Archytas clan: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
__FORCETOC__
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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|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|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, and 2430/2401 gives quasisuper. Pajara is discussed under [[Diaschismic_family|diaschismic family]], dominant under [[Meantone_family|meantone family]], augene under [[Augmented_family|augmented family]] and porcupine under [[Porcupine_family|porcupine family]]. The rest are considered below.
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-12-16 16:34:32 UTC</tt>.<br>
: The original revision id was <tt>570337903</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc]]


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|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, and 2430/2401 gives quasisuper. Pajara is discussed under [[diaschismic family]], dominant under [[meantone family]], augene under [[augmented family]] and porcupine under [[porcupine family]]. The rest are considered below.
=Mother=
 
=Mother=  
Commas: 16/15, 21/20
Commas: 16/15, 21/20


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


Map: [&lt;1 0 4 6|, &lt;0 1 -1 -2|]
Map: [&lt;1 0 4 6|, &lt;0 1 -1 -2|]
Wedgie: &lt;&lt;1 -1 -2 -4 -6 -2||
Wedgie: &lt;&lt;1 -1 -2 -4 -6 -2||
EDOs: 5, 148, 153
EDOs: 5, 148, 153
Badness: 0.0242
Badness: 0.0242


=Blacksmith=  
=Blacksmith=
Commas: 28/27, 49/48
Commas: 28/27, 49/48


[[POTE tuning|POTE generator]]: ~5/4 = 392.767
[[POTE_tuning|POTE generator]]: ~5/4 = 392.767


Map: [&lt;5 8 0 14|, &lt;0 0 1 0|]
Map: [&lt;5 8 0 14|, &lt;0 0 1 0|]
Wedgie: &lt;&lt;0 5 0 8 0 -14||
Wedgie: &lt;&lt;0 5 0 8 0 -14||
EDOs: 5, 10, 15, 40b, 55b
EDOs: 5, 10, 15, 40b, 55b
Badness: 0.0256
Badness: 0.0256


==11-limit==  
==11-limit==
Commas: 28/27, 49/48, 55/54
Commas: 28/27, 49/48, 55/54


Line 36: Line 34:


Map: [&lt;5 8 0 14 29|, &lt;0 0 1 0 -1|]
Map: [&lt;5 8 0 14 29|, &lt;0 0 1 0 -1|]
EDOs: 5, 10, 15, 40be, 55be, 70bde, 85bcde
EDOs: 5, 10, 15, 40be, 55be, 70bde, 85bcde
Badness: 0.0246
Badness: 0.0246


==13-limit==  
==13-limit==
Commas: 28/27, 40/39, 49/48, 55/54
Commas: 28/27, 40/39, 49/48, 55/54


Line 45: Line 45:


Map: [&lt;5 8 0 14 29 7|, &lt;0 0 1 0 -1 1|]
Map: [&lt;5 8 0 14 29 7|, &lt;0 0 1 0 -1 1|]
EDOs: 5, 10, 15, 25e, 40bef
EDOs: 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 54: Line 56:


Map: [&lt;5 8 0 14 -6|, &lt;0 0 1 0 2|]
Map: [&lt;5 8 0 14 -6|, &lt;0 0 1 0 2|]
EDOs: 5e, 15
EDOs: 5e, 15
Badness: 0.0292
Badness: 0.0292


Line 63: Line 67:


Map: [&lt;5 8 0 14 -6 7|, &lt;0 0 1 0 2 1|]
Map: [&lt;5 8 0 14 -6 7|, &lt;0 0 1 0 2 1|]
EDOs: 5e, 10e, 15
EDOs: 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 72: Line 78:


Map: [&lt;5 8 0 14 6|, &lt;0 0 1 0 1|]
Map: [&lt;5 8 0 14 6|, &lt;0 0 1 0 1|]
EDOs: 10
EDOs: 10
Badness: 0.0309
Badness: 0.0309


[[File:blacksmith10.jpg|alt=blacksmith10.jpg|blacksmith10.jpg]]


[[image:blacksmith10.jpg]]
==Blackwood==
 
''Blackwood (5-limit)''
==Blackwood==  
//Blackwood (5-limit)//


Comma: 256/243
Comma: 256/243


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


Map: [&lt;5 8 0|, &lt;0 0 1|]
Map: [&lt;5 8 0|, &lt;0 0 1|]
EDOs: 5, 10, 15
EDOs: 5, 10, 15
Badness: 0.0638
Badness: 0.0638


=Superpyth=  
=Superpyth=
[[Superpyth|Main article]]
[[Superpyth|Main article]]
Commas: 64/63, 245/243
Commas: 64/63, 245/243


