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 |
mNo edit summary |
||
| Line 1: | Line 1: | ||
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. | ||
| Line 5: | Line 5: | ||
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 | ||
| Line 386: | Line 386: | ||
* [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 | ||
Revision as of 22:01, 2 June 2021
The archytas clan (or archy family) 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 their respective 5-limit families are mother, dominant, augene, porcupine, pajara, catalan, modus, and immunized. The rest are considered below.
Archy
Subgroup: 2.3.7
Comma list: 64/63
Sval mapping: [⟨1 0 6], ⟨0 1 -2]]
Sval mapping generators: ~2, ~3
Gencom mapping: [⟨1 1 0 4], ⟨0 1 0 -2]]
Gencom: [2 3/2; 64/63]
POTE generator: ~3/2 = 709.321
Scales: archy5, archy7, archy12
Supra
Subgroup: 2.3.7.11
Comma list: 64/63, 99/98
Sval mapping: [⟨1 0 6 13], ⟨0 1 -2 -6]]
Sval mapping generators: ~2, ~3
Gencom mapping: [⟨1 1 0 4 7], ⟨0 1 0 -2 -6]]
Gencom: [2 3/2; 64/63 99/98]
POTE generator: ~3/2 = 707.192
Vals: Template:Val list
Supraphon
Subgroup: 2.3.7.11.13
Comma list: 64/63, 78/77, 99/98
Sval mapping: [⟨1 0 6 13 18], ⟨0 1 -2 -6 -9]]
Sval mapping generators: ~2, ~3
Gencom mapping: [⟨1 1 0 4 7 9], ⟨0 1 0 -2 -6 -9]]
Gencom: [2 3/2; 64/63 78/77 99/98]
POTE generator: ~3/2 = 706.137
Vals: Template:Val list
Suhajira
Subgroup: 2.3.7.11
Comma list: 64/63, 243/242
Sval mapping: [⟨1 1 4 2], ⟨0 2 -4 5]]
Sval mapping generators: ~2, ~11/9
Gencom mapping: [⟨1 1 0 4 2], ⟨0 1 0 -4 5]]
Gencom: [2 3/2; 64/63 99/98]
POTE generator: ~11/9 = 353.958
Vals: Template:Val list
Scales: suhajira7, suhajira10, suhajira17
2.3.7.11.13
Subgroup: 2.3.7.11.13
Comma list: 64/63, 78/77, 144/143
Sval mapping: [⟨1 1 4 2 4], ⟨0 2 -4 5 -1]]
Sval mapping generators: ~2, ~11/9
Gencom mapping: [⟨1 1 0 4 2 4], ⟨0 1 0 -4 5 -1]]
Gencom: [2 3/2; 64/63 78/77 99/98]
POTE generator: ~11/9 = 353.775
Vals: Template:Val list
Scales: suhajira7, suhajira10, suhajira17
Superpyth
Subgroup: 2.3.5.7
Comma list: 64/63, 245/243
Mapping: [⟨1 0 -12 6], ⟨0 1 9 -2]]
Wedgie: ⟨⟨ 1 9 -2 12 -6 -30 ]]
POTE generator: ~3/2 = 710.291
Badness: 0.032318
11-limit
Subgroup: 2.3.5.7.11
Comma list: 64/63, 100/99, 245/243
Mapping: [⟨1 0 -12 6 -22], ⟨0 1 9 -2 16]]
POTE generator: ~3/2 = 710.175
Vals: Template:Val list
Badness: 0.024976
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 64/63, 78/77, 91/90, 100/99
Mapping: [⟨1 0 -12 6 -22 -17], ⟨0 1 9 -2 16 13]]
POTE generator: ~3/2 = 710.479
Vals: Template:Val list
Badness: 0.024673
Suprapyth
Subgroup: 2.3.5.7.11
Comma list: 55/54, 64/63, 99/98
Mapping: [⟨1 0 -12 6 13], ⟨0 1 9 -2 -6]]
POTE generator: ~3/2 = 709.495
Vals: Template:Val list
Badness: 0.032768
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 55/54, 64/63, 65/63, 99/98
Mapping: [⟨1 0 -12 6 13 18], ⟨0 1 9 -2 -6 -9]]
POTE generator: ~3/2 = 708.703
Vals: Template:Val list
Badness: 0.036336
Quasisuper
Subgroup: 2.3.5.7
Comma list: 64/63, 2430/2401
Mapping: [⟨1 0 23 6], ⟨0 1 -13 -2]]
Wedgie: ⟨⟨ 1 -13 -2 -23 -6 32 ]]
POTE generator: ~3/2 = 708.328
Badness: 0.063794
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).
