Archytas clan: Difference between revisions

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__FORCETOC__
The '''archytas clan''' tempers out the [[64/63|Archytas comma]], 64/63. This means that four stacked 3/2 fifths equal a 9/7 major third. (Note the similarity in function to [[81/80]] in meantone, where four stacked 3/2 fifths equal a 5/4 major third.) This leads to tunings with 3s and 7s quite sharp, such as those of [[22edo]]. Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, 2430/2401 gives quasisuper, and 4375/4374 gives modus.  
The ''archytas clan'' tempers out the [[64/63|Archytas comma]], 64/63. This means that four stacked 3/2 fifths equal a 9/7 major third. (Note the similarity in function to [[81/80]] in meantone, where four stacked 3/2 fifths equal a 5/4 major third.) This leads to tunings with 3s and 7s quite sharp, such as those of [[22edo]]. Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, 2430/2401 gives quasisuper, and 4375/4374 gives modus.  


Discussed under their respective 5-limit families are [[Diaschismic family #Pajara|pajara]], [[Meantone family #Dominant|dominant]], [[Augmented family #Augene|augene]], [[porcupine family|porcupine]], and [[Tetracot family #Modus|modus]]. The rest are considered below.
Discussed under subgroup temperaments is the 2.3.7 [[Subgroup temperaments #Archy|archy]]. Under their respective 5-limit families are [[Diaschismic family #Pajara|pajara]], [[Meantone family #Dominant|dominant]], [[Augmented family #Augene|augene]], [[porcupine family|porcupine]], and [[Tetracot family #Modus|modus]]. The rest are considered below.


= Mother =
= Mother =
{{see also| Father family }}
Commas: 16/15, 21/20
Commas: 16/15, 21/20


[[POTE_tuning|POTE generator]]: 721.569
[[POTE generator]]: 721.569


Map: [<1 0 4 6|, <0 1 -1 -2|]
Map: [<1 0 4 6|, <0 1 -1 -2|]
Line 13: Line 14:
Wedgie: <<1 -1 -2 -4 -6 -2||
Wedgie: <<1 -1 -2 -4 -6 -2||


EDOs: {{EDOs|5, 148, 153}}
{{EDOs|legend=1| 5, 148, 153 }}


Badness: 0.0242
Badness: 0.0242
Line 21: Line 22:
Comma: 256/243
Comma: 256/243


[[POTE_tuning|POTE generator]]: 399.594
[[POTE generator]]: 399.594


Map: [<5 8 0|, <0 0 1|]
Map: [<5 8 0|, <0 0 1|]


EDOs: {{EDOs|5, 10, 15}}
{{EDOs|legend=1| 5, 10, 15}}


Badness: 0.0638
Badness: 0.0638
Line 38: Line 39:
Wedgie: <<0 5 0 8 0 -14||
Wedgie: <<0 5 0 8 0 -14||


EDOs: {{EDOs|5, 10, 15, 40b, 55b}}
{{EDOs|legend=1| 5, 10, 15, 40b, 55b}}


Badness: 0.0256
Badness: 0.0256
Line 49: Line 50:
Map: [<5 8 0 14 29|, <0 0 1 0 -1|]
Map: [<5 8 0 14 29|, <0 0 1 0 -1|]


EDOs: {{EDOs|5, 10, 15, 40be, 55be, 70bde, 85bcde}}
{{EDOs|legend=1| 5, 10, 15, 40be, 55be, 70bde, 85bcde}}


Badness: 0.0246
Badness: 0.0246
Line 60: Line 61:
Map: [<5 8 0 14 29 7|, <0 0 1 0 -1 1|]
Map: [<5 8 0 14 29 7|, <0 0 1 0 -1 1|]


EDOs: {{EDOs|5, 10, 15, 25e, 40bef}}
{{EDOs|legend=1| 5, 10, 15, 25e, 40bef}}


Badness: 0.0205
Badness: 0.0205


==Farrier==
== Farrier ==
Commas: 28/27, 49/48, 77/75
Commas: 28/27, 49/48, 77/75