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


Map: [&lt;1 0 -12 6|, &lt;0 1 9 -2|]
Map: [&lt;1 0 -12 6|, &lt;0 1 9 -2|]
Wedgie: &lt;&lt;1 9 -2 12 -6 -30||
Wedgie: &lt;&lt;1 9 -2 12 -6 -30||
EDOs: 5, 17, 22, 27, 49
EDOs: 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


[[POTE tuning|POTE generator]]: 710.175
[[POTE_tuning|POTE generator]]: 710.175


Map: [&lt;1 0 -12 6 -22|, &lt;0 1 9 -2 16|]
Map: [&lt;1 0 -12 6 -22|, &lt;0 1 9 -2 16|]
EDOs: 22, 49
EDOs: 22, 49
Badness: 0.0250
Badness: 0.0250


Line 115: Line 130:


Map: [&lt;1 0 -12 6 -22 -17|, &lt;0 1 9 -2 16 13|]
Map: [&lt;1 0 -12 6 -22 -17|, &lt;0 1 9 -2 16 13|]
EDOs: 22, 27e, 49, 76bcde
EDOs: 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 124: Line 141:


Map: [&lt;1 0 -12 6 13|, &lt;0 1 9 -2 -6|]
Map: [&lt;1 0 -12 6 13|, &lt;0 1 9 -2 -6|]
EDOs: 5, 7, 12, 17, 22
EDOs: 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 133: Line 152:


Map: [&lt;1 0 -12 6 13 18|, &lt;0 1 9 -2 -6 -9|]
Map: [&lt;1 0 -12 6 13 18|, &lt;0 1 9 -2 -6 -9|]
EDOs: 17, 22, 83cdf
EDOs: 17, 22, 83cdf
Badness: 0.0363
Badness: 0.0363


=Beatles=  
=Beatles=
Comma: 524288/492075
Comma: 524288/492075


Line 142: Line 163:


Map: [&lt;1 1 5|,&lt;0 2 -9|]
Map: [&lt;1 1 5|,&lt;0 2 -9|]
EDOs: 10, 17c, 27, 64b, 91bc, 118bc
EDOs: 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_tuning|POTE generator]]: ~49/40 = 355.904


Map: [&lt;1 1 5 4|,&lt;0 2 -9 -4|]
Map: [&lt;1 1 5 4|,&lt;0 2 -9 -4|]
Wedgie: &lt;&lt;2 -9 -4 -19 -12 16||
Wedgie: &lt;&lt;2 -9 -4 -19 -12 16||
EDOs: 10, 17c, 27, 64b, 91bcd, 118bcd
EDOs: 10, 17c, 27, 64b, 91bcd, 118bcd
Badness: 0.0459
Badness: 0.0459


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 163: Line 189:


Map: [&lt;1 1 5 4 10|,&lt;0 2 -9 -4 -22|]
Map: [&lt;1 1 5 4 10|,&lt;0 2 -9 -4 -22|]
EDOs: 27e, 37, 64be, 91bcde
EDOs: 27e, 37, 64be, 91bcde
Badness: 0.0456
Badness: 0.0456


==13-limit==  
==13-limit==
Commas: 64/63, 91/90, 100/99, 169/168
Commas: 64/63, 91/90, 100/99, 169/168


Line 172: Line 200:


Map: [&lt;1 1 5 4 10 4|,&lt;0 2 -9 -4 -22 -1|]
Map: [&lt;1 1 5 4 10 4|,&lt;0 2 -9 -4 -22 -1|]
EDOs: 27e, 37, 64be
EDOs: 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 181: Line 211:


Map: [&lt;1 1 5 4 2|,&lt;0 2 -9 -4 5|]
Map: [&lt;1 1 5 4 2|,&lt;0 2 -9 -4 5|]
EDOs: 10, 17c, 27e
EDOs: 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 190: Line 222:


Map: [&lt;1 1 5 4 2 4|,&lt;0 2 -9 -4 5 -1|]
Map: [&lt;1 1 5 4 2 4|,&lt;0 2 -9 -4 5 -1|]
EDOs: 10, 17c, 27e
EDOs: 10, 17c, 27e
Badness: 0.0226
Badness: 0.0226


=Schism=  
=Schism=
Commas: 64/63, 360/343
Commas: 64/63, 360/343


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


Map: [&lt;1 0 15 6|, &lt;0 1 -8 -2|]
Map: [&lt;1 0 15 6|, &lt;0 1 -8 -2|]
Wedgie: &lt;&lt;1 -8 -2 -15 -6 18||
Wedgie: &lt;&lt;1 -8 -2 -15 -6 18||
EDOs: 12, 41d, 53d
EDOs: 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 209: Line 246:


Map: [&lt;1 0 15 6 13|, &lt;0 1 -8 -2 -6|]
Map: [&lt;1 0 15 6 13|, &lt;0 1 -8 -2 -6|]
EDOs: 12, 29de, 41de
EDOs: 12, 29de, 41de
Badness: 0.0375
Badness: 0.0375


