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== Telepathy ==
== Telepathy ==
Commas: 55/54, 99/98, 176/175
 
Subgroup: 2.3.5.7.11
 
Comma list: 55/54, 99/98, 176/175
 
Mapping: [<1 0 2 -1 -1|, <0 5 1 12 14|]


POTE generator: ~5/4 = 381.019
POTE generator: ~5/4 = 381.019


Map: [<1 0 2 -1 -1|, <0 5 1 12 14|]
{{Val list|legend=1| 19e, 22, 41e, 63e }}
 
{{EDOs|legend=1| 19e, 22, 41e, 63e }}


Badness: 0.0271
Badness: 0.0271


=== 13-limit ===
=== 13-limit ===
Commas: 55/54, 65/64, 91/90, 99/98
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 55/54, 65/64, 91/90, 99/98
 
Mapping: [<1 0 2 -1 -1 4|, <0 5 1 12 14 -1|]


POTE generator: ~5/4 = 380.520
POTE generator: ~5/4 = 380.520


Map: [<1 0 2 -1 -1 4|, <0 5 1 12 14 -1|]
{{Val list|legend=1| 19e, 22, 41ef }}
 
{{EDOs|legend=1| 19e, 22, 41ef }}


Badness: 0.0255
Badness: 0.0255


== Horcrux ==
== Horcrux ==
Commas: 45/44, 56/55, 245/243
 
Subgroup: 2.3.5.7.11
 
Comma list: 45/44, 56/55, 245/243
 
Mapping: [<1 0 2 -1 0|, <0 5 1 12 11|]


POTE generator: ~5/4 = 379.642
POTE generator: ~5/4 = 379.642


Map: [<1 0 2 -1 0|, <0 5 1 12 11|]
{{Val list|legend=1| 19, 41e, 60e }}
 
{{EDOs|legend=1| 19, 41e, 60e }}


Badness: 0.0393
Badness: 0.0393


== Divination ==
== Divination ==
Commas: 121/120, 225/224, 245/243
 
Subgroup: 2.3.5.7.11
 
Comma list: 121/120, 225/224, 245/243
 
Mapping: [<2 0 4 -2 5|, <0 5 1 12 3|]


POTE generator: ~5/4 = 380.233
POTE generator: ~5/4 = 380.233


Map: [<2 0 4 -2 5|, <0 5 1 12 3|]
{{Val list|legend=1| 22, 38d, 60e, 142cde }}
 
{{EDOs|legend=1| 22, 38d, 60e, 142cde }}


Badness: 0.0359
Badness: 0.0359


=== 13-limit ===
=== 13-limit ===
Commas: 105/104, 121/120, 196/195, 245/243
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 105/104, 121/120, 196/195, 245/243
 
Mapping: [<2 0 4 -2 5 -4|, <0 5 1 12 3 18|]


POTE generator: ~5/4 = 379.920
POTE generator: ~5/4 = 379.920


Map: [<2 0 4 -2 5 -4|, <0 5 1 12 3 18|]
{{Val list|legend=1| 22f, 60e }}
 
{{EDOs|legend=1| 22f, 60e }}


Badness: 0.0346
Badness: 0.0346


== Soothsaying ==
== Soothsaying ==
Commas: 100/99, 225/224, 245/243, 1352/1331
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 100/99, 225/224, 245/243, 1352/1331
 
Mapping: [<2 0 4 -2 12 15|, <0 5 1 12 -8 -12|]


POTE generator: ~5/4 = 380.508
POTE generator: ~5/4 = 380.508


Map: [<2 0 4 -2 12 15|, <0 5 1 12 -8 -12|]
{{Val list|legend=1| 22, 60, 82 }}
 
{{EDOs|legend=1| 22, 60, 82 }}


Badness: 0.0554
Badness: 0.0554


== Witchcraft ==
== Witchcraft ==
Commas: 225/224, 245/243, 441/440
 
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 245/243, 441/440
 
Mapping: [<1 0 2 -1 -7|, <0 5 1 12 33|]