Line 71: Line 72:
Map: [<5 8 0 14 -6|, <0 0 1 0 2|]
Map: [<5 8 0 14 -6|, <0 0 1 0 2|]


EDOs: 5e, 15
{{EDOs|legend=1| 5e, 15 }}


Badness: 0.0292
Badness: 0.0292


===13-limit===
=== 13-limit ===
Commas: 28/27, 40/39, 49/48, 66/65
Commas: 28/27, 40/39, 49/48, 66/65


Line 82: Line 83:
Map: [<5 8 0 14 -6 7|, <0 0 1 0 2 1|]
Map: [<5 8 0 14 -6 7|, <0 0 1 0 2 1|]


EDOs: 5e, 10e, 15
{{EDOs|legend=1| 5e, 10e, 15 }}


Badness: 0.0223
Badness: 0.0223


==Ferrum==
== Ferrum ==
Commas: 28/27, 35/33, 49/48
Commas: 28/27, 35/33, 49/48


Line 93: Line 94:
Map: [<5 8 0 14 6|, <0 0 1 0 1|]
Map: [<5 8 0 14 6|, <0 0 1 0 1|]


EDOs: 10
{{EDOs|legend=1| 10 }}


Badness: 0.0309
Badness: 0.0309
Line 99: Line 100:
[[File:blacksmith10.jpg|alt=blacksmith10.jpg|blacksmith10.jpg]]
[[File:blacksmith10.jpg|alt=blacksmith10.jpg|blacksmith10.jpg]]


=Superpyth=
= Superpyth =
{{main|Superpyth}}
{{main| Superpyth }}


Commas: 64/63, 245/243
Commas: 64/63, 245/243


[[POTE_tuning|POTE generator]]: 710.291
[[POTE generator]]: 710.291


Map: [<1 0 -12 6|, <0 1 9 -2|]
Map: [<1 0 -12 6|, <0 1 9 -2|]
Line 110: Line 111:
Wedgie: <<1 9 -2 12 -6 -30||
Wedgie: <<1 9 -2 12 -6 -30||


EDOs: {{EDOs|5, 17, 22, 27, 49}}
{{EDOs|legend=1| 5, 17, 22, 27, 49 }}


Badness: 0.0323
Badness: 0.0323


==11-limit==
== 11-limit ==
Commas: 64/63, 100/99, 245/243
Commas: 64/63, 100/99, 245/243


Line 121: Line 122:
Map: [<1 0 -12 6 -22|, <0 1 9 -2 16|]
Map: [<1 0 -12 6 -22|, <0 1 9 -2 16|]


EDOs: {{EDOs|22, 49}}
{{EDOs|legend=1| 22, 49 }}


Badness: 0.0250
Badness: 0.0250
Line 132: Line 133:
Map: [<1 0 -12 6 -22 -17|, <0 1 9 -2 16 13|]
Map: [<1 0 -12 6 -22 -17|, <0 1 9 -2 16 13|]


EDOs: {{EDOs|22, 27e, 49, 76bcde}}
{{EDOs|legend=1| 22, 27e, 49, 76bcde }}


Badness: 0.0247
Badness: 0.0247


==Suprapyth==
== Suprapyth ==
Commas: 55/54, 64/63, 99/98
Commas: 55/54, 64/63, 99/98


Line 143: Line 144:
Map: [<1 0 -12 6 13|, <0 1 9 -2 -6|]
Map: [<1 0 -12 6 13|, <0 1 9 -2 -6|]


EDOs: {{EDOs|5, 7, 12, 17, 22}}
{{EDOs|legend=1| 5, 7, 12, 17, 22 }}


Badness: 0.0328
Badness: 0.0328


===13-limit===
=== 13-limit ===
Commas: 55/54, 64/63, 65/63, 364/363
Commas: 55/54, 64/63, 65/63, 364/363


Line 154: Line 155:
Map: [<1 0 -12 6 13 18|, <0 1 9 -2 -6 -9|]
Map: [<1 0 -12 6 13 18|, <0 1 9 -2 -6 -9|]


EDOs: 17, 22, 83cdf
{{EDOs|legend=1| 17, 22, 83cdf }}


Badness: 0.0363
Badness: 0.0363
Line 166: Line 167:
Map: [<1 1 5|,<0 2 -9|]
Map: [<1 1 5|,<0 2 -9|]


