Archytas clan: Difference between revisions

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~~: sval mapping generators: ~2, ~3~~

: mapping generators: ~2, ~3

: ~~[[gencom]]~~: [2 3~~; 64/63]~~

[[Optimal tuning]]s:

* [[~~CTE~~]]: ~2 = ~~1200~~.~~000~~, ~3/2 = ~~709~~.~~595~~

* [[WE]]: ~2 = 1196.9552{{c}}, ~3/2 = 707.5215{{c}}

: [[error map]]: {{val| 0.~~000~~ +7.~~640~~ +11.~~984~~ }}

: [[error map]]: {{val| -3.045 +2.522 +3.952 }}

* [[~~POTE~~]]: ~2 = 1200.~~000~~, ~3/2 = 709.~~321~~

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 709.3901{{c}}

: error map: {{val| 0.000 +7.~~366~~ +12.~~532~~ }}

: error map: {{val| 0.000 +7.435 +12.394 }}

{{Optimal ET sequence|legend=1| 2, 3, 5, 12, 17, 22, 137bdd, 159bddd, 181bbddd }}

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==== 7-limit extensions ====

The second comma in the comma list defines which [[7-limit]] family member we are looking at:

* [[#Schism|Schism]] adds 360/343, for ~~an [[exotemperament]] well tuned~~ around [[12edo]];

* [[#Schism|Schism]] adds [[360/343]], for a tuning around [[12edo]];

* Dominant adds [[36/35]], for a tuning ~~flat of~~ [[17edo|17c-edo]];

* [[Meantone family #Dominant|Dominant]] adds [[36/35]], for a tuning between [[12edo]] and [[17edo|17c-edo]];

* [[#Quasisuper|Quasisuper]] adds [[2430/2401]], for a tuning between 17c-edo and [[22edo]];

* [[#Superpyth|Superpyth]] adds [[245/243]], for a tuning between 22edo and [[27edo]];

* [[#Quasiultra|Quasiultra]] adds 33614/32805, for a tuning between 27edo and [[32edo]];

* [[#Quasiultra|Quasiultra]] adds [[33614/32805]], for a tuning between 27edo and [[32edo]];

* [[#Ultrapyth|Ultrapyth]] adds 6860/6561, for a tuning sharp of 32edo;

* [[#Ultrapyth|Ultrapyth]] adds [[6860/6561]], for a tuning sharp of 32edo;

* Mother adds [[16/15]], for an exotemperament well tuned around [[5edo]].

These all use the same generators as archy.

[[686/675]] gives beatles~~, splitting~~ the fifth in two. [[8748/8575]] gives immunized, splitting the twelfth in two. [[50/49]] gives pajara with a semioctave period. [[392/375]] gives progress, splitting the twelfth in three. [[250/243]] gives porcupine, splitting the fourth in three. [[126/125]] gives augene with a 1/3-octave period. [[4375/4374]] gives modus, splitting the fifth in four. [[3125/3024]] gives brightstone. [[9604/9375]] gives fervor. [[3125/2916]] gives sixix. [[3125/3087]] gives passion. Those split the generator in five in various ways. [[28/27]] gives ~~blacksmith with a 1/5-octave period~~. Finally, [[~~15625~~/~~15552~~]] gives ~~catalan~~, ~~splitting~~ the ~~twelfth in six~~.

[[25/24]] gives dichotic. [[686/675]] gives beatles. Those split the fifth in two. [[8748/8575]] gives immunized, splitting the twelfth in two. [[50/49]] gives pajara with a semioctave period. [[392/375]] gives progress, splitting the twelfth in three. [[250/243]] gives porcupine, splitting the fourth in three. [[126/125]] gives augene with a 1/3-octave period. [[4375/4374]] gives modus, splitting the fifth in four. [[3125/3024]] gives brightstone. [[9604/9375]] gives fervor. [[3125/2916]] gives sixix. [[3125/3087]] gives passion. Those split the generator in five in various ways. [[15625/15552]] gives catalan, splitting the twelfth in six. Finally, [[28/27]] gives blackwood and [[17496/16807]] gives [[gothic]], reducing the intervals of 3 and 7 to the same chain of 1/5- and 1/17-octave periods, respectively.