POTE generator: ~5/4 = 380.232
POTE generator: ~5/4 = 380.232


Map: [<1 0 2 -1 -7|, <0 5 1 12 33|]
{{Val list|legend=1| 41, 60e, 101cd, 243cde }}
 
{{EDOs|legend=1| 41, 60e, 101cd, 243cde }}


Badness: 0.0307
Badness: 0.0307


=== 13-limit ===
=== 13-limit ===
Commas: 105/104, 196/195, 245/243, 275/273
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 105/104, 196/195, 245/243, 275/273
 
Mapping: [<1 0 2 -1 -7 -2|, <0 5 1 12 33 18|]


POTE generator: ~5/4 = 380.189
POTE generator: ~5/4 = 380.189


Map: [<1 0 2 -1 -7 -2|, <0 5 1 12 33 18|]
{{Val list|legend=1| 41, 60e, 101cd }}
 
{{EDOs|legend=1| 41, 60e, 101cd }}


Badness: 0.0235
Badness: 0.0235


= Muggles =
= Muggles =
Aside from 3125/3072 and 525/512 muggles also tempers out 126/125 and 1323/1280. A good muggles tuning is [[19edo]], in which tuning it's the same thing as magic. Muggles works better for small scales than magic in the sense that 7 or 10 note MOS are reasonable choices. The muggles wedgie is <<5 1 -7 -10 -25 -19||.
Aside from 3125/3072 and 525/512 muggles also tempers out [[126/125]] and 1323/1280. A good muggles tuning is [[19edo]], in which tuning it's the same thing as magic. Muggles works better for small scales than magic in the sense that 7 or 10 note MOS are reasonable choices.  
 
Subgroup: 2.3.5.7
 
[[Comma list]]: 126/125, 525/512
 
[[Mapping]]: [<1 0 2 5|, <0 5 1 -7|]


Commas: 126/125, 525/512
{{Multival|legend=1| 5 1 -7 -10 -25 -19 }}


[[POTE generator]]: ~5/4 = 378.479
[[POTE generator]]: ~5/4 = 378.479


Map: [<1 0 2 5|, <0 5 1 -7|]
{{Val list|legend=1| 16, 19, 73bcd, 92bcd }}


{{EDOs|legend=1| 16, 19, 73bcd, 92bcd }}
[[Badness]]: 0.0562
 
== 11-limit ==


Badness: 0.0562
Subgroup: 2.3.5.7.11


== 11-limit ==
Comma list: 45/44, 126/125, 385/384
Commas: 45/44, 126/125, 385/384


[[POTE generator]]: ~5/4 = 377.724
Mapping: [<1 0 2 5 0|, <0 5 1 -7 11|]


Map: [<1 0 2 5 0|, <0 5 1 -7 11|]
POTE generator: ~5/4 = 377.724


{{EDOs|legend=1| 16, 19, 35, 54bd }}
{{Val list|legend=1| 16, 19, 35, 54bd }}


Badness: 0.0480
Badness: 0.0480


== 13-limit ==
== 13-limit ==
Commas: 45/44, 65/64, 78/77, 126/125


[[POTE_tuning|POTE generator]]: ~5/4 = 377.724
Subgroup: 2.3.5.7.11.13
 
Comma list: 45/44, 65/64, 78/77, 126/125
 
Mapping: [<1 0 2 5 0 4|, <0 5 1 -7 11 -1|]


Map: [<1 0 2 5 0 4|, <0 5 1 -7 11 -1|]
POTE generator: ~5/4 = 377.724


{{EDOs|legend=1| 16, 19, 35f, 54bdf }}
{{Val list|legend=1| 16, 19, 35f, 54bdf }}


Badness: 0.0309
Badness: 0.0309


= Astrology =
= Astrology =
Commas: 50/49, 3125/3072


POTE generator: ~5/4 = 380.578
Subgroup: 2.3.5.7
 
[[Comma list]]: 50/49, 3125/3072


Map: [<2 0 4 5|, <0 5 1 1|]
[[Mapping]]: [<2 0 4 5|, <0 5 1 1|]