EDOs: 10, 17c, 27, 64b, 91bc, 118bc
{{EDOs|legend=1| 10, 17c, 27, 64b, 91bc, 118bc }}


Badness: 0.3585
Badness: 0.3585


==7-limit==
== 7-limit ==
Commas: 64/63, 686/675
Commas: 64/63, 686/675


[[POTE_tuning|POTE generator]]: ~49/40 = 355.904
[[POTE generator]]: ~49/40 = 355.904


Map: [<1 1 5 4|,<0 2 -9 -4|]
Map: [<1 1 5 4|,<0 2 -9 -4|]
Line 179: Line 180:
Wedgie: <<2 -9 -4 -19 -12 16||
Wedgie: <<2 -9 -4 -19 -12 16||


EDOs: 10, 17c, 27, 64b, 91bcd, 118bcd
{{EDOs|legend=1| 10, 17c, 27, 64b, 91bcd, 118bcd }}


Badness: 0.0459
Badness: 0.0459
Line 185: Line 186:
Music: [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/beatles-improv.mp3 Beatles Improv] by Herman Miller
Music: [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/beatles-improv.mp3 Beatles Improv] by Herman Miller


==11-limit==
== 11-limit ==
Commas: 64/63, 100/99, 686/675
Commas: 64/63, 100/99, 686/675


Line 192: Line 193:
Map: [<1 1 5 4 10|,<0 2 -9 -4 -22|]
Map: [<1 1 5 4 10|,<0 2 -9 -4 -22|]


EDOs: {{EDOs|27e, 37, 64be, 91bcde}}
{{EDOs|legend=1| 27e, 37, 64be, 91bcde }}


Badness: 0.0456
Badness: 0.0456
Line 203: Line 204:
Map: [<1 1 5 4 10 4|,<0 2 -9 -4 -22 -1|]
Map: [<1 1 5 4 10 4|,<0 2 -9 -4 -22 -1|]


EDOs: {{EDOs|27e, 37, 64be}}
{{EDOs|legend=1| 27e, 37, 64be }}


Badness: 0.0302
Badness: 0.0302


==Ringo==
== Ringo ==
Commas: 56/55, 64/63, 540/539
Commas: 56/55, 64/63, 540/539


Line 214: Line 215:
Map: [<1 1 5 4 2|,<0 2 -9 -4 5|]
Map: [<1 1 5 4 2|,<0 2 -9 -4 5|]


EDOs: {{EDOs|10, 17c, 27e}}
{{EDOs|legend=1| 10, 17c, 27e }}


Badness: 0.0329
Badness: 0.0329


===13-limit===
=== 13-limit ===
Commas: 56/55, 64/63, 78/77, 91/90
Commas: 56/55, 64/63, 78/77, 91/90


Line 225: Line 226:
Map: [<1 1 5 4 2 4|,<0 2 -9 -4 5 -1|]
Map: [<1 1 5 4 2 4|,<0 2 -9 -4 5 -1|]


EDOs: {{EDOs|10, 17c, 27e}}
{{EDOs|legend=1| 10, 17c, 27e }}


Badness: 0.0226
Badness: 0.0226
Line 234: Line 235:
Commas: 64/63, 360/343
Commas: 64/63, 360/343


[[POTE_tuning|POTE generator]]: ~3/2 = 701.556
[[POTE generator]]: ~3/2 = 701.556


Map: [<1 0 15 6|, <0 1 -8 -2|]
Map: [<1 0 15 6|, <0 1 -8 -2|]
Line 240: Line 241:
Wedgie: <<1 -8 -2 -15 -6 18||
Wedgie: <<1 -8 -2 -15 -6 18||


EDOs: {{EDOs|12, 41d, 53d}}
{{EDOs|legend=1| 12, 41d, 53d }}


Badness: 0.0566
Badness: 0.0566


==11-limit==
== 11-limit ==
Commas: 45/44, 64/63, 99/98
Commas: 45/44, 64/63, 99/98