Temperaments discussed elsewhere are:

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* [[Dominant (temperament)|Dominant]] (+36/35) → [[Meantone family #Dominant|Meantone family]]

* ''[[Medusa]]'' (+15/14) → [[Very low accuracy temperaments #Medusa|Very low accuracy temperaments]]

* ''[[Dichotic]]'' (+25/24) → [[Dicot family #Dichotic|Dicot family]]

* ''[[Immunized]]'' (+8748/8575) → [[Immunity family #Immunized|Immunity family]]

* [[Pajara]] (+50/49) → [[Diaschismic family #Pajara|Diaschismic family]]

* [[Augene]] (+126/125) → [[Augmented family #~~Augene~~|Augmented family]]

* [[Augene]] (+126/125) → [[Augmented family #Septimal augmented (augene)|Augmented family]]

* [[Porcupine]] (+250/243) → [[Porcupine family #Septimal porcupine|Porcupine family]]

* ''[[Modus]]'' (+4375/4374) → [[Tetracot family #Modus|Tetracot family]]

* [[Modus]] (+4375/4374) → [[Tetracot family #Modus|Tetracot family]]

* ''[[Brightstone]]'' (+3125/3024) → [[Magic family #Brightstone|Magic family]]

* ''[[Passion]]'' (+3125/3087) → [[Passion family #Septimal passion|Passion family]]

* ''[[Blacksmith]]'' (+28/27) → [[Limmic temperaments #Blacksmith|Limmic temperaments]]

* ''[[Catalan]]'' (+15625/15552) → [[Kleismic family #Catalan|Kleismic family]]

* [[Blackwood]] (+28/27) → [[Blackwood family #Blackwood|Blackwood family]]

* ''[[Gothic]]'' (+17496/16807) → [[17th-octave temperaments #Gothic|17th-octave temperaments]]

Considered below are superpyth, quasisuper, ultrapyth, quasiultra, schism, beatles, progress, fervor, and sixix.

==== Subgroup extensions ====

Omitting prime 5, archy can be extended to the 2.3.7.11 subgroup by identifying 11/8 as a diminished fourth (~~C–Gb~~). This is called supra, given right below. Discussed elsewhere is [[suhajira]] of the [[~~neutral~~ clan #Suhajira|~~neutral~~ clan]].

Omitting prime 5, archy can be extended to the 2.3.7.11 subgroup by identifying 11/8 as a diminished fourth (C–G♭). This is called supra, given right below. Discussed elsewhere is [[suhajira]] of the [[rastmic clan #Suhajira|rastmic clan]].

=== Supra ===

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Comma list: 64/63, 99/98

~~Sval~~ mapping: {{mapping| 1 0 6 13 | 0 1 -2 -6 }}

Subgroup-val mapping: {{mapping| 1 0 6 13 | 0 1 -2 -6 }}

Gencom mapping: {{mapping| 1 0 0 6 13 | 0 1 0 -2 -6 }}

~~: gencom: [2 3; 64/63 99/98]~~

Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~3/2 = ~~708~~.~~456~~

* WE: ~2 = 1197.2650{{c}}, ~3/2 = 705.5803{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~3/2 = 707.~~192~~

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 707.4981{{c}}

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==== Supraphon ====

This extension maps [[13/11]] to the minor third (C–E♭), [[12/11]][[~]][[14/13]] to the augmented unison (C–C♯), and [[13/12]] to the diminished third (C–E𝄫).

Subgroup: 2.3.7.11.13

Comma list: 64/63, 78/77, 99/98

~~Sval~~ mapping: {{mapping| 1 0 6 13 18 | 0 1 -2 -6 -9 }}

Subgroup-val mapping: {{mapping| 1 0 6 13 18 | 0 1 -2 -6 -9 }}

Gencom mapping: {{mapping| 1 0 0 6 13 18 | 0 1 0 -2 -6 -9 }}

~~: gencom: [2 3; 64/63 78/77 99/98]~~

Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~3/2 = ~~707~~.~~344~~

* WE: ~2 = 1197.1909{{c}}, ~3/2 = 704.4836{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~3/2 = 706.~~137~~

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 706.4289{{c}}

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: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Superpyth (5-limit)]].''

