Archytas clan: Difference between revisions
m 22EDO now via redirect (both are valid, for the most prominent EDOs it absolutely makes sense), more direct link for Porcupine family #Porcupine |
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The '''archytas clan''' (or '''archy family''') 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]]. | The '''archytas clan''' (or '''archy family''') 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|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. | 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. | ||
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Discussed under their respective 5-limit families are [[Father family #Mother|mother]], [[Meantone family #Dominant|dominant]], [[Augmented family #Augene|augene]], [[Porcupine family #Porcupine|porcupine]], [[Diaschismic family #Pajara|pajara]], [[Kleismic family #Catalan|catalan]], [[Tetracot family #Modus|modus]], and [[Immunity family #Immunized|immunized]]. The rest are considered below. | Discussed under their respective 5-limit families are [[Father family #Mother|mother]], [[Meantone family #Dominant|dominant]], [[Augmented family #Augene|augene]], [[Porcupine family #Porcupine|porcupine]], [[Diaschismic family #Pajara|pajara]], [[Kleismic family #Catalan|catalan]], [[Tetracot family #Modus|modus]], and [[Immunity family #Immunized|immunized]]. The rest are considered below. | ||
= Archy = | == Archy == | ||
Subgroup: 2.3.7 | Subgroup: 2.3.7 | ||
| Line 24: | Line 24: | ||
Scales: [[archy5]], [[archy7]], [[archy12]] | Scales: [[archy5]], [[archy7]], [[archy12]] | ||
== Supra == | === Supra === | ||
Subgroup: 2.3.7.11 | Subgroup: 2.3.7.11 | ||
| Line 43: | Line 43: | ||
Scales: [[supra7]], [[supra12]] | Scales: [[supra7]], [[supra12]] | ||
=== Supraphon === | ==== Supraphon ==== | ||
Subgroup: 2.3.7.11.13 | Subgroup: 2.3.7.11.13 | ||
| Line 62: | Line 62: | ||
Scales: [[supra7]], [[supra12]] | Scales: [[supra7]], [[supra12]] | ||
== Suhajira == | === Suhajira === | ||
Subgroup: 2.3.7.11 | Subgroup: 2.3.7.11 | ||
| Line 81: | Line 81: | ||
Scales: [[suhajira7]], [[suhajira10]], [[suhajira17]] | Scales: [[suhajira7]], [[suhajira10]], [[suhajira17]] | ||
=== 2.3.7.11.13 === | ==== 2.3.7.11.13 ==== | ||
Subgroup: 2.3.7.11.13 | Subgroup: 2.3.7.11.13 | ||
| Line 100: | Line 100: | ||
Scales: [[suhajira7]], [[suhajira10]], [[suhajira17]] | Scales: [[suhajira7]], [[suhajira10]], [[suhajira17]] | ||
= Superpyth = | == Superpyth == | ||
{{main| Superpyth }} | {{main| Superpyth }} | ||
| Line 117: | Line 117: | ||
[[Badness]]: 0.032318 | [[Badness]]: 0.032318 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 130: | Line 130: | ||
Badness: 0.024976 | Badness: 0.024976 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 143: | Line 143: | ||
Badness: 0.024673 | Badness: 0.024673 | ||
== Suprapyth == | === Suprapyth === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 156: | Line 156: | ||
Badness: 0.032768 | Badness: 0.032768 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 169: | Line 169: | ||
Badness: 0.036336 | Badness: 0.036336 | ||
= Quasisuper = | == Quasisuper == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 184: | Line 184: | ||
[[Badness]]: 0.063794 | [[Badness]]: 0.063794 | ||
== Quasisupra == | === 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). | 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). | ||
| Line 199: | Line 199: | ||
Badness: 0.032203 | Badness: 0.032203 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 212: | Line 212: | ||
Badness: 0.030219 | Badness: 0.030219 | ||
== Quasisoup == | === Quasisoup === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 225: | Line 225: | ||
Badness: 0.083490 | Badness: 0.083490 | ||
= Schism = | == Schism == | ||
{{see also|Schismatic family #Schism}} | {{see also|Schismatic family #Schism}} | ||
| Line 242: | Line 242: | ||
[[Badness]]: 0.056648 | [[Badness]]: 0.056648 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 255: | Line 255: | ||
Badness: 0.037482 | Badness: 0.037482 | ||
= Blacksmith = | == Blacksmith == | ||
[[File:blacksmith10.jpg|alt=blacksmith10.jpg|thumb|Lattice of blacksmith]] | [[File:blacksmith10.jpg|alt=blacksmith10.jpg|thumb|Lattice of blacksmith]] | ||
