 0 -7 -2 0 -3 }}

Optimal tunings:

Line 190:

Comma list: 170/169, 224/221, 343/338

~~Subgroup-val mapping:~~ {{~~mapping~~| 1 3 3 4 4 | 0 -7 -2 -3 1 }}

~~Gencom mapping:~~ {{~~mapping~~| 1 0 3 3 0 4 4 | 0 0 -7 -2 0 -3 1 }}

Optimal tunings:

Line 207:

Comma list: 170/169, 224/221, 343/338, 476/475

~~Subgroup-val mapping:~~ {{~~mapping~~| 1 3 3 4 4 3 | 0 -7 -2 -3 1 13 }}

~~Gencom mapping:~~ {{~~mapping~~| 1 0 3 3 0 4 4 3 | 0 0 -7 -2 0 -3 1 13 }}

Optimal tunings:

Line 219:

Badness (Sintel): 0.759

[[Category:Quince clan| ]]

[[Category:Temperament clans]]

[[Category:~~Quince clan| ]] <!~~-~~- main article -->~~

[[Category:Catalogs of rank-2 temperaments]]

~~[[Category:Rank~~ 2]]

@@ Line 9: / Line 9: @@
 [[Comma list]]: 823543/819200
-{{Mapping|legend=2| 1 3 3 | 0 -7 -2 }}
+{{Mapping|legend=3| 1 3 3 | 0 -7 -2 }}
-{{Mapping|legend=3| 1 0 3 3 | 0 0 -7 -2 }}
+{{Mapping|legend=5| 1 0 3 3 | 0 0 -7 -2 }}
 : mapping generators: ~2, ~343/320
@@ Line 37: / Line 37: @@
 == Countermiracle ==
-The countermiracle temperament tempers out the porwell comma ([[6144/6125]]), the trimyna comma ([[50421/50000]]) and the quince comma ([[823543/819200]]). It can be described as the {{nowrap| 31 & 145 }} temperament, and finds the [[3/2|perfect fifth]] -25 generators away (normalized for 2.5.7) as opposed to miracle's +6 generators. It has the [[ploidacot]] signature of 22-sheared 25-cot.
+The countermiracle temperament tempers out the porwell comma ([[6144/6125]]), the trimyna comma ([[50421/50000]]) and the quince comma ([[823543/819200]]). It can be described as the {{nowrap| 31 & 176 }} temperament, and finds the [[3/2|perfect fifth]] -25 generators away (normalized for 2.5.7) as opposed to miracle's +6 generators. It has the [[ploidacot]] signature of 22-sheared 25-cot (or omega-heptaseph).
-Like miracle, it is naturally an 11-limit temperament with the generator representing [[77/72]], but here the generator does not represent [[15/14]] or [[16/15]].
+Like miracle, it is naturally an [[11-limit]] temperament with the generator representing [[77/72]], but here the generator does not represent [[15/14]] or [[16/15]]. [[176edo]] makes for a recommendable tuning for both the 7- and 11-limit.
-Countermiracle extends less naturally to the 13- and 17-limit, with countermiraculous (31 & 145), countermanna (145 & 176), and counterbenediction (176 & 207) being possible candidates, each favoring a tuning range shown by the [[temperament merging|equal-temperament joins]].
+Countermiracle extends less naturally to the [[13-limit|13-]] and [[17-limit]], with countermiraculous (31 & 145), countermanna (145 & 176), and counterbenediction (176 & 207) being possible candidates, each favoring a tuning range shown by the [[temperament merging|equal-temperament joins]].
 [[Subgroup]]: 2.3.5.7
@@ Line 65: / Line 65: @@