Line 251: Line 252:
Map: [<1 0 15 6 13|, <0 1 -8 -2 -6|]
Map: [<1 0 15 6 13|, <0 1 -8 -2 -6|]


EDOs: {{EDOs|12, 29de, 41de}}
{{EDOs|legend=1| 12, 29de, 41de }}


Badness: 0.0375
Badness: 0.0375
Line 263: Line 264:
Map: [<1 2 2|, <0 -5 4|]
Map: [<1 2 2|, <0 -5 4|]


EDOs: {{EDOs|11, 12, 49, 61, 73}}
{{EDOs|legend=1| 11, 12, 49, 61, 73 }}


Badness: 0.1686
Badness: 0.1686
Line 274: Line 275:
Map: [<1 2 2 3|, <0 -5 4 -2|]
Map: [<1 2 2 3|, <0 -5 4 -2|]


EDOs: {{EDOs|1, 11, 12, 49d}}
{{EDOs|legend=1| 1, 11, 12, 49d }}


Badness: 0.0751
Badness: 0.0751
Line 281: Line 282:
Commas: 64/63, 3125/3087
Commas: 64/63, 3125/3087


[[POTE_tuning|POTE generator]]: ~16/15 = 98.153
[[POTE generator]]: ~16/15 = 98.153


Map: [<1 2 2 2|, <0 -5 4 10|]
Map: [<1 2 2 2|, <0 -5 4 10|]
Line 289: Line 290:
Generators: 2, 16/15
Generators: 2, 16/15


EDOs: {{EDOs|12, 37, 49, 110bcd}}
{{EDOs|legend=1| 12, 37, 49, 110bcd }}


Badness: 0.0623
Badness: 0.0623


==11-limit==
== 11-limit ==
Commas: 64/63, 100/99, 1375/1372
Commas: 64/63, 100/99, 1375/1372


Line 300: Line 301:
Map: [<1 2 2 2 2|, <0 -5 4 10 18|]
Map: [<1 2 2 2 2|, <0 -5 4 10 18|]


EDOs: {{EDOs|12, 37, 49}}
{{EDOs|legend=1| 12, 37, 49 }}


Badness: 0.0408
Badness: 0.0408


==13-limit==
== 13-limit ==
Commas: 64/63 100/99 196/195 275/273
Commas: 64/63, 100/99, 196/195, 275/273


POTE generator: ~16/15 = 97.910
POTE generator: ~16/15 = 97.910
Line 311: Line 312:
Map: [<1 2 2 2 2 2|, <0 -5 4 10 18 21|]
Map: [<1 2 2 2 2 2|, <0 -5 4 10 18 21|]


EDOs: {{EDOs|12f, 37, 49f}}
{{EDOs|legend=1| 12f, 37, 49f }}


Badness: 0.0309
Badness: 0.0309
Line 323: Line 324:
Map: [<1 4 -2|, <0 -5 9|]
Map: [<1 4 -2|, <0 -5 9|]


EDOs: {{EDOs|25, 27}}
{{EDOs|legend=1| 25, 27 }}


Badness: 0.8526
Badness: 0.8526


==7-limit==
== 7-limit ==
Commas: 64/63, 9604/9375
Commas: 64/63, 9604/9375


Line 336: Line 337:
Wedgie: <<5 -9 -10 -26 -30 2||
Wedgie: <<5 -9 -10 -26 -30 2||


EDOs: {{EDOs|25, 27}}
{{EDOs|legend=1| 25, 27 }}


Badness: 0.1085
Badness: 0.1085


==11-limit==
== 11-limit ==
Commas: 56/55, 64/63, 1350/1331
Commas: 56/55, 64/63, 1350/1331


Line 347: Line 348:
Map: [<1 4 -2 -2 3|, <0 -5 9 10 1|]
Map: [<1 4 -2 -2 3|, <0 -5 9 10 1|]


EDOs: {{EDOs|25e, 27e}}
{{EDOs|legend=1| 25e, 27e }}


Badness: 0.0521
Badness: 0.0521


==13-limit==
== 13-limit ==
Commas: 56/55, 64/63, 78/77, 507/500
Commas: 56/55, 64/63, 78/77, 507/500