== 5-limit (blackwood) == | === 5-limit (blackwood) === | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 273: | Line 273: | ||
[[Badness]]: 0.063760 | [[Badness]]: 0.063760 | ||
== 7-limit == | === 7-limit === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 290: | Line 290: | ||
[[Badness]]: 0.025640 | [[Badness]]: 0.025640 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 303: | Line 303: | ||
Badness: 0.024641 | Badness: 0.024641 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 316: | Line 316: | ||
Badness: 0.020498 | Badness: 0.020498 | ||
== Farrier == | === Farrier === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 329: | Line 329: | ||
Badness: 0.029200 | Badness: 0.029200 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 342: | Line 342: | ||
Badness: 0.022325 | Badness: 0.022325 | ||
== Ferrum == | === Ferrum === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 355: | Line 355: | ||
Badness: 0.030883 | Badness: 0.030883 | ||
= Beatles = | == Beatles == | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 368: | Line 368: | ||
[[Badness]]: 0.358542 | [[Badness]]: 0.358542 | ||
== 7-limit == | === 7-limit === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/beatles-improv.mp3 Beatles Improv] by Herman Miller | * [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/beatles-improv.mp3 Beatles Improv] by Herman Miller | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 399: | Line 399: | ||
Badness: 0.045639 | Badness: 0.045639 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 412: | Line 412: | ||
Badness: 0.030161 | Badness: 0.030161 | ||
== Ringo == | === Ringo === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 425: | Line 425: | ||
Badness: 0.032863 | Badness: 0.032863 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 438: | Line 438: | ||
Badness: 0.022619 | Badness: 0.022619 | ||
= Passion = | == Passion == | ||
Passion tempers out 262144/253125 (saquingu) in the 5-limit. This temperament can be described as 12&49 temperament, which tempers out 64/63 and the gariboh (3125/3087). Alternative extension [[Marvel temperaments #Passive|passive]] (1&11) tempers out the same 5-limit comma as the passion, but with the marvel (225/224) rather than 64/63 tempered out. | |||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 453: | Line 455: | ||
[[Badness]]: 0.168550 | [[Badness]]: 0.168550 | ||
== 7-limit == | === 7-limit === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 470: | Line 472: | ||
[[Badness]]: 0.062327 | [[Badness]]: 0.062327 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 483: | Line 485: | ||
Badness: 0.040809 | Badness: 0.040809 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 496: | Line 498: | ||
Badness: 0.030886 | Badness: 0.030886 | ||
= Fervor = | == Fervor == | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 509: | Line 511: | ||
[[Badness]]: 0.852612 | [[Badness]]: 0.852612 | ||
== 7-limit == | === 7-limit === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 524: | Line 526: | ||
[[Badness]]: 0.108455 | [[Badness]]: 0.108455 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 537: | Line 539: | ||
Badness: 0.052054 | Badness: 0.052054 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 550: | Line 552: | ||
Badness: 0.039705 | Badness: 0.039705 | ||
= Progress = | == Progress == | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 563: | Line 565: | ||
Badness: 0.246073 | Badness: 0.246073 | ||
== 7-limit == | === 7-limit === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 578: | Line 580: | ||
[[Badness]]: 0.066400 | [[Badness]]: 0.066400 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 591: | Line 593: | ||
Badness: 0.031036 | Badness: 0.031036 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 604: | Line 606: | ||
Badness: 0.026214 | Badness: 0.026214 | ||
== Progressive == | === Progressive === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 617: | Line 619: | ||
Badness: 0.032721 | Badness: 0.032721 | ||
= Sixix = | == Sixix == | ||
:''See also: [[Dual-fifth temperaments#Dual-3 Sixix]]'' | :''See also: [[Dual-fifth temperaments#Dual-3 Sixix]]'' | ||
| Line 632: | Line 634: | ||
[[Badness]]: 0.153088 | [[Badness]]: 0.153088 | ||
== 7-limit == | === 7-limit === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||