 Comma list: 441/440, 3388/3375, 6144/6125
-Mapping: {{mapping| 1 -21 -4 1 -39 | 0 25 7 2 47 }}
+{{Mapping|legend=0| 1 -21 -4 1 -39 | 0 25 7 2 47 }}
 Optimal tunings:
@@ Line 80: / Line 80: @@
 Comma list: 196/195, 352/351, 1001/1000, 6144/6125
-Mapping: {{mapping| 1 -21 -4 1 -39 29 | 0 25 7 2 47 -28 }}
+{{Mapping|legend=0| 1 -21 -4 1 -39 29 | 0 25 7 2 47 -28 }}
 Optimal tunings:
@@ Line 95: / Line 95: @@
 Comma list: 196/195, 256/255, 352/351, 1001/1000, 1225/1224
-Mapping: {{mapping| 1 -21 -4 1 -39 29 33 | 0 25 7 2 47 -28 -32 }}
+{{Mapping|legend=0| 1 -21 -4 1 -39 29 33 | 0 25 7 2 47 -28 -32 }}
 Optimal tunings:
@@ Line 110: / Line 110: @@
 Comma list: 351/350, 441/440, 3146/3125, 3584/3575
-Mapping: {{mapping| 1 -21 -4 1 -39 29 57 | 0 25 7 2 47 -59 }}
+{{Mapping|legend=0| 1 -21 -4 1 -39 29 57 | 0 25 7 2 47 -59 }}
 Optimal tunings:
@@ Line 125: / Line 125: @@
 Comma list: 351/350, 441/440, 561/560, 1632/1625, 3146/3125
-Mapping: {{mapping| 1 -21 -4 1 -39 29 57 61 | 0 25 7 2 47 -59 -63 }}
+{{Mapping|legend=0| 1 -21 -4 1 -39 29 57 61 | 0 25 7 2 47 -59 -63 }}
 Optimal tunings:
@@ Line 140: / Line 140: @@
 Comma list: 364/363, 441/440, 3388/3375, 6144/6125
-Mapping: {{mapping| 1 -21 -4 1 -39 -102 | 0 25 7 2 47 117 }}
+{{Mapping|legend=0| 1 -21 -4 1 -39 -102 | 0 25 7 2 47 117 }}
 Optimal tunings:
@@ Line 155: / Line 155: @@
 Comma list: 364/363, 441/440, 595/594, 1632/1625, 3388/3375
-Mapping: {{mapping| 1 -21 -4 1 -39 -102 -98 | 0 25 7 2 47 117 113 }}
+{{Mapping|legend=0| 1 -21 -4 1 -39 -102 -98 | 0 25 7 2 47 117 113 }}
 Optimal tunings:
@@ Line 173: / Line 173: @@
 Comma list: 343/338, 640/637
-Subgroup-val mapping: {{mapping| 1 3 3 4 | 0 -7 -2 -3 }}
+{{Mapping|legend=2| 1 3 3 4 | 0 -7 -2 -3 }}
-Gencom mapping: {{mapping| 1 0 3 3 0 4 | 0 0 -7 -2 0 -3 }}
+{{Mapping|legend=4| 1 0 3 3 0 4 | 0 0 -7 -2 0 -3 }}
 Optimal tunings:
@@ Line 190: / Line 190: @@
 Comma list: 170/169, 224/221, 343/338
-Subgroup-val mapping: {{mapping| 1 3 3 4 4 | 0 -7 -2 -3 1 }}
+{{Mapping|legend=2| 1 3 3 4 4 | 0 -7 -2 -3 1 }}
-Gencom mapping: {{mapping| 1 0 3 3 0 4 4 | 0 0 -7 -2 0 -3 1 }}
+{{Mapping|legend=4| 1 0 3 3 0 4 4 | 0 0 -7 -2 0 -3 1 }}
 Optimal tunings:
@@ Line 207: / Line 207: @@
 Comma list: 170/169, 224/221, 343/338, 476/475
-Subgroup-val mapping: {{mapping| 1 3 3 4 4 3 | 0 -7 -2 -3 1 13 }}
+{{Mapping|legend=2| 1 3 3 4 4 3 | 0 -7 -2 -3 1 13 }}
-Gencom mapping: {{mapping| 1 0 3 3 0 4 4 3 | 0 0 -7 -2 0 -3 1 13 }}
+{{Mapping|legend=4| 1 0 3 3 0 4 4 3 | 0 0 -7 -2 0 -3 1 13 }}
 Optimal tunings:
@@ Line 219: / Line 219: @@
 Badness (Sintel): 0.759
+[[Category:Quince clan| ]] <!-- main article -->
 [[Category:Temperament clans]]
-[[Category:Quince clan| ]] <!-- main article -->
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Rank 2]]

Quince clan: Difference between revisions

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