=Passion=  
=Passion=


==5-limit==
==5-limit==
Line 220: Line 259:


Map: [&lt;1 2 2|, &lt;0 -5 4|]
Map: [&lt;1 2 2|, &lt;0 -5 4|]
EDOs: 11, 12, 49, 61, 73
EDOs: 11, 12, 49, 61, 73
Badness: 0.1686
Badness: 0.1686


Line 229: Line 270:


Map: [&lt;1 2 2 3|, &lt;0 -5 4 -2|]
Map: [&lt;1 2 2 3|, &lt;0 -5 4 -2|]
EDOs: 1, 11, 12, 49d
EDOs: 1, 11, 12, 49d
Badness: 0.0751
Badness: 0.0751


Line 235: Line 278:
Commas: 64/63, 3125/3087
Commas: 64/63, 3125/3087


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


Map: [&lt;1 2 2 2|, &lt;0 -5 4 10|]
Map: [&lt;1 2 2 2|, &lt;0 -5 4 10|]
Wedgie: &lt;&lt;5 -4 -10 -18 -30 -12||
Wedgie: &lt;&lt;5 -4 -10 -18 -30 -12||
Generators: 2, 16/15
Generators: 2, 16/15
EDOs: 12, 37, 49, 110bcd
EDOs: 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 249: Line 296:


Map: [&lt;1 2 2 2 2|, &lt;0 -5 4 10 18|]
Map: [&lt;1 2 2 2 2|, &lt;0 -5 4 10 18|]
EDOs: 12, 37, 49
EDOs: 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


Line 258: Line 307:


Map: [&lt;1 2 2 2 2 2|, &lt;0 -5 4 10 18 21|]
Map: [&lt;1 2 2 2 2 2|, &lt;0 -5 4 10 18 21|]
EDOs: 12f, 37, 49f
EDOs: 12f, 37, 49f
Badness: 0.0309
Badness: 0.0309


=Fervor=  
=Fervor=
Comma: 67108864/61509375
Comma: 67108864/61509375


Line 267: Line 318:


Map: [&lt;1 4 -2|, &lt;0 -5 9|]
Map: [&lt;1 4 -2|, &lt;0 -5 9|]
EDOs: 25, 27
EDOs: 25, 27
Badness: 0.8526
Badness: 0.8526


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


Line 276: Line 329:


Map: [&lt;1 4 -2 -2|, &lt;0 -5 9 10|]
Map: [&lt;1 4 -2 -2|, &lt;0 -5 9 10|]
Wedgie: &lt;&lt;5 -9 -10 -26 -30 2||
Wedgie: &lt;&lt;5 -9 -10 -26 -30 2||
EDOs: 25, 27
EDOs: 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 286: Line 342:


Map: [&lt;1 4 -2 -2 3|, &lt;0 -5 9 10 1|]
Map: [&lt;1 4 -2 -2 3|, &lt;0 -5 9 10 1|]
EDOs: 25e, 27e
EDOs: 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 295: Line 353:


Map: [&lt;1 4 -2 -2 3 -4|, &lt;0 -5 9 10 1 16|]
Map: [&lt;1 4 -2 -2 3 -4|, &lt;0 -5 9 10 1 16|]
EDOs: 27e
EDOs: 27e
Badness: 0.0397
Badness: 0.0397


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


[[POTE tuning|POTE generator]]: 708.328
[[POTE_tuning|POTE generator]]: 708.328


Map: [&lt;1 0 23 6|, &lt;0 1 -13 -2|]
Map: [&lt;1 0 23 6|, &lt;0 1 -13 -2|]
Wedgie: &lt;&lt;1 -13 -2 -23 -2 -6 32||
Wedgie: &lt;&lt;1 -13 -2 -23 -2 -6 32||
EDOs: 22, 61
EDOs: 22, 61
Badness: 0.0638
Badness: 0.0638


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


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).
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).


POTE generator: ~3/2 = 708.205
POTE generator: ~3/2 = 708.205


Map: [&lt;1 2 -3 2 1|, &lt;0 -1 13 2 6|]
Map: [&lt;1 2 -3 2 1|, &lt;0 -1 13 2 6|]
EDOs: 17c, 22, 27c, 39d, 61d
EDOs: 17c, 22, 27c, 39d, 61d
Badness: 0.0322
Badness: 0.0322


Line 325: Line 390:


Map: [&lt;1 0 23 6 13 18|, &lt;0 1 -13 -2 -6 -9|]
Map: [&lt;1 0 23 6 13 18|, &lt;0 1 -13 -2 -6 -9|]
EDOs: 17c, 22, 39d, 61df, 100bcdf
EDOs: 17c, 22, 39d, 61df, 100bcdf
Badness: 0.0302
Badness: 0.0302