Wedgie: <<10 2 2 -20 -25 -1||
{{Multival|legend=1| 10 2 2 -20 -25 -1 }}


{{EDOs|legend=1| 6, 16, 22, 60d, 82d }}
[[POTE generator]]: ~5/4 = 380.578


Badness: 0.0827
{{Val list|legend=1| 6, 16, 22, 60d, 82d }}
 
[[Badness]]: 0.0827


== 11-limit ==
== 11-limit ==
Commas: 50/49, 121/120, 176/175
 
Subgroup: 2.3.5.7.11
 
Comma list: 50/49, 121/120, 176/175
 
Mapping: [<2 0 4 5 5|, <0 5 1 1 3|]


POTE generator: ~5/4 = 380.530
POTE generator: ~5/4 = 380.530


Map: [<2 0 4 5 5|, <0 5 1 1 3|]
{{Val list|legend=1| 6, 16, 22, 60de, 82de }}
 
{{EDOs|legend=1| 6, 16, 22, 60de, 82de }}


Badness: 0.0392
Badness: 0.0392


=== 13-limit ===
=== 13-limit ===
Commas: 50/49, 65/64, 78/77, 121/120
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 50/49, 65/64, 78/77, 121/120
 
Mapping: [<2 0 4 5 5 8|, <0 5 1 1 3 -1|]


POTE generator: ~5/4 = 379.787
POTE generator: ~5/4 = 379.787


Map: [<2 0 4 5 5 8|, <0 5 1 1 3 -1|]
{{Val list|legend=1| 6, 16, 22, 38f }}
 
{{EDOs|legend=1| 6, 16, 22, 38f }}


Badness: 0.0344
Badness: 0.0344


[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/AstrologyPercQuintet1_c.mp3 Astrology Percussion Quintet No 1] by [https://soundcloud.com/joelgranttaylor/astrology-percussion-quintet Joel Taylor]
; Music
* [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/AstrologyPercQuintet1_c.mp3 Astrology Percussion Quintet No 1] by [https://soundcloud.com/joelgranttaylor/astrology-percussion-quintet Joel Taylor]


=== Horoscope ===
=== Horoscope ===
Commas: 50/49, 66/65, 105/104, 121/120
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 50/49, 66/65, 105/104, 121/120
 
Mapping: [<2 0 4 5 5 3|, <0 5 1 1 3 7|]


POTE generator: ~5/4 = 379.837
POTE generator: ~5/4 = 379.837


Map: [<2 0 4 5 5 3|, <0 5 1 1 3 7|]
{{Val list|legend=1| 16, 22f, 38 }}
 
{{EDOs|legend=1| 16, 22f, 38 }}


Badness: 0.0353
Badness: 0.0353


= Spell =
= Spell =
Commas: 49/48, 3125/3072


POTE generator: ~28/25 = 189.927
Subgroup: 2.3.5.7
 
[[Comma list]]: 49/48, 3125/3072
 
[[Mapping]]: [<1 0 2 2|, <0 10 2 5|]


Map: [<1 0 2 2|, <0 10 2 5|]
{{Multival|legend=1| 10 2 5 -20 -20 6 }}


Wedgie: <<10 2 5 -20 -20 6||
[[POTE generator]]: ~28/25 = 189.927


{{EDOs|legend=1| 6, 19, 82d }}
{{Val list|legend=1| 6, 19, 82d }}


Badness: 0.0810
[[Badness]]: 0.0810


== 11-limit ==
== 11-limit ==
Commas: 49/48, 56/55, 125/121
 
Subgroup: 2.3.5.7.11
 
Comma list: 49/48, 56/55, 125/121
 
Mapping: [<1 0 2 2 3|, <0 10 2 5 3|]


