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Breed family: Difference between revisions

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Implement the proposed changes (see talk)
m Restore the category of the corresponding temp
 
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Line 69: Line 69:
Comma list: 243/242, 364/363, 441/440
Comma list: 243/242, 364/363, 441/440


Mapping: {{mapping| 1 1 1 2 2 1 | 0 2 1 1 5 11 | 0 0 2 1 0 -1 }}
{{Mapping|legend=0| 1 1 1 2 2 1 | 0 2 1 1 5 11 | 0 0 2 1 0 -1 }}


Optimal tunings:
Optimal tunings:
Line 88: Line 88:
Comma list: 243/242, 364/363, 441/440, 595/594
Comma list: 243/242, 364/363, 441/440, 595/594


Mapping: {{mapping| 1 1 1 2 2 1 3 | 0 2 1 1 5 11 9 | 0 0 2 1 0 -1 -3 }}
{{Mapping|legend=0| 1 1 1 2 2 1 3 | 0 2 1 1 5 11 9 | 0 0 2 1 0 -1 -3 }}


Optimal tunings:
Optimal tunings:
Line 106: Line 106:
Comma list: 243/242, 364/363, 441/440, 1452/1445
Comma list: 243/242, 364/363, 441/440, 1452/1445


Mapping: {{mapping| 1 1 1 2 2 1 3 | 0 4 0 1 10 23 12 | 0 0 2 1 0 -1 -1 }}
{{Mapping|legend=0| 1 1 1 2 2 1 3 | 0 4 0 1 10 23 12 | 0 0 2 1 0 -1 -1 }}
: Mapping generators: ~2, ~119/108, ~27/17
: Mapping generators: ~2, ~119/108, ~27/17


Line 122: Line 122:
Comma list: 171/170, 243/242, 324/323, 364/363, 441/440
Comma list: 171/170, 243/242, 324/323, 364/363, 441/440


Mapping: {{mapping| 1 1 1 2 2 1 3 3 | 0 4 0 1 10 23 12 4 | 0 0 2 1 0 -1 -1 1 }}
{{Mapping|legend=0| 1 1 1 2 2 1 3 3 | 0 4 0 1 10 23 12 4 | 0 0 2 1 0 -1 -1 1 }}


Optimal tunings:
Optimal tunings:
Line 137: Line 137:
Comma list: 243/242, 351/350, 441/440
Comma list: 243/242, 351/350, 441/440


Mapping: {{mapping| 1 1 1 2 2 2 | 0 2 1 1 5 -3 | 0 0 2 1 0 5 }}
{{Mapping|legend=0| 1 1 1 2 2 2 | 0 2 1 1 5 -3 | 0 0 2 1 0 5 }}


Optimal tunings:
Optimal tunings:
Line 152: Line 152:
Comma list: 144/143, 196/195, 243/242
Comma list: 144/143, 196/195, 243/242


Mapping: {{mapping| 1 1 1 2 2 4 | 0 2 1 1 5 -1 | 0 0 2 1 0 0 }}
{{Mapping|legend=0| 1 1 1 2 2 4 | 0 2 1 1 5 -1 | 0 0 2 1 0 0 }}


Optimal tunings:
Optimal tunings:
Line 167: Line 167:
Comma list: 243/242, 441/440, 676/675
Comma list: 243/242, 441/440, 676/675


Mapping: {{mapping| 2 0 1 3 -1 -1 | 0 2 1 1 5 4 | 0 0 2 1 0 2 }}
{{Mapping|legend=0| 2 0 1 3 -1 -1 | 0 2 1 1 5 4 | 0 0 2 1 0 2 }}
: mapping generators: ~55/39, ~26/15, ~10/7
: mapping generators: ~55/39, ~26/15, ~10/7


Line 179: Line 179:


== Agni ==
== Agni ==
Agni tempers out [[385/384]] and [[1375/1372]], so that a stack of three 10/7 generators is identified with [[16/11]] plus an octave. [[140edo]], [[212edo]] and [[284edo]] show how it can be tuned distinctly from [[#Jove|jove]].
This temperament suggests at least two extensions to the 13-limit: pavaka (31 & 68 & 72), named after an alias of Agni, tempers out [[625/624]]; and svaha (41 & 68 & 72), named after Agni's wife, tempers out [[325/324]]. The edos above can be used to tune both, which reduce them to [[quadritikleismic]] without much additional damage, but note pavaka is a detemperament of [[benediction]] whereas svaha is a detemperament of [[manna]].
[[Subgroup]]: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


Line 211: Line 215:
Comma list: 385/384, 625/624, 1375/1372
Comma list: 385/384, 625/624, 1375/1372