Line 334: Line 401:


Map: [&lt;1 0 23 6 -22|, &lt;0 1 -13 -2 16|]
Map: [&lt;1 0 23 6 -22|, &lt;0 1 -13 -2 16|]
EDOs: 22
EDOs: 22
Badness: 0.0835
Badness: 0.0835


=Progress=  
=Progress=
Comma: 32768/30375
Comma: 32768/30375


Line 343: Line 412:


Map: [&lt;1 0 5|, &lt;0 3 -5|]
Map: [&lt;1 0 5|, &lt;0 3 -5|]
EDOs: 4, 13, 15, 32c, 47bc, 62bc
EDOs: 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 352: Line 423:


Map: [&lt;1 0 5 6|, &lt;0 3 -5 -6|]
Map: [&lt;1 0 5 6|, &lt;0 3 -5 -6|]
Wedgie: &lt;&lt;3 -5 -6 -15 -18 0||
Wedgie: &lt;&lt;3 -5 -6 -15 -18 0||
EDOs: 13, 15, 32c, 79bcc, 111bcc
EDOs: 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 362: Line 436:


Map: [&lt;1 0 5 6 4|, &lt;0 3 -5 -6 -1|]
Map: [&lt;1 0 5 6 4|, &lt;0 3 -5 -6 -1|]
EDOs: 13, 15, 32c, 47bc, 79bcce
EDOs: 13, 15, 32c, 47bc, 79bcce
Badness: 0.0310
Badness: 0.0310


==13-limit==  
==13-limit==
Commas: 56/55, 64/63, 66/65, 77/75
Commas: 56/55, 64/63, 66/65, 77/75


Line 371: Line 447:


Map: [&lt;1 0 5 6 4 0|, &lt;0 3 -5 -6 -1 7|]
Map: [&lt;1 0 5 6 4 0|, &lt;0 3 -5 -6 -1 7|]
EDOs: 15, 17c, 32cf
EDOs: 15, 17c, 32cf
Badness: 0.0262
Badness: 0.0262


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


Line 380: Line 458:


Map: [&lt;1 0 5 6 4 9|, &lt;0 3 -5 -6 -1 -10|]
Map: [&lt;1 0 5 6 4 9|, &lt;0 3 -5 -6 -1 -10|]
EDOs: 15f, 17c, 32c, 49c
EDOs: 15f, 17c, 32c, 49c
Badness: 0.0327</pre></div>
 