POTE generator: ~11/10 = 190.285
POTE generator: ~11/10 = 190.285


Map: [<1 0 2 2 3|, <0 10 2 5 3|]
{{Val list|legend=1| 6, 19, 44de, 63de, 82de }}
 
{{EDOs|legend=1| 6, 19, 44de, 63de, 82de }}


Badness: 0.0598
Badness: 0.0598


=== 13-limit ===
=== 13-limit ===
Commas: 49/48, 56/55, 78/77, 125/121
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 49/48, 56/55, 78/77, 125/121
 
Mapping: [<1 0 2 2 3 4|, <0 10 2 5 3 -2|]


POTE generator: ~11/10 = 189.928
POTE generator: ~11/10 = 189.928


Map: [<1 0 2 2 3 4|, <0 10 2 5 3 -2|]
{{Val list|legend=1| 6, 19, 82def }}
 
{{EDOs|legend=1| 6, 19, 82def }}


Badness: 0.0456
Badness: 0.0456


=== Cantrip ===
=== Cantrip ===
Commas: 49/48, 56/55, 91/90, 125/121
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 49/48, 56/55, 91/90, 125/121
 
Mapping: [<1 0 2 2 3 1|, <0 10 2 5 3 17|]


POTE generator: ~11/10 = 190.360
POTE generator: ~11/10 = 190.360


Map: [<1 0 2 2 3 1|, <0 10 2 5 3 17|]
{{Val list|legend=1| 19, 44de, 63de, 82de }}
 
{{EDOs|legend=1| 19, 44de, 63de, 82de }}


Badness: 0.0416
Badness: 0.0416


= Hocum =
= Hocum =
Commas: 3125/3072, 4000/3969


POTE generator: ~63/50 = 400.108
Subgroup: 2.3.5.7
 
[[Comma list]]: 3125/3072, 4000/3969
 
[[Mapping]]: [<1 5 3 -3|, <0 -10 -2 17|]


Map: [<1 5 3 -3|, <0 -10 -2 17|]
{{Multival|legend=1| 10 2 -17 -20 -55 -45 }}


Wedgie: <<10 2 -17 -20 -55 -45||
[[POTE generator]]: ~63/50 = 400.108


{{EDOs|legend=1| 38, 41, 161c, 202c, 243c, 284c }}
{{Val list|legend=1| 38, 41, 161c, 202c, 243c, 284c }}


Badness: 0.1071
[[Badness]]: 0.1071


== Hocus ==
== Hocus ==
Commas: 225/224, 243/242, 245/242
 
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 243/242, 245/242
 
Mapping: [<1 5 3 11 12|, <0 -10 -2 -24 -25|]


POTE generator: ~14/11 = 409.910
POTE generator: ~14/11 = 409.910


Map: [<1 5 3 11 12|, <0 -10 -2 -24 -25|]
{{Val list|legend=1| 38d, 41, 120cd, 161cd, 202cd }}
 
{{EDOs|legend=1| 38d, 41, 120cd, 161cd, 202cd }}


Badness: 0.0385
Badness: 0.0385


== 13-limit ==
== 13-limit ==
Commas: 105/104, 196/195, 243/242, 245/242
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 105/104, 196/195, 243/242, 245/242
 
Mapping: [<1 5 3 11 12 16|, <0 -10 -2 -24 -25 -36|]


POTE generator: ~14/11 = 410.004
POTE generator: ~14/11 = 410.004


Map: [<1 5 3 11 12 16|, <0 -10 -2 -24 -25 -36|]
{{Val list|legend=1| 41, 79d, 120cd }}
 
{{EDOs|legend=1| 41, 79d, 120cd }}


Badness: 0.0303
Badness: 0.0303


= Trismegistus =
= Trismegistus =
Commas: 3125/3072, 1029/1024


POTE generator: ~147/100 = 673.290
Subgroup: 2.3.5.7
 
[[Comma list]]: 3125/3072, 1029/1024
 
[[Mapping]]: [<1 10 4 0|, <0 -15 -3 5|]