Superpyth, virtually the canonical extension, adds [[245/243]] and [[1728/1715]] to the comma list and can be described as {{nowrap| 22 & 27 }}. ~5/4 is found at +9 generator steps, as an augmented second (~~C–D#~~). 49edo remains an obvious tuning choice.

Superpyth, virtually the canonical extension, adds [[245/243]] and [[1728/1715]] to the comma list and can be described as {{nowrap| [[22edo|22]] [[&]] [[27edo|27]] }}. ~[[5/4]] is found at +9 generator steps, as an augmented second (C–D♯). In the [[11-limit]] it finds the ~[[11/8]] at +16 generator steps, as a double-augmented second (C–D𝄪). [[49edo]] remains an obvious tuning choice in either case.

Extending superpyth to the [[13-limit]] is more diffcult. Tridecimal superpyth finds the ~[[13/8]] at +13 generator steps, as a double-augmented fourth (C–F𝄪), for which 27edo can be recommended as a tuning since it is the only [[13-odd-limit]] [[diamond monotone]] tuning. The other extension, called uberpyth, is more flexible with its tunings, but unfortunately tends to tune the 13 very sharp.

[[Subgroup]]: 2.3.5.7

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[[Optimal tuning]]s:

* [[~~CTE~~]]: ~2 = ~~1200~~.~~000~~, ~3/2 = ~~709~~.~~591~~

* [[WE]]: ~2 = 1197.0549{{c}}, ~3/2 = 708.5478{{c}}

: [[error map]]: {{val| 0.~~000~~ +7.~~636 +~~0.~~002~~ +11.~~993~~ }}

: [[error map]]: {{val| -2.945 +3.648 -0.548 +2.298 }}

* [[~~POTE~~]]: ~2 = 1200.~~000~~, ~3/2 = 710.~~291~~

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 710.1193{{c}}

: error map: {{val| 0.000 +8.~~336~~ +6.~~305~~ +10.~~592~~ }}

: error map: {{val| 0.000 +8.164 +4.760 +10.935 }}

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=== 11-limit ===

~~The canonical extension to the 13-limit finds the ~11/8 at +16 generator steps, as a double-augmented second (C–Dx) and finds the ~13/8 at +13 generator steps, as a double-augmented fourth (C–Fx).~~

Subgroup: 2.3.5.7.11

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Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~3/2 = ~~709~~.~~514~~

* WE: ~2 = 1197.0673{{c}}, ~3/2 = 708.4391{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~3/2 = 710.~~175~~

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 710.0129{{c}}

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Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~3/2 = ~~709~~.~~836~~

* WE: ~2 = 1197.3011{{c}}, ~3/2 = 708.8813{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~3/2 = 710.~~479~~

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 710.3219{{c}}

Badness (Sintel): 1.02

==== Uberpyth ====

Subgroup: 2.3.5.7.11.13

Comma list: 64/63, 100/99, 144/143, 245/243

Mapping: {{mapping| 1 0 -12 6 -22 26 | 0 1 9 -2 16 -14 }}

Optimal tunings:

* WE: ~2 = 1196.6666{{c}}, ~3/2 = 708.3602{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 710.2878{{c}}

{{Optimal ET sequence|legend=0| 22f, 27e, 49f, 125bcddeeeff, 174bbcdddeeeeffff }}

Badness (Sintel): 1.11

==== Thomas ====

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Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~16/13 = 354.~~759~~

* WE: ~2 = 1197.4942{{c}}, ~16/13 = 354.2950{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~16/13 = ~~355~~.~~036~~

* CWE: ~2 = 1200.0000{{c}}, ~16/13 = 354.9824{{c}}

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=== Suprapyth ===

Suprapyth finds the ~11/8 at the diminished fifth (~~C–Gb~~), and finds the ~13/8 at the diminished seventh (~~C–Bbb~~).

Suprapyth finds the ~11/8 at the diminished fifth (C–G♭), and finds the ~13/8 at the diminished seventh (C–B𝄫).