<h4>Original HTML content:</h4>
Badness: 0.0327
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Archytas clan&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:80:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Mother"&gt;Mother&lt;/a&gt;&lt;/div&gt;
[[Category:archytas]]
&lt;!-- ws:end:WikiTextTocRule:81 --&gt;&lt;!-- ws:start:WikiTextTocRule:82: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Blacksmith"&gt;Blacksmith&lt;/a&gt;&lt;/div&gt;
[[Category:clan]]
&lt;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Blacksmith-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
[[Category:overview]]
&lt;!-- ws:end:WikiTextTocRule:83 --&gt;&lt;!-- ws:start:WikiTextTocRule:84: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Blacksmith-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
[[Category:temperaments]]
&lt;!-- ws:end:WikiTextTocRule:84 --&gt;&lt;!-- ws:start:WikiTextTocRule:85: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Blacksmith-Farrier"&gt;Farrier&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:85 --&gt;&lt;!-- ws:start:WikiTextTocRule:86: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Blacksmith-Farrier-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:86 --&gt;&lt;!-- ws:start:WikiTextTocRule:87: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Blacksmith-Ferrum"&gt;Ferrum&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:87 --&gt;&lt;!-- ws:start:WikiTextTocRule:88: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Blacksmith-Blackwood"&gt;Blackwood&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Superpyth"&gt;Superpyth&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Superpyth-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Superpyth-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;!-- ws:start:WikiTextTocRule:92: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Superpyth-Suprapyth"&gt;Suprapyth&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:92 --&gt;&lt;!-- ws:start:WikiTextTocRule:93: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Superpyth-Suprapyth-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:93 --&gt;&lt;!-- ws:start:WikiTextTocRule:94: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Beatles"&gt;Beatles&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:94 --&gt;&lt;!-- ws:start:WikiTextTocRule:95: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Beatles-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:95 --&gt;&lt;!-- ws:start:WikiTextTocRule:96: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Beatles-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:96 --&gt;&lt;!-- ws:start:WikiTextTocRule:97: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Beatles-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:97 --&gt;&lt;!-- ws:start:WikiTextTocRule:98: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Beatles-Ringo"&gt;Ringo&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:98 --&gt;&lt;!-- ws:start:WikiTextTocRule:99: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Beatles-Ringo-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:99 --&gt;&lt;!-- ws:start:WikiTextTocRule:100: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Schism"&gt;Schism&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:100 --&gt;&lt;!-- ws:start:WikiTextTocRule:101: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Schism-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:101 --&gt;&lt;!-- ws:start:WikiTextTocRule:102: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Passion"&gt;Passion&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:102 --&gt;&lt;!-- ws:start:WikiTextTocRule:103: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Passion-5-limit"&gt;5-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:103 --&gt;&lt;!-- ws:start:WikiTextTocRule:104: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Passion-5-limit-Passive"&gt;Passive&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:104 --&gt;&lt;!-- ws:start:WikiTextTocRule:105: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Passion-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:105 --&gt;&lt;!-- ws:start:WikiTextTocRule:106: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Passion-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:106 --&gt;&lt;!-- ws:start:WikiTextTocRule:107: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Passion-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:107 --&gt;&lt;!-- ws:start:WikiTextTocRule:108: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Fervor"&gt;Fervor&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:108 --&gt;&lt;!-- ws:start:WikiTextTocRule:109: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Fervor-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:109 --&gt;&lt;!-- ws:start:WikiTextTocRule:110: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Fervor-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:110 --&gt;&lt;!-- ws:start:WikiTextTocRule:111: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Fervor-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:111 --&gt;&lt;!-- ws:start:WikiTextTocRule:112: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Quasisuper"&gt;Quasisuper&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:112 --&gt;&lt;!-- ws:start:WikiTextTocRule:113: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quasisuper-Quasisupra"&gt;Quasisupra&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:113 --&gt;&lt;!-- ws:start:WikiTextTocRule:114: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Quasisuper-Quasisupra-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:114 --&gt;&lt;!-- ws:start:WikiTextTocRule:115: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quasisuper-Quasisoup"&gt;Quasisoup&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:115 --&gt;&lt;!-- ws:start:WikiTextTocRule:116: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Progress"&gt;Progress&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:116 --&gt;&lt;!-- ws:start:WikiTextTocRule:117: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Progress-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:117 --&gt;&lt;!-- ws:start:WikiTextTocRule:118: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Progress-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:118 --&gt;&lt;!-- ws:start:WikiTextTocRule:119: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Progress-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:119 --&gt;&lt;!-- ws:start:WikiTextTocRule:120: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Progress-Progressive"&gt;Progressive&lt;/a&gt;&lt;/div&gt;