Map: [<1 10 4 0|, <0 -15 -3 5|]
{{Multival|legend=1| 15 3 -5 -30 -50 -20 }}


Wedgie: <<15 3 -5 -30 -50 -20||
[[POTE generator]]: ~147/100 = 673.290


{{EDOs|legend=1| 16, 25, 41, 139c, 180c, 221c, 262c }}
{{Val list|legend=1| 16, 25, 41, 139c, 180c, 221c, 262c }}


Badness: 0.0983
[[Badness]]: 0.0983


== 11-limit ==
== 11-limit ==
Commas: 385/384, 441/440, 625/616
 
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 441/440, 625/616


POTE generator: ~22/15 = 673.340
POTE generator: ~22/15 = 673.340


Map: [<1 10 4 0 13|, <0 -15 -3 5 -17|]
Mapping: [<1 10 4 0 13|, <0 -15 -3 5 -17|]


{{EDOs|legend=1| 16, 25e, 41, 98c, 139c, 180c }}
{{Val list|legend=1| 16, 25e, 41, 98c, 139c, 180c }}


Badness: 0.0456
Badness: 0.0456


==13-limit==
== 13-limit ==
Commas: 105/104, 144/143, 275/273, 625/616
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 105/104, 144/143, 275/273, 625/616
 
Mapping: [<1 10 4 0 13 11|, <0 -15 -3 5 -17 -13|]


POTE generator: ~22/15 = 673.359
POTE generator: ~22/15 = 673.359


Map: [<1 10 4 0 13 11|, <0 -15 -3 5 -17 -13|]
{{Val list|legend=1| 16, 25e, 41, 98c, 139cf }}
 
{{EDOs|legend=1| 16, 25e, 41, 98c, 139cf }}


Badness: 0.0331
Badness: 0.0331


= Quadrimage =
= Quadrimage =
Commas: 2401/2400, 3125/3072


POTE generator: ~28/25 = 204.987
Subgroup: 2.3.5.7
 
[[Comma list]]: 2401/2400, 3125/3072
 
[[Mapping]]: [<1 5 3 4|, <0 -20 -4 -7|]


Map: [<1 5 3 4|, <0 -20 -4 -7|]
{{Multival|legend=1| 20 4 7 -40 -45 5 }}


Wedgie: <<20 4 7 -40 -45 5||
[[POTE generator]]: ~28/25 = 204.987


{{EDOs|legend=1| 6, 35, 41, 158cd, 199cd, 240cd, 281cd }}
{{Val list|legend=1| 6, 35, 41, 158cd, 199cd, 240cd, 281cd }}


Badness: 0.1274
[[Badness]]: 0.1274


== 11-limit ==
== 11-limit ==
Commas: 245/242, 385/384, 625/616
 
Subgroup: 2.3.5.7.11
 
Comma list: 245/242, 385/384, 625/616
 
Mapping: [<1 5 3 4 5|, <0 -20 -4 -7 -9|]


POTE generator: ~28/25 = 204.956
POTE generator: ~28/25 = 204.956


Map: [<1 5 3 4 5|, <0 -20 -4 -7 -9|]
{{Val list|legend=1| 6, 35, 41, 199cde, 240cde, 281cde }}
 
{{EDOs|legend=1| 6, 35, 41, 199cde, 240cde, 281cde }}


Badness: 0.0616
Badness: 0.0616


== 13-limit ==
== 13-limit ==
Commas: 105/104, 144/143, 245/242, 625/616
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 105/104, 144/143, 245/242, 625/616
 
Mapping: [<1 5 3 4 5 9|, <0 -20 -4 -7 -9 -31|]


POTE generator: ~28/25 = 205.028
POTE generator: ~28/25 = 205.028


Map: [<1 5 3 4 5 9|, <0 -20 -4 -7 -9 -31|]
{{Val list|legend=1| 41, 117c, 158cd, 199cdef }}
 
{{EDOs|legend=1| 41, 117c, 158cd, 199cdef }}


Badness: 0.0440
Badness: 0.0440


[[Category:Theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Magic]]
[[Category:Magic]]
[[Category:Rank 2]]
[[Category:Rank 2]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/Magic_family"