Line 358: Line 359:
Map: [<1 4 -2 -2 3 -4|, <0 -5 9 10 1 16|]
Map: [<1 4 -2 -2 3 -4|, <0 -5 9 10 1 16|]


EDOs: {{EDOs|27e}}
{{EDOs|legend=1| 27e }}


Badness: 0.0397
Badness: 0.0397


=Quasisuper=
= Quasisuper =
Commas: 64/63, 2430/2401
Commas: 64/63, 2430/2401


Line 371: Line 372:
Wedgie: <<1 -13 -2 -23 -2 -6 32||
Wedgie: <<1 -13 -2 -23 -2 -6 32||


EDOs: {{EDOs|22, 61}}
{{EDOs|legend=1| 22, 61 }}


Badness: 0.0638
Badness: 0.0638


==Quasisupra==
== Quasisupra ==
Quasisupra can be viewed as an extension of the excellent 2.3.7.11 temperament [[Supra|supra]], with the quasisuper mapping of 5 thrown in (rather than the superpyth mapping of 5, which results in suprapyth).
Quasisupra can be viewed as an extension of the excellent 2.3.7.11 temperament [[supra]], with the quasisuper mapping of 5 thrown in (rather than the superpyth mapping of 5, which results in suprapyth).


Commas: 64/63, 99/98, 121/120
Commas: 64/63, 99/98, 121/120
Line 384: Line 385:
Map: [<1 2 -3 2 1|, <0 -1 13 2 6|]
Map: [<1 2 -3 2 1|, <0 -1 13 2 6|]


EDOs: {{EDOs|17c, 22, 27c, 39d, 61d}}
{{EDOs|legend=1| 17c, 22, 27c, 39d, 61d }}


Badness: 0.0322
Badness: 0.0322


===13-limit===
=== 13-limit ===
Commas: 64/63, 78/77, 91/90, 121/120
Commas: 64/63, 78/77, 91/90, 121/120


Line 395: Line 396:
Map: [<1 0 23 6 13 18|, <0 1 -13 -2 -6 -9|]
Map: [<1 0 23 6 13 18|, <0 1 -13 -2 -6 -9|]


EDOs: {{EDOs|17c, 22, 39d, 61df, 100bcdf}}
{{EDOs|legend=1| 17c, 22, 39d, 61df, 100bcdf }}


Badness: 0.0302
Badness: 0.0302


==Quasisoup==
== Quasisoup ==
Commas: 55/54, 64/63, 2430/2401
Commas: 55/54, 64/63, 2430/2401


Line 406: Line 407:
Map: [<1 0 23 6 -22|, <0 1 -13 -2 16|]
Map: [<1 0 23 6 -22|, <0 1 -13 -2 16|]


EDOs: {{EDOs|22}}
{{EDOs|legend=1| 22 }}


Badness: 0.0835
Badness: 0.0835
Line 418: Line 419:
Map: [<1 0 5|, <0 3 -5|]
Map: [<1 0 5|, <0 3 -5|]


EDOs: {{EDOs|4, 13, 15, 32c, 47bc, 62bc}}
{{EDOs|legend=1| 4, 13, 15, 32c, 47bc, 62bc }}


Badness: 0.2461
Badness: 0.2461


==7-limit==
== 7-limit ==
Commas: 64/63, 392/375
Commas: 64/63, 392/375


Line 431: Line 432:
Wedgie: <<3 -5 -6 -15 -18 0||
Wedgie: <<3 -5 -6 -15 -18 0||


EDOs: {{EDOs|13, 15, 32c, 79bcc, 111bcc}}
{{EDOs|legend=1| 13, 15, 32c, 79bcc, 111bcc }}


Badness: 0.0664
Badness: 0.0664


==11-limit==
== 11-limit ==
Commas: 56/55, 64/63, 77/75
Commas: 56/55, 64/63, 77/75


Line 442: Line 443:
Map: [<1 0 5 6 4|, <0 3 -5 -6 -1|]
Map: [<1 0 5 6 4|, <0 3 -5 -6 -1|]