Subgroup: 2.3.5.7.11

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Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~3/2 = ~~709~~.~~356~~

* WE: ~2 = 1198.6960{{c}}, ~3/2 = 708.7235{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~3/2 = 709.~~495~~

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 709.4699{{c}}

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Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~3/2 = 708.~~702~~

* WE: ~2 = 1199.9871{{c}}, ~3/2 = 708.6952{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~3/2 = 708.~~703~~

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 708.7028{{c}}

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== Quasisuper ==

Quasisuper can be described as {{nowrap| 17c & 22 }}, with the ~5/4 mapped to -13 generator steps, as a double-diminished fifth (~~C–Gbb~~).

Quasisuper can be described as {{nowrap| 17c & 22 }}, with the ~5/4 mapped to -13 generator steps, as a double-diminished fifth (C–G𝄫). The 11-limit version, quasisupra, can be viewed as an extension of the excellent 2.3.7.11-subgroup 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

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[[Optimal tuning]]s:

* [[~~CTE~~]]: ~2 = ~~1200~~.~~000~~, ~3/2 = ~~708~~.~~769~~

* [[WE]]: ~2 = 1196.9830{{c}}, ~3/2 = 706.4578{{c}}

: [[error map]]: {{val| 0.~~000~~ +6.~~814~~ -0.~~310~~ +13.~~636~~ }}

: [[error map]]: {{val| -3.017 +1.486 -0.435 +6.190 }}

* [[~~POTE~~]]: ~2 = 1200.~~000~~, ~3/2 = 708.~~238~~

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 708.3716{{c}}

: error map: {{val| 0.000 +6.~~283~~ +6.~~586~~ +14.~~697~~ }}

: error map: {{val| 0.000 +6.417 +4.855 +14.431 }}

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=== 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

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Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~3/2 = ~~708~~.~~713~~

* WE: ~2 = 1197.5675{{c}}, ~3/2 = 706.7690{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~3/2 = 708.~~205~~

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 708.3200{{c}}

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Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~3/2 = ~~708~~.~~411~~

* WE: ~2 = 1198.2543{{c}}, ~3/2 = 706.9736{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~3/2 = 708.~~004~~

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 708.0936{{c}}

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Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~3/2 = ~~709~~.~~043~~

* WE: ~2 = 1198.8446{{c}}, ~3/2 = 708.3388{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~3/2 = ~~709~~.~~021~~

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 708.0252{{c}}

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== Ultrapyth ==

: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Ultrapyth (5-limit)]].''

Ultrapyth can be viewed as an extension of the excellent 2.3.7.13/5 [[the Biosphere #Oceanfront|oceanfront]] temperament, mapping the ~5/4 to +14 fifths as a double-augmented unison (~~C–Cx~~).

Ultrapyth can be viewed as an extension of the excellent 2.3.7.13/5 [[the Biosphere #Oceanfront|oceanfront]] temperament, mapping the ~5/4 to +14 fifths as a double-augmented unison (C–C𝄪).

[[Subgroup]]: 2.3.5.7

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[[Optimal tuning]]s:

* [[~~CTE~~]]: ~2 = ~~1200~~.~~000~~, ~3/2 = ~~713~~.~~218~~

* [[WE]]: ~2 = 1197.2673{{c}}, ~3/2 = 712.0258{{c}}

: [[error map]]: {{val| 0.~~000~~ +11.~~263~~ -1.~~264 +4~~.~~738~~ }}

: [[error map]]: {{val| -2.733 +7.338 -1.557 -3.808 }}

* [[~~POTE~~]]: ~2 = 1200.~~000~~, ~3/2 = 713.~~651~~

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 713.5430{{c}}

: error map: {{val| 0.000 +11.~~696~~ +4.~~800~~ +3.~~872~~ }}

: error map: {{val| 0.000 +11.588 +3.288 +4.088 }}

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Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~3/2 = ~~713~~.~~282~~

* WE: ~2 = 1198.0290{{c}}, ~3/2 = 712.2235{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~3/2 = 713.~~395~~

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 713.3754{{c}}

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Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~3/2 = ~~713~~.~~309~~

* WE: ~2 = 1198.1911{{c}}, ~3/2 = 712.4243{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~3/2 = 713.~~500~~