Subgroup: 2.3.5.7.11
Comma list: 64/63, 99/98, 121/120
Mapping: [⟨1 0 23 6 13], ⟨0 1 -13 -2 -6]]
POTE generator: ~3/2 = 708.205
Vals: Template:Val list
Badness: 0.032203
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 64/63, 78/77, 91/90, 121/120
Mapping: [⟨1 0 23 6 13 18], ⟨0 1 -13 -2 -6 -9]]
POTE generator: ~3/2 = 708.004
Vals: Template:Val list
Badness: 0.030219
Quasisoup
Subgroup: 2.3.5.7.11
Comma list: 55/54, 64/63, 2430/2401
Mapping: [⟨1 0 23 6 -22], ⟨0 1 -13 -2 16]]
POTE generator: ~3/2 = 709.021
Vals: Template:Val list
Badness: 0.083490
Schism
Subgroup: 2.3.5.7
Comma list: 64/63, 360/343
Mapping: [⟨1 0 15 6], ⟨0 1 -8 -2]]
Wedgie: ⟨⟨ 1 -8 -2 -15 -6 18 ]]
POTE generator: ~3/2 = 701.556
Badness: 0.056648
11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 64/63, 99/98
Mapping: [⟨1 0 15 6 13], ⟨0 1 -8 -2 -6]]
POTE generator: ~3/2 = 702.136
Vals: Template:Val list
Badness: 0.037482
Blacksmith
5-limit (blackwood)
Subgroup: 2.3.5
Comma: 256/243
Mapping: [⟨5 8 0], ⟨0 0 1]]
Mapping generators: ~9/8, ~5
POTE generator: ~5/4 = 399.594
Badness: 0.063760
7-limit
Subgroup: 2.3.5.7
Comma list: 28/27, 49/48
Mapping: [⟨5 8 0 14], ⟨0 0 1 0]]
Mapping generators: ~7/6, ~5
Wedgie: ⟨⟨ 0 5 0 8 0 -14 ]]
POTE generator: ~5/4 = 392.767
Badness: 0.025640
11-limit
Subgroup: 2.3.5.7.11
Comma list: 28/27, 49/48, 55/54
Mapping: [⟨5 8 0 14 29], ⟨0 0 1 0 -1]]
POTE generator: ~5/4 = 394.948
Vals: Template:Val list
Badness: 0.024641
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 28/27, 40/39, 49/48, 55/54
Mapping: [⟨5 8 0 14 29 7], ⟨0 0 1 0 -1 1]]
POTE generator: ~5/4 = 391.037
Vals: Template:Val list
Badness: 0.020498
Farrier
Subgroup: 2.3.5.7.11
Comma list: 28/27, 49/48, 77/75
Mapping: [⟨5 8 0 14 -6], ⟨0 0 1 0 2]]
POTE generator: ~5/4 = 398.070
Vals: Template:Val list
Badness: 0.029200
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 28/27, 40/39, 49/48, 66/65
Mapping: [⟨5 8 0 14 -6 7], ⟨0 0 1 0 2 1]]
POTE generator: ~5/4 = 396.812
Vals: Template:Val list
Badness: 0.022325
Ferrum
Subgroup: 2.3.5.7.11
Comma list: 28/27, 35/33, 49/48
Mapping: [⟨5 8 0 14 6], ⟨0 0 1 0 1]]
POTE generator: ~5/4 = 374.763
Vals: Template:Val list
Badness: 0.030883
Beatles
Subgroup: 2.3.5
Comma: 524288/492075
Mapping: [⟨1 1 5], ⟨0 2 -9]]
POTE generator: ~512/405 = 355.930
Badness: 0.358542
7-limit
Subgroup: 2.3.5.7
Comma list: 64/63, 686/675
Mapping: [⟨1 1 5 4], ⟨0 2 -9 -4]]
Wedgie: ⟨⟨ 2 -9 -4 -19 -12 16 ]]
POTE generator: ~49/40 = 355.904
Badness: 0.045872
- Music
- Beatles Improv by Herman Miller
11-limit
Subgroup: 2.3.5.7.11
Comma list: 64/63, 100/99, 686/675
Mapping: [⟨1 1 5 4 10], ⟨0 2 -9 -4 -22]]
POTE generator: ~49/40 = 356.140
Vals: Template:Val list
Badness: 0.045639
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 64/63, 91/90, 100/99, 169/168
Mapping: [⟨1 1 5 4 10 4], ⟨0 2 -9 -4 -22 -1]]
POTE generator: ~16/13 = 356.229
Vals: Template:Val list
Badness: 0.030161
Ringo
Subgroup: 2.3.5.7.11
Comma list: 56/55, 64/63, 540/539