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&lt;!-- ws:end:WikiTextTocRule:121 --&gt;&lt;br /&gt;
The &lt;em&gt;archytas clan&lt;/em&gt; tempers out the &lt;a class="wiki_link" href="/64_63"&gt;Archytas comma&lt;/a&gt;, 64/63. This means that four stacked 3/2 fifths equal a 9/7 major third. (Note the similarity in function to &lt;a class="wiki_link" href="/81_80"&gt;81/80&lt;/a&gt; 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 &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;. 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, and 2430/2401 gives quasisuper. Pajara is discussed under &lt;a class="wiki_link" href="/diaschismic%20family"&gt;diaschismic family&lt;/a&gt;, dominant under &lt;a class="wiki_link" href="/meantone%20family"&gt;meantone family&lt;/a&gt;, augene under &lt;a class="wiki_link" href="/augmented%20family"&gt;augmented family&lt;/a&gt; and porcupine under &lt;a class="wiki_link" href="/porcupine%20family"&gt;porcupine family&lt;/a&gt;. The rest are considered below.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Mother"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Mother&lt;/h1&gt;
Commas: 16/15, 21/20&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 721.569&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 4 6|, &amp;lt;0 1 -1 -2|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;1 -1 -2 -4 -6 -2||&lt;br /&gt;
EDOs: 5, 148, 153&lt;br /&gt;
Badness: 0.0242&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Blacksmith"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Blacksmith&lt;/h1&gt;
Commas: 28/27, 49/48&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~5/4 = 392.767&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;5 8 0 14|, &amp;lt;0 0 1 0|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;0 5 0 8 0 -14||&lt;br /&gt;
EDOs: 5, 10, 15, 40b, 55b&lt;br /&gt;
Badness: 0.0256&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Blacksmith-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
Commas: 28/27, 49/48, 55/54&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 394.948&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;5 8 0 14 29|, &amp;lt;0 0 1 0 -1|]&lt;br /&gt;
EDOs: 5, 10, 15, 40be, 55be, 70bde, 85bcde&lt;br /&gt;
Badness: 0.0246&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Blacksmith-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
Commas: 28/27, 40/39, 49/48, 55/54&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 391.0367&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;5 8 0 14 29 7|, &amp;lt;0 0 1 0 -1 1|]&lt;br /&gt;
EDOs: 5, 10, 15, 25e, 40bef&lt;br /&gt;
Badness: 0.0205&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Blacksmith-Farrier"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Farrier&lt;/h2&gt;
Commas: 28/27, 49/48, 77/75&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 398.070&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;5 8 0 14 -6|, &amp;lt;0 0 1 0 2|]&lt;br /&gt;
EDOs: 5e, 15&lt;br /&gt;
Badness: 0.0292&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Blacksmith-Farrier-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13-limit&lt;/h3&gt;
Commas: 28/27, 40/39, 49/48, 66/65&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 396.812&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;5 8 0 14 -6 7|, &amp;lt;0 0 1 0 2 1|]&lt;br /&gt;
EDOs: 5e, 10e, 15&lt;br /&gt;
Badness: 0.0223&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Blacksmith-Ferrum"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Ferrum&lt;/h2&gt;
Commas: 28/27, 35/33, 49/48&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 374.763&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;5 8 0 14 6|, &amp;lt;0 0 1 0 1|]&lt;br /&gt;
EDOs: 10&lt;br /&gt;
Badness: 0.0309&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:122:&amp;lt;img src=&amp;quot;/file/view/blacksmith10.jpg/271383136/blacksmith10.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/blacksmith10.jpg/271383136/blacksmith10.jpg" alt="blacksmith10.jpg" title="blacksmith10.jpg" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:122 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Blacksmith-Blackwood"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Blackwood&lt;/h2&gt;
&lt;em&gt;Blackwood (5-limit)&lt;/em&gt;&lt;br /&gt;
&lt;br /&gt;
Comma: 256/243&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 399.594&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;5 8 0|, &amp;lt;0 0 1|]&lt;br /&gt;
EDOs: 5, 10, 15&lt;br /&gt;
Badness: 0.0638&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Superpyth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Superpyth&lt;/h1&gt;
&lt;a class="wiki_link" href="/Superpyth"&gt;Main article&lt;/a&gt;&lt;br /&gt;
Commas: 64/63, 245/243&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 710.291&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 -12 6|, &amp;lt;0 1 9 -2|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;1 9 -2 12 -6 -30||&lt;br /&gt;
EDOs: 5, 17, 22, 27, 49&lt;br /&gt;
Badness: 0.0323&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Superpyth-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;11-limit&lt;/h2&gt;
Commas: 64/63, 100/99, 245/243&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 710.175&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 -12 6 -22|, &amp;lt;0 1 9 -2 16|]&lt;br /&gt;
EDOs: 22, 49&lt;br /&gt;
Badness: 0.0250&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Superpyth-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;13-limit&lt;/h2&gt;
Commas: 64/63, 78/77, 91/90, 100/99&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 710.479&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 -12 6 -22 -17|, &amp;lt;0 1 9 -2 16 13|]&lt;br /&gt;
EDOs: 22, 27e, 49, 76bcde&lt;br /&gt;
Badness: 0.0247&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Superpyth-Suprapyth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Suprapyth&lt;/h2&gt;
Commas: 55/54, 64/63, 99/98&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 709.495&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 -12 6 13|, &amp;lt;0 1 9 -2 -6|]&lt;br /&gt;
EDOs: 5, 7, 12, 17, 22&lt;br /&gt;