Mapping: {{mapping| 1 1 1 2 5 -1 | 0 2 1 1 0 2 | 0 0 2 1 -3 8 }}
{{Mapping|legend=0| 1 1 1 2 5 -1 | 0 2 1 1 0 2 | 0 0 2 1 -3 8 }}


Optimal tunings:
Optimal tunings:
Line 226: Line 230:
Comma list: 325/324, 385/384, 1375/1372
Comma list: 325/324, 385/384, 1375/1372


Mapping: {{mapping| 1 1 1 2 5 4 | 0 2 1 1 0 6 | 0 0 2 1 -3 -4 }}
{{Mapping|legend=0| 1 1 1 2 5 4 | 0 2 1 1 0 6 | 0 0 2 1 -3 -4 }}


Optimal tunings:
Optimal tunings:
Line 258: Line 262:
Comma list: 1001/1000, 1716/1715, 4096/4095
Comma list: 1001/1000, 1716/1715, 4096/4095


Mapping: {{mapping| 1 1 1 2 -3 7 | 0 2 1 1 8 -6 | 0 0 2 1 8 -3 }}
{{Mapping|legend=0| 1 1 1 2 -3 7 | 0 2 1 1 8 -6 | 0 0 2 1 8 -3 }}


Optimal tunings:
Optimal tunings:
Line 294: Line 298:
Comma list: 2080/2079, 2401/2400, 4096/4095
Comma list: 2080/2079, 2401/2400, 4096/4095


Mapping: {{mapping| 1 1 1 2 8 7 | 0 2 1 1 -12 -6 | 0 0 2 1 -2 -3 }}
{{Mapping|legend=0| 1 1 1 2 8 7 | 0 2 1 1 -12 -6 | 0 0 2 1 -2 -3 }}


Optimal tunings:  
Optimal tunings:  
Line 309: Line 313:
Comma list: 1216/1215, 1729/1728, 2080/2079, 2401/2400
Comma list: 1216/1215, 1729/1728, 2080/2079, 2401/2400


Subgroup-val mapping: {{mapping| 1 1 1 2 8 7 0 | 0 2 1 1 -12 -6 11 | 0 0 2 1 -2 -3 2 }}
{{Mapping|legend=2| 1 1 1 2 8 7 0 | 0 2 1 1 -12 -6 11 | 0 0 2 1 -2 -3 2 }}


Optimal tunings:  
Optimal tunings:  
Line 347: Line 351:
Comma list: 2080/2079, 2401/2400, 10648/10647
Comma list: 2080/2079, 2401/2400, 10648/10647


Mapping: {{mapping| 1 1 1 2 -1 -2 | 0 2 1 1 17 23 | 0 0 2 1 -1 -2 }}
{{Mapping|legend=0| 1 1 1 2 -1 -2 | 0 2 1 1 17 23 | 0 0 2 1 -1 -2 }}


Optimal tunings:  
Optimal tunings:  
Line 362: Line 366:
Comma list: 1216/1215, 1540/1539, 2080/2079, 2401/2400
Comma list: 1216/1215, 1540/1539, 2080/2079, 2401/2400


Mapping: {{mapping| 1 1 1 2 -1 -2 0 | 0 2 1 1 17 23 11 | 0 0 2 1 -1 -2 2 }}
{{Mapping|legend=0| 1 1 1 2 -1 -2 0 | 0 2 1 1 17 23 11 | 0 0 2 1 -1 -2 2 }}


Optimal tunings:  
Optimal tunings:  
Line 402: Line 406:
Comma list: 676/675, 1001/1000, 1716/1715
Comma list: 676/675, 1001/1000, 1716/1715


Mapping: {{mapping| 2 0 1 3 7 -1 | 0 2 1 1 -2 4 | 0 0 2 1 3 2 }}
{{Mapping|legend=0| 2 0 1 3 7 -1 | 0 2 1 1 -2 4 | 0 0 2 1 3 2 }}


Optimal tunings:
Optimal tunings:
Line 411: Line 415:


Badness (Sintel): 0.415
Badness (Sintel): 0.415
Complexity spectrum: 15/13, 7/5, 8/7, 7/6, 4/3, 15/14, 5/4, 18/13, 13/12, 14/13, 13/10, 6/5, 16/15, 11/10, 9/7, 9/8, 16/13, 10/9, 14/11, 11/8, 15/11, 12/11, 13/11, 11/9