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 713.4684{{c}}

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Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~3/2 = ~~713~~.~~395~~

* WE: ~2 = 1197.2230{{c}}, ~3/2 = 712.1393{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~3/2 = 713.~~791~~

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 713.6928{{c}}

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Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~3/2 = ~~713~~.~~708~~

* WE: ~2 = 1197.2739{{c}}, ~3/2 = 712.1893{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~3/2 = 713.~~811~~

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 713.7079{{c}}

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== Quasiultra ==

Quasiultra is to ultrapyth what quasisuper is to superpyth. It is the {{nowrap| 27 & 32 }} temperament, mapping the ~5/4 to -18 fifths as a double diminished sixth (~~C–Abbb~~).

Quasiultra is to ultrapyth what quasisuper is to superpyth. It is the {{nowrap| 27 & 32 }} temperament, mapping the ~5/4 to -18 fifths as a double diminished sixth (C–A𝄫♭).

[[Subgroup]]: 2.3.5.7

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[[Optimal tuning]]s:

* [[~~CTE~~]]: ~2 = ~~1200~~.~~000~~, ~3/2 = ~~711~~.~~838~~

* [[WE]]: ~2 = 1196.9257{{c}}, ~3/2 = 709.6211{{c}}

: [[error map]]: {{val| 0.000 +9.883 +0.608 +7.499 }}

* [[CWE]]: ~2 = 1200.~~000~~, ~3/2 = 711.~~543~~

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 711.5429{{c}}

: error map: {{val| 0.000 +9.588 +5.914 +8.088 }}

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Schism tempers out the [[schisma]], mapping the ~5/4 to -8 fifths as a diminished fourth (~~C–Fb~~) as does any schismic temperament. 12edo is recommendable tuning, though 29edo (29d val), 41edo (41d val), and 53edo (53dd val) can be used.

Schism tempers out the [[schisma]], mapping the ~5/4 to -8 fifths as a diminished fourth (C–F♭) as does any schismic temperament. 12edo is recommendable tuning, though 29edo (29d val), 41edo (41d val), and 53edo (53dd val) can be used.

[[Subgroup]]: 2.3.5.7

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[[Optimal tuning]]s:

* [[~~CTE~~]]: ~2 = ~~1200~~.~~000~~, ~3/2 = ~~702~~.~~270~~

* [[WE]]: ~2 = 1197.3598{{c}}, ~3/2 = 700.0126{{c}}

: [[error map]]: {{val| 0.~~000 +0~~.~~315~~ -4.~~471~~ +26.~~635~~ }}

: [[error map]]: {{val| -2.640 -4.583 -4.896 +20.588 }}

* [[~~POTE~~]]: ~2 = 1200.~~000~~, ~3/2 = 701.~~556~~

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7376{{c}}

: error map: {{val| 0.000 -0.~~399 +1~~.~~237~~ +28.~~062~~ }}

: error map: {{val| 0.000 -0.217 -0.214 +27.699 }}

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Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~3/2 = ~~703~~.~~383~~

* WE: ~2 = 1196.1607{{c}}, ~3/2 = 699.8897{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~3/2 = 702.~~136~~

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.4385{{c}}

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== Beatles ==

: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Beatles]].''

Beatles tempers out 686/675, which may also be characterized by saying it tempers out [[2401/2400]]. It may be described as the {{nowrap| 10 & 17c }} temperament. It splits the fifth into two neutral-third generators of 49/40~60/49; its [[ploidacot]] is dicot. 5/4 may be found at -9 generator steps, as a semidiminished fourth (C–Fd). 27edo is an obvious tuning, though 17c-edo and 37edo are among the possibilities.

Beatles extends easily to the no-11 13-limit, as the generator can be interpreted as ~16/13, tempering out 91/90, 169/168, and 196/195.