EDOs: {{EDOs|13, 15, 32c, 47bc, 79bcce}}
{{EDOs|legend=1| 13, 15, 32c, 47bc, 79bcce }}


Badness: 0.0310
Badness: 0.0310
Line 453: Line 454:
Map: [<1 0 5 6 4 0|, <0 3 -5 -6 -1 7|]
Map: [<1 0 5 6 4 0|, <0 3 -5 -6 -1 7|]


EDOs: {{EDOs|15, 17c, 32cf}}
{{EDOs|legend=1| 15, 17c, 32cf }}


Badness: 0.0262
Badness: 0.0262
Line 464: Line 465:
Map: [<1 0 5 6 4 9|, <0 3 -5 -6 -1 -10|]
Map: [<1 0 5 6 4 9|, <0 3 -5 -6 -1 -10|]


EDOs: {{EDOs|15f, 17c, 32c, 49c}}
{{EDOs|legend=1| 15f, 17c, 32c, 49c }}


Badness: 0.0327
Badness: 0.0327

Revision as of 15:13, 9 January 2021

The archytas clan tempers out the Archytas comma, 64/63. This means that four stacked 3/2 fifths equal a 9/7 major third. (Note the similarity in function to 81/80 in meantone, where four stacked 3/2 fifths equal a 5/4 major third.) This leads to tunings with 3s and 7s quite sharp, such as those of 22edo. Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, 2430/2401 gives quasisuper, and 4375/4374 gives modus.

Discussed under subgroup temperaments is the 2.3.7 archy. Under their respective 5-limit families are pajara, dominant, augene, porcupine, and modus. The rest are considered below.

Mother

See also: Father family

Commas: 16/15, 21/20

POTE generator: 721.569

Map: [<1 0 4 6|, <0 1 -1 -2|]

Wedgie: <<1 -1 -2 -4 -6 -2||

EDOs: 5, 148, 153

Badness: 0.0242

Blacksmith

5-limit (blackwood)

Comma: 256/243

POTE generator: 399.594

Map: [<5 8 0|, <0 0 1|]

EDOs: 5, 10, 15

Badness: 0.0638

7-limit

Commas: 28/27, 49/48

POTE generator: ~5/4 = 392.767

Map: [<5 8 0 14|, <0 0 1 0|]

Wedgie: <<0 5 0 8 0 -14||

EDOs: 5, 10, 15, 40b, 55b

Badness: 0.0256

11-limit

Commas: 28/27, 49/48, 55/54

POTE generator: ~5/4 = 394.948

Map: [<5 8 0 14 29|, <0 0 1 0 -1|]

EDOs: 5, 10, 15, 40be, 55be, 70bde, 85bcde

Badness: 0.0246

13-limit

Commas: 28/27, 40/39, 49/48, 55/54

POTE generator: ~5/4 = 391.0367

Map: [<5 8 0 14 29 7|, <0 0 1 0 -1 1|]

EDOs: 5, 10, 15, 25e, 40bef

Badness: 0.0205

Farrier

Commas: 28/27, 49/48, 77/75

POTE generator: ~5/4 = 398.070

Map: [<5 8 0 14 -6|, <0 0 1 0 2|]

EDOs: 5e, 15

Badness: 0.0292

13-limit

Commas: 28/27, 40/39, 49/48, 66/65

POTE generator: ~5/4 = 396.812

Map: [<5 8 0 14 -6 7|, <0 0 1 0 2 1|]

EDOs: 5e, 10e, 15

Badness: 0.0223

Ferrum

Commas: 28/27, 35/33, 49/48

POTE generator: ~5/4 = 374.763

Map: [<5 8 0 14 6|, <0 0 1 0 1|]

EDOs: 10

Badness: 0.0309

blacksmith10.jpg

Superpyth

Main article: Superpyth

Commas: 64/63, 245/243

POTE generator: 710.291

Map: [<1 0 -12 6|, <0 1 9 -2|]

Wedgie: <<1 9 -2 12 -6 -30||

EDOs: 5, 17, 22, 27, 49

Badness: 0.0323

11-limit

Commas: 64/63, 100/99, 245/243

POTE generator: 710.175

Map: [<1 0 -12 6 -22|, <0 1 9 -2 16|]