Projection pairs: <code>2 19600/9801, 3 676/225, 5 10400/2079, 7 20384000/2910897, 11 19208000000000000/1750211597736459, 13 5026736/385875</code> to 10/7.200/99.26/15
Projection pairs: <code>2 19600/9801, 3 676/225, 5 10400/2079, 7 20384000/2910897, 11 19208000000000000/1750211597736459, 13 5026736/385875</code> to 10/7.200/99.26/15
Line 421: Line 423:
Comma list: 289/288, 442/441, 561/560, 676/675
Comma list: 289/288, 442/441, 561/560, 676/675


Mapping: {{mapping| 2 0 1 3 7 -1 5 | 0 2 1 1 -2 4 2 | 0 0 2 1 3 2 0 }}
{{Mapping|legend=0| 2 0 1 3 7 -1 5 | 0 2 1 1 -2 4 2 | 0 0 2 1 3 2 0 }}


Optimal tunings:
Optimal tunings:
Line 463: Line 465:
Comma list: 2401/2400, 3025/3024, 4096/4095
Comma list: 2401/2400, 3025/3024, 4096/4095


Mapping: {{mapping| 1 1 -1 1 5 10 | 0 2 3 2 1 -9 | 0 0 4 2 -3 -6 }}
{{Mapping|legend=0| 1 1 -1 1 5 10 | 0 2 3 2 1 -9 | 0 0 4 2 -3 -6 }}


Optimal tunings:
Optimal tunings:
Line 482: Line 484:
Comma list: 2080/2079, 2401/2400, 3025/3024
Comma list: 2080/2079, 2401/2400, 3025/3024


Mapping: {{mapping| 1 1 -1 1 5 5 | 0 2 3 2 1 6 | 0 0 4 2 -3 -5 }}
{{Mapping|legend=0| 1 1 -1 1 5 5 | 0 2 3 2 1 6 | 0 0 4 2 -3 -5 }}


Optimal tunings:
Optimal tunings:
Line 497: Line 499:
Comma list: 1540/1539, 2080/2079, 2401/2400, 3025/3024
Comma list: 1540/1539, 2080/2079, 2401/2400, 3025/3024


Subgroup-val mapping: {{mapping| 1 1 -1 1 5 5 3 | 0 2 3 2 1 6 -2 | 0 0 4 2 -3 -5 3 }}
{{Mapping|legend=2| 1 1 -1 1 5 5 3 | 0 2 3 2 1 6 -2 | 0 0 4 2 -3 -5 3 }}


Optimal tunings:
Optimal tunings:
Line 514: Line 516:
Comma list: 1001/1000, 1716/1715, 3025/3024
Comma list: 1001/1000, 1716/1715, 3025/3024


Mapping: {{mapping| 1 1 -1 1 5 -6 | 0 2 3 2 1 6 | 0 0 4 2 -3 13 }}
{{Mapping|legend=0| 1 1 -1 1 5 -6 | 0 2 3 2 1 6 | 0 0 4 2 -3 13 }}


Optimal tunings:
Optimal tunings:
Line 547: Line 549:
Comma list: 1001/1000, 1716/1715, 4225/4224
Comma list: 1001/1000, 1716/1715, 4225/4224


Mapping: {{mapping| 1 1 -1 1 -4 3 | 0 2 3 2 6 1 | 0 0 6 3 14 1 }}
{{Mapping|legend=0| 1 1 -1 1 -4 3 | 0 2 3 2 6 1 | 0 0 6 3 14 1 }}


Optimal tunings:
Optimal tunings:
Line 580: Line 582:
Comma list: 1001/1000, 1716/1715, 10648/10647
Comma list: 1001/1000, 1716/1715, 10648/10647


Mapping: {{mapping| 1 1 -7 -2 -7 -9 | 0 2 3 2 4 3 | 0 0 10 5 11 14 }}
{{Mapping|legend=0| 1 1 -7 -2 -7 -9 | 0 2 3 2 4 3 | 0 0 10 5 11 14 }}


Optimal tunings:
Optimal tunings:
Line 617: Line 619:
Comma list: 2080/2079, 2401/2400, 4375/4374
Comma list: 2080/2079, 2401/2400, 4375/4374


Mapping: {{mapping| 9 1 1 12 0 -31 | 0 2 3 2 0 5 | 0 0 0 0 1 1 }}
{{Mapping|legend=0| 9 1 1 12 0 -31 | 0 2 3 2 0 5 | 0 0 0 0 1 1 }}


Optimal tunings:
Optimal tunings:
Line 628: Line 630:


[[Category:Breed family| ]] <!-- main article -->
[[Category:Breed family| ]] <!-- main article -->
[[Category:Breed| ]] <!-- key article -->
[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Catalogs of rank-3 temperaments]]
[[Category:Catalogs of rank-3 temperaments]]
Retrieved from "https://en.xen.wiki/w/Breed_family"