[[Subgroup]]: 2.3.5.7

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[[Optimal tuning]]s:

* [[~~CTE~~]]: ~2 = ~~1200~~.~~000~~, ~49/40 = ~~356~~.~~634~~

* [[WE]]: ~2 = 1196.6244{{c}}, ~49/40 = 354.9029{{c}}

: [[error map]]: {{val| 0.~~000~~ +11.~~312~~ +3.~~984 +4~~.~~640~~ }}

: [[error map]]: {{val| -3.376 +4.475 +2.682 -1.940 }}

* [[~~POTE~~]]: ~2 = 1200.~~000~~, ~49/40 = ~~355~~.~~904~~

* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 356.0819{{c}}

: error map: {{val| 0.000 +9.~~853~~ +10.~~549~~ +7.~~558~~ }}

: error map: {{val| 0.000 +10.209 +8.949 +6.847 }}

{{Optimal ET sequence|legend=1| 10, 17c, 27, 64b, 91bcd, 118bccd }}

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Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~49/40 = ~~356~~.~~719~~

* WE: ~2 = 1196.7001{{c}}, ~49/40 = 355.1606{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~49/40 = 356.~~140~~

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 356.2795{{c}}

{{Optimal ET sequence|legend=0| 10e, 17cee, 27e, 64be, 91bcdee }}

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Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~16/13 = ~~356~~.~~722~~

* WE: ~2 = 1197.2504{{c}}, ~16/13 = 355.4132{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~16/13 = 356.~~229~~

* CWE: ~2 = 1200.0000{{c}}, ~16/13 = 356.3273{{c}}

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Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~11/9 = ~~355~~.~~992~~

* WE: ~2 = 1195.4102{{c}}, ~11/9 = 354.0597{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~11/9 = 355.~~419~~

* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 355.5207{{c}}

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Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~11/9 = ~~356~~.~~004~~

* WE: ~2 = 1195.9943{{c}}, ~11/9 = 354.2695{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~11/9 = 355.~~456~~

* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 355.5398{{c}}

Line 500:

Line 517:

Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~49/40 = 356.~~694~~

* WE: ~2 = 1197.9660{{c}}, ~49/40 = 356.1056{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~49/40 = 356.~~710~~

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 356.7075{{c}}

Line 515:

Line 532:

Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~16/13 = 356.~~700~~

* WE: ~2 = 1198.1741{{c}}, ~16/13 = 356.1582{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~16/13 = 356.~~701~~

* CWE: ~2 = 1200.0000{{c}}, ~16/13 = 356.7008{{c}}

Line 523:

Line 540:

== Progress ==

: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Progress]].''

Progress tempers out 392/375 and may be described as {{nowrap| 15 & 17c }}. It splits the perfect twelfth into three generators of ~10/7; its ploidacot is alpha-tricot. 32c-edo gives an obvious tuning.

[[Subgroup]]: 2.3.5.7

Line 534:

Line 554:

[[Optimal tuning]]s:

* [[~~CTE~~]]: ~2 = ~~1200~~.~~000~~, ~10/7 = ~~638~~.~~782~~

* [[WE]]: ~2 = 1195.1377{{c}}, ~10/7 = 635.2932{{c}}

: [[error map]]: {{val| 0.~~000~~ +14.~~391~~ +19.~~777~~ -1.~~518~~ }}

: [[error map]]: {{val| -4.862 +3.925 +12.908 -9.759 }}

* [[~~POTE~~]]: ~2 = 1200.~~000~~, ~10/7 = ~~637~~.~~878~~

* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 638.0791{{c}}

: error map: {{val| 0.000 +11.~~679~~ +24.~~297~~ +3.~~907~~ }}

: error map: {{val| 0.000 +12.282 +23.291 +2.700 }}

Line 551:

Line 571:

Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~10/7 = ~~638~~.~~846~~

* WE: ~2 = 1195.4920{{c}}, ~10/7 = 635.5183{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~10/7 = ~~637~~.~~915~~

* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 638.0884{{c}}

Line 566:

Line 586:

Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~10/7 = ~~637~~.~~871~~

* WE: ~2 = 1195.0786{{c}}, ~10/7 = 635.0197{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~10/7 = 637.~~635~~

* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 637.6691{{c}}

Line 581:

Line 601:

Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~10/7 = ~~637~~.~~797~~

* WE: ~2 = 1196.0245{{c}}, ~10/7 = 634.6516{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~10/7 = 636.~~761~~

* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 636.9528{{c}}

Line 590:

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== Fervor ==

: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Fervor]].''