EDOs: 22, 49

Badness: 0.0250

13-limit

Commas: 64/63, 78/77, 91/90, 100/99

POTE generator: ~3/2 = 710.479

Map: [<1 0 -12 6 -22 -17|, <0 1 9 -2 16 13|]

EDOs: 22, 27e, 49, 76bcde

Badness: 0.0247

Suprapyth

Commas: 55/54, 64/63, 99/98

POTE generator: ~3/2 = 709.495

Map: [<1 0 -12 6 13|, <0 1 9 -2 -6|]

EDOs: 5, 7, 12, 17, 22

Badness: 0.0328

13-limit

Commas: 55/54, 64/63, 65/63, 364/363

POTE generator: ~3/2 = 708.703

Map: [<1 0 -12 6 13 18|, <0 1 9 -2 -6 -9|]

EDOs: 17, 22, 83cdf

Badness: 0.0363

Beatles

5-limit

Comma: 524288/492075

POTE generator: ~512/405 = 355.930

Map: [<1 1 5|,<0 2 -9|]

EDOs: 10, 17c, 27, 64b, 91bc, 118bc

Badness: 0.3585

7-limit

Commas: 64/63, 686/675

POTE generator: ~49/40 = 355.904

Map: [<1 1 5 4|,<0 2 -9 -4|]

Wedgie: <<2 -9 -4 -19 -12 16||

EDOs: 10, 17c, 27, 64b, 91bcd, 118bcd

Badness: 0.0459

Music: Beatles Improv by Herman Miller

11-limit

Commas: 64/63, 100/99, 686/675

POTE generator: ~49/40 = 356.140

Map: [<1 1 5 4 10|,<0 2 -9 -4 -22|]

EDOs: 27e, 37, 64be, 91bcde

Badness: 0.0456

13-limit

Commas: 64/63, 91/90, 100/99, 169/168

POTE generator: ~16/13 = 356.229

Map: [<1 1 5 4 10 4|,<0 2 -9 -4 -22 -1|]

EDOs: 27e, 37, 64be

Badness: 0.0302

Ringo

Commas: 56/55, 64/63, 540/539

POTE generator: ~11/9 = 355.419

Map: [<1 1 5 4 2|,<0 2 -9 -4 5|]

EDOs: 10, 17c, 27e

Badness: 0.0329

13-limit

Commas: 56/55, 64/63, 78/77, 91/90

POTE generator: ~11/9 = 355.456

Map: [<1 1 5 4 2 4|,<0 2 -9 -4 5 -1|]

EDOs: 10, 17c, 27e

Badness: 0.0226

Schism

See also: Schismatic family § Schism

Commas: 64/63, 360/343

POTE generator: ~3/2 = 701.556

Map: [<1 0 15 6|, <0 1 -8 -2|]

Wedgie: <<1 -8 -2 -15 -6 18||

EDOs: 12, 41d, 53d

Badness: 0.0566

11-limit

Commas: 45/44, 64/63, 99/98

POTE generator ~3/2 = 702.136

Map: [<1 0 15 6 13|, <0 1 -8 -2 -6|]

EDOs: 12, 29de, 41de

Badness: 0.0375

Passion

5-limit

Comma: 262144/253125

POTE generator: ~16/15 = 98.670

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

EDOs: 11, 12, 49, 61, 73

Badness: 0.1686

Passive

Commas: 225/224, 256/245

POTE generator: ~16/15 = 98.809

Map: [<1 2 2 3|, <0 -5 4 -2|]

EDOs: 1, 11, 12, 49d

Badness: 0.0751

7-limit

Commas: 64/63, 3125/3087

POTE generator: ~16/15 = 98.153

Map: [<1 2 2 2|, <0 -5 4 10|]

Wedgie: <<5 -4 -10 -18 -30 -12||

Generators: 2, 16/15

EDOs: 12, 37, 49, 110bcd

Badness: 0.0623

11-limit

Commas: 64/63, 100/99, 1375/1372

POTE generator: ~16/15 = 98.019

Map: [<1 2 2 2 2|, <0 -5 4 10 18|]