Badness: 0.0328&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc12"&gt;&lt;a name="Superpyth-Suprapyth-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;13-limit&lt;/h3&gt;
Commas: 55/54, 64/63, 65/63, 364/363&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 708.703&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 -12 6 13 18|, &amp;lt;0 1 9 -2 -6 -9|]&lt;br /&gt;
EDOs: 17, 22, 83cdf&lt;br /&gt;
Badness: 0.0363&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc13"&gt;&lt;a name="Beatles"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Beatles&lt;/h1&gt;
Comma: 524288/492075&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~512/405 = 355.930&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 5|,&amp;lt;0 2 -9|]&lt;br /&gt;
EDOs: 10, 17c, 27, 64b, 91bc, 118bc&lt;br /&gt;
Badness: 0.3585&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Beatles-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;7-limit&lt;/h2&gt;
Commas: 64/63, 686/675&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~49/40 = 355.904&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 5 4|,&amp;lt;0 2 -9 -4|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;2 -9 -4 -19 -12 16||&lt;br /&gt;
EDOs: 10, 17c, 27, 64b, 91bcd, 118bcd&lt;br /&gt;
Badness: 0.0459&lt;br /&gt;
&lt;br /&gt;
Music: &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/beatles-improv.mp3" rel="nofollow"&gt;Beatles Improv&lt;/a&gt; by Herman Miller&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Beatles-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;11-limit&lt;/h2&gt;
Commas: 64/63, 100/99, 686/675&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~49/40 = 356.140&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 5 4 10|,&amp;lt;0 2 -9 -4 -22|]&lt;br /&gt;
EDOs: 27e, 37, 64be, 91bcde&lt;br /&gt;
Badness: 0.0456&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Beatles-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;13-limit&lt;/h2&gt;
Commas: 64/63, 91/90, 100/99, 169/168&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~16/13 = 356.229&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 5 4 10 4|,&amp;lt;0 2 -9 -4 -22 -1|]&lt;br /&gt;
EDOs: 27e, 37, 64be&lt;br /&gt;
Badness: 0.0302&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Beatles-Ringo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Ringo&lt;/h2&gt;
Commas: 56/55, 64/63, 540/539&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~11/9 = 355.419&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 5 4 2|,&amp;lt;0 2 -9 -4 5|]&lt;br /&gt;
EDOs: 10, 17c, 27e&lt;br /&gt;
Badness: 0.0329&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc18"&gt;&lt;a name="Beatles-Ringo-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;13-limit&lt;/h3&gt;
Commas: 56/55, 64/63, 78/77, 91/90&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~11/9 = 355.456&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 5 4 2 4|,&amp;lt;0 2 -9 -4 5 -1|]&lt;br /&gt;
EDOs: 10, 17c, 27e&lt;br /&gt;
Badness: 0.0226&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Schism"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Schism&lt;/h1&gt;
Commas: 64/63, 360/343&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~3/2 = 701.556&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 15 6|, &amp;lt;0 1 -8 -2|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;1 -8 -2 -15 -6 18||&lt;br /&gt;
EDOs: 12, 41d, 53d&lt;br /&gt;
Badness: 0.0566&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Schism-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;11-limit&lt;/h2&gt;
Commas: 45/44, 64/63, 99/98&lt;br /&gt;
&lt;br /&gt;
POTE generator ~3/2 = 702.136&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 15 6 13|, &amp;lt;0 1 -8 -2 -6|]&lt;br /&gt;
EDOs: 12, 29de, 41de&lt;br /&gt;
Badness: 0.0375&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc21"&gt;&lt;a name="Passion"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Passion&lt;/h1&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Passion-5-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;5-limit&lt;/h2&gt;
Comma: 262144/253125&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~16/15 = 98.670&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2|, &amp;lt;0 -5 4|]&lt;br /&gt;
EDOs: 11, 12, 49, 61, 73&lt;br /&gt;
Badness: 0.1686&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc23"&gt;&lt;a name="Passion-5-limit-Passive"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;Passive&lt;/h3&gt;
Commas: 225/224, 256/245&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~16/15 = 98.809&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3|, &amp;lt;0 -5 4 -2|]&lt;br /&gt;
EDOs: 1, 11, 12, 49d&lt;br /&gt;
Badness: 0.0751&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="Passion-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;7-limit&lt;/h2&gt;
Commas: 64/63, 3125/3087&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~16/15 = 98.153&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 2|, &amp;lt;0 -5 4 10|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;5 -4 -10 -18 -30 -12||&lt;br /&gt;
Generators: 2, 16/15&lt;br /&gt;
EDOs: 12, 37, 49, 110bcd&lt;br /&gt;
Badness: 0.0623&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="Passion-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;11-limit&lt;/h2&gt;
Commas: 64/63, 100/99, 1375/1372&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~16/15 = 98.019&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 2 2|, &amp;lt;0 -5 4 10 18|]&lt;br /&gt;
EDOs: 12, 37, 49&lt;br /&gt;
Badness: 0.0408&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="Passion-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;13-limit&lt;/h2&gt;
Commas: 64/63 100/99 196/195 275/273&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~16/15 = 97.910&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 2 2 2|, &amp;lt;0 -5 4 10 18 21|]&lt;br /&gt;
EDOs: 12f, 37, 49f&lt;br /&gt;
Badness: 0.0309&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc27"&gt;&lt;a name="Fervor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;Fervor&lt;/h1&gt;
Comma: 67108864/61509375&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~64/45 = 577.705&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -2|, &amp;lt;0 -5 9|]&lt;br /&gt;
EDOs: 25, 27&lt;br /&gt;
Badness: 0.8526&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Fervor-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;7-limit&lt;/h2&gt;