Mapping: [⟨1 1 5 4 2], ⟨0 2 -9 -4 5]]
POTE generator: ~11/9 = 355.419
Vals: Template:Val list
Badness: 0.032863
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 64/63, 78/77, 91/90
Mapping: [⟨1 1 5 4 2 4], ⟨0 2 -9 -4 5 -1]]
POTE generator: ~11/9 = 355.456
Vals: Template:Val list
Badness: 0.022619
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 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
Comma: 262144/253125
Mapping: [⟨1 2 2], ⟨0 -5 4]]
Mapping generators: 2, 16/15
POTE generator: ~16/15 = 98.670
Badness: 0.168550
7-limit
Subgroup: 2.3.5.7
Comma list: 64/63, 3125/3087
Mapping: [⟨1 2 2 2], ⟨0 -5 4 10]]
Mapping generators: 2, 16/15
Wedgie: ⟨⟨ 5 -4 -10 -18 -30 -12 ]]
POTE generator: ~16/15 = 98.153
Badness: 0.062327
11-limit
Subgroup: 2.3.5.7.11
Comma list: 64/63, 100/99, 1375/1372
Mapping: [⟨1 2 2 2 2], ⟨0 -5 4 10 18]]
POTE generator: ~16/15 = 98.019
Vals: Template:Val list
Badness: 0.040809
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 64/63, 100/99, 196/195, 275/273
Mapping: [⟨1 2 2 2 2 2], ⟨0 -5 4 10 18 21]]
POTE generator: ~16/15 = 97.910
Vals: Template:Val list
Badness: 0.030886
Fervor
Subgroup: 2.3.5
Comma: 67108864/61509375
Mapping: [⟨1 4 -2], ⟨0 -5 9]]
POTE generator: ~64/45 = 577.705
Badness: 0.852612
7-limit
Subgroup: 2.3.5.7
Comma list: 64/63, 9604/9375
Mapping: [⟨1 4 -2 -2], ⟨0 -5 9 10]]
Wedgie: ⟨⟨ 5 -9 -10 -26 -30 2 ]]
POTE generator: ~7/5 = 577.776
Badness: 0.108455
11-limit
Subgroup: 2.3.5.7.11
Comma list: 56/55, 64/63, 1350/1331
Mapping: [⟨1 4 -2 -2 3], ⟨0 -5 9 10 1]]
POTE generator: ~7/5 = 577.850
Vals: Template:Val list
Badness: 0.052054
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 64/63, 78/77, 507/500
Mapping: [⟨1 4 -2 -2 3 -4], ⟨0 -5 9 10 1 16]]
POTE generator: ~7/5 = 578.060
Vals: Template:Val list
Badness: 0.039705
Progress
Subgroup: 2.3.5
Comma: 32768/30375
Mapping: [⟨1 0 5], ⟨0 3 -5]]
POTE generator: ~64/45 = 561.264
Badness: 0.246073
7-limit
Subgroup: 2.3.5.7
Comma list: 64/63, 392/375
Mapping: [⟨1 0 5 6], ⟨0 3 -5 -6]]
Wedgie: ⟨⟨ 3 -5 -6 -15 -18 0 ]]
POTE generator: ~7/5 = 562.122
Badness: 0.066400
11-limit
Subgroup: 2.3.5.7.11
Comma list: 56/55, 64/63, 77/75
Mapping: [⟨1 0 5 6 4], ⟨0 3 -5 -6 -1]]
POTE generator: ~7/5 = 562.085
Vals: Template:Val list
Badness: 0.031036
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 64/63, 66/65, 77/75
Mapping: [⟨1 0 5 6 4 0], ⟨0 3 -5 -6 -1 7]]
POTE generator: ~7/5 = 562.365
Vals: Template:Val list
Badness: 0.026214
Progressive
Subgroup: 2.3.5.7.11.13
Comma list: 26/25, 56/55, 64/63, 77/75
Mapping: [⟨1 0 5 6 4 9], ⟨0 3 -5 -6 -1 -10]]
POTE generator: ~7/5 = 563.239
Vals: Template:Val list
Badness: 0.032721
Sixix
- See also: Dual-fifth temperaments#Dual-3 Sixix
Subgroup: 2.3.5
Comma: 3125/2916
Mapping: [⟨1 3 4], ⟨0 -5 -6]]
POTE generator: ~6/5 = 338.365
Badness: 0.153088
7-limit
Subgroup: 2.3.5.7
Comma list: 64/63, 3125/2916
Mapping: [⟨1 3 4 0], ⟨0 -5 -6 10]]
Wedgie: ⟨⟨ 5 6 -10 -2 -30 -40 ]]
POTE generator: ~6/5 = 337.442
Badness: 0.158903