EDOs: 12, 37, 49

Badness: 0.0408

13-limit

Commas: 64/63, 100/99, 196/195, 275/273

POTE generator: ~16/15 = 97.910

Map: [<1 2 2 2 2 2|, <0 -5 4 10 18 21|]

EDOs: 12f, 37, 49f

Badness: 0.0309

Fervor

5-limit

Comma: 67108864/61509375

POTE generator: ~64/45 = 577.705

Map: [<1 4 -2|, <0 -5 9|]

EDOs: 25, 27

Badness: 0.8526

7-limit

Commas: 64/63, 9604/9375

POTE generator: ~7/5 = 577.777

Map: [<1 4 -2 -2|, <0 -5 9 10|]

Wedgie: <<5 -9 -10 -26 -30 2||

EDOs: 25, 27

Badness: 0.1085

11-limit

Commas: 56/55, 64/63, 1350/1331

POTE generator: ~7/5 = 577.850

Map: [<1 4 -2 -2 3|, <0 -5 9 10 1|]

EDOs: 25e, 27e

Badness: 0.0521

13-limit

Commas: 56/55, 64/63, 78/77, 507/500

POTE generator: ~7/5 = 578.060

Map: [<1 4 -2 -2 3 -4|, <0 -5 9 10 1 16|]

EDOs: 27e

Badness: 0.0397

Quasisuper

Commas: 64/63, 2430/2401

POTE generator: 708.328

Map: [<1 0 23 6|, <0 1 -13 -2|]

Wedgie: <<1 -13 -2 -23 -2 -6 32||

EDOs: 22, 61

Badness: 0.0638

Quasisupra

Quasisupra can be viewed as an extension of the excellent 2.3.7.11 temperament supra, with the quasisuper mapping of 5 thrown in (rather than the superpyth mapping of 5, which results in suprapyth).

Commas: 64/63, 99/98, 121/120

POTE generator: ~3/2 = 708.205

Map: [<1 2 -3 2 1|, <0 -1 13 2 6|]

EDOs: 17c, 22, 27c, 39d, 61d

Badness: 0.0322

13-limit

Commas: 64/63, 78/77, 91/90, 121/120

POTE generator: ~3/2 = 708.004

Map: [<1 0 23 6 13 18|, <0 1 -13 -2 -6 -9|]

EDOs: 17c, 22, 39d, 61df, 100bcdf

Badness: 0.0302

Quasisoup

Commas: 55/54, 64/63, 2430/2401

POTE generator: ~3/2 = 709.021

Map: [<1 0 23 6 -22|, <0 1 -13 -2 16|]

EDOs: 22

Badness: 0.0835

Progress

5-limit

Comma: 32768/30375

POTE generator: ~64/45 = 561.264

Map: [<1 0 5|, <0 3 -5|]

EDOs: 4, 13, 15, 32c, 47bc, 62bc

Badness: 0.2461

7-limit

Commas: 64/63, 392/375

POTE generator: ~7/5 = 562.122

Map: [<1 0 5 6|, <0 3 -5 -6|]

Wedgie: <<3 -5 -6 -15 -18 0||

EDOs: 13, 15, 32c, 79bcc, 111bcc

Badness: 0.0664

11-limit

Commas: 56/55, 64/63, 77/75

POTE generator: ~7/5 = 562.085

Map: [<1 0 5 6 4|, <0 3 -5 -6 -1|]

EDOs: 13, 15, 32c, 47bc, 79bcce

Badness: 0.0310

13-limit

Commas: 56/55, 64/63, 66/65, 77/75

POTE generator: ~7/5 = 562.365

Map: [<1 0 5 6 4 0|, <0 3 -5 -6 -1 7|]

EDOs: 15, 17c, 32cf

Badness: 0.0262

Progressive

Commas: 26/25, 56/55, 64/63, 77/75

POTE generator: ~7/5 = 563.239

Map: [<1 0 5 6 4 9|, <0 3 -5 -6 -1 -10|]

EDOs: 15f, 17c, 32c, 49c

Badness: 0.0327

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