Commas: 64/63, 9604/9375&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 577.777&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -2 -2|, &amp;lt;0 -5 9 10|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;5 -9 -10 -26 -30 2||&lt;br /&gt;
EDOs: 25, 27&lt;br /&gt;
Badness: 0.1085&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc29"&gt;&lt;a name="Fervor-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;11-limit&lt;/h2&gt;
Commas: 56/55, 64/63, 1350/1331&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 577.850&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -2 -2 3|, &amp;lt;0 -5 9 10 1|]&lt;br /&gt;
EDOs: 25e, 27e&lt;br /&gt;
Badness: 0.0521&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc30"&gt;&lt;a name="Fervor-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;13-limit&lt;/h2&gt;
Commas: 56/55, 64/63, 78/77, 507/500&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 578.060&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -2 -2 3 -4|, &amp;lt;0 -5 9 10 1 16|]&lt;br /&gt;
EDOs: 27e&lt;br /&gt;
Badness: 0.0397&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc31"&gt;&lt;a name="Quasisuper"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;Quasisuper&lt;/h1&gt;
Commas: 64/63, 2430/2401&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 708.328&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 23 6|, &amp;lt;0 1 -13 -2|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;1 -13 -2 -23 -2 -6 32||&lt;br /&gt;
EDOs: 22, 61&lt;br /&gt;
Badness: 0.0638&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc32"&gt;&lt;a name="Quasisuper-Quasisupra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;Quasisupra&lt;/h2&gt;
Commas: 64/63, 99/98, 121/120&lt;br /&gt;
&lt;br /&gt;
Quasisupra can be viewed as an extension of the excellent 2.3.7.11 temperament &lt;a class="wiki_link" href="/supra"&gt;supra&lt;/a&gt;, with the quasisuper mapping of 5 thrown in (rather than the superpyth mapping of 5, which results in suprapyth).&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 708.205&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 -3 2 1|, &amp;lt;0 -1 13 2 6|]&lt;br /&gt;
EDOs: 17c, 22, 27c, 39d, 61d&lt;br /&gt;
Badness: 0.0322&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc33"&gt;&lt;a name="Quasisuper-Quasisupra-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;13-limit&lt;/h3&gt;
Commas: 64/63, 78/77, 91/90, 121/120&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 708.004&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 23 6 13 18|, &amp;lt;0 1 -13 -2 -6 -9|]&lt;br /&gt;
EDOs: 17c, 22, 39d, 61df, 100bcdf&lt;br /&gt;
Badness: 0.0302&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc34"&gt;&lt;a name="Quasisuper-Quasisoup"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;Quasisoup&lt;/h2&gt;
Commas: 55/54, 64/63, 2430/2401&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 709.021&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 23 6 -22|, &amp;lt;0 1 -13 -2 16|]&lt;br /&gt;
EDOs: 22&lt;br /&gt;
Badness: 0.0835&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc35"&gt;&lt;a name="Progress"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;Progress&lt;/h1&gt;
Comma: 32768/30375&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~64/45 = 561.264&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 5|, &amp;lt;0 3 -5|]&lt;br /&gt;
EDOs: 4, 13, 15, 32c, 47bc, 62bc&lt;br /&gt;
Badness: 0.2461&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:72:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc36"&gt;&lt;a name="Progress-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:72 --&gt;7-limit&lt;/h2&gt;
Commas: 64/63, 392/375&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 562.122&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 5 6|, &amp;lt;0 3 -5 -6|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;3 -5 -6 -15 -18 0||&lt;br /&gt;
EDOs: 13, 15, 32c, 79bcc, 111bcc&lt;br /&gt;
Badness: 0.0664&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:74:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc37"&gt;&lt;a name="Progress-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:74 --&gt;11-limit&lt;/h2&gt;
Commas: 56/55, 64/63, 77/75&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 562.085&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 5 6 4|, &amp;lt;0 3 -5 -6 -1|]&lt;br /&gt;
EDOs: 13, 15, 32c, 47bc, 79bcce&lt;br /&gt;
Badness: 0.0310&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:76:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc38"&gt;&lt;a name="Progress-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:76 --&gt;13-limit&lt;/h2&gt;
Commas: 56/55, 64/63, 66/65, 77/75&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 562.365&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 5 6 4 0|, &amp;lt;0 3 -5 -6 -1 7|]&lt;br /&gt;
EDOs: 15, 17c, 32cf&lt;br /&gt;
Badness: 0.0262&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:78:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc39"&gt;&lt;a name="Progress-Progressive"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:78 --&gt;Progressive&lt;/h2&gt;
Commas: 26/25, 56/55, 64/63, 77/75&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 563.239&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 5 6 4 9|, &amp;lt;0 3 -5 -6 -1 -10|]&lt;br /&gt;
EDOs: 15f, 17c, 32c, 49c&lt;br /&gt;
Badness: 0.0327&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

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, and 2430/2401 gives quasisuper. Pajara is discussed under diaschismic family, dominant under meantone family, augene under augmented family and porcupine under porcupine family. The rest are considered below.

Mother

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

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

Blackwood

Blackwood (5-limit)

Comma: 256/243

POTE generator: 399.594

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

EDOs: 5, 10, 15

Badness: 0.0638

Superpyth

Main article

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

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

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

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

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

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).

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

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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