Fervor tempers out 9704/9375 and may be described as {{nowrap| 25 & 27 }}. It splits the 6th harmonic into five generators of ~10/7; its ploidacot is beta-pentacot. 27edo is about as accurate as it can be tuned.

[[Subgroup]]: 2.3.5.7

Line 595:

Line 617:

[[Comma list]]: 64/63, 9604/9375

: mapping generators: ~2, ~7/5

: mapping generators: ~2, ~10/7

[[Optimal tuning]]s:

* [[~~CTE~~]]: ~2 = ~~1200~~.~~000~~, ~7/5 = ~~577~~.~~353~~

* [[WE]]: ~2 = 1196.2742{{c}}, ~10/7 = 620.2918{{c}}

: [[error map]]: {{val| 0.~~000~~ +11.~~278~~ +9.~~867 +4~~.~~709~~ }}

: [[error map]]: {{val| -3.726 +3.230 +4.980 -1.550 }}

* [[~~POTE~~]]: ~2 = 1200.~~000~~, ~7/5 = ~~577~~.~~776~~

* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 622.3179{{c}}

: error map: {{val| 0.000 +9.~~163~~ +13.~~673~~ +8.~~937~~ }}

: error map: {{val| 0.000 +9.634 +12.826 +7.996 }}

Line 614:

Line 636:

Comma list: 56/55, 64/63, 1350/1331

Mapping: {{mapping| 1 4 ~~-2 -2 3~~ | 0 -5 9 10 1 }}

Mapping: {{mapping| 1 -1 7 8 4 | 0 5 -9 -10 -1 }}

Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~7/5 = ~~577~~.~~296~~

* WE: ~2 = 1195.4148{{c}}, ~10/7 = 619.7729{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~7/5 = ~~577~~.~~850~~

* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 622.2525{{c}}

Line 629:

Line 651:

Comma list: 56/55, 64/63, 78/77, 507/500

Mapping: {{mapping| 1 ~~4 -2 -2 3~~ -4 | 0 -5 9 10 1 16 }}

Mapping: {{mapping| 1 -1 7 8 4 12 | 0 5 -9 -10 -1 -16 }}

Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~7/5 = ~~577~~.~~374~~

* WE: ~2 = 1195.6284{{c}}, ~10/7 = 619.6738{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~7/5 = ~~578~~.~~060~~

* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 622.0631{{c}}

Line 643:

Line 665:

Sixix is related to the [[kleismic family]] in a way similar to the one between [[meantone]] and [[mavila]]. In both cases the generator is nominally a 6/5 and the complexity to generate major and minor chords is the same, but in sixix it is tuned extremely sharply, to the point where the 3rd and 5th harmonics are reached by going down instead of up, inverting the logic of chord construction.

Sixix tempers out 3125/2916 and may be described as {{nowrap| 25 & 32 }}. It is related to the [[kleismic family]] in a way similar to the one between [[meantone]] and [[mavila]]. In both cases the generator is nominally a 6/5 and the complexity to generate major and minor chords is the same, but in sixix it is tuned extremely sharply, to the point where the 3rd and 5th harmonics are reached by going down instead of up, inverting the logic of chord construction. Its ploidacot is gamma-pentacot.

[[Subgroup]]: 2.3.5.7

Line 652:

Line 674:

[[Optimal tuning]]s:

* [[~~CTE~~]]: ~2 = ~~1200~~.~~000~~, ~6/5 = 337.~~519~~

* [[WE]]: ~2 = 1198.9028{{c}}, ~6/5 = 337.1334{{c}}

: [[error map]]: {{val| 0.~~000~~ +10.~~449~~ -11.~~429~~ +6.~~366~~ }}

: [[error map]]: {{val| -1.097 +9.086 -13.503 +2.508 }}

* [[~~POTE~~]]: ~2 = 1200.~~000~~, ~6/5 = 337.~~442~~

* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 337.4588{{c}}

: error map: {{val| 0.000 +10.~~835~~ -10.~~965~~ +5.~~594~~ }}

: error map: {{val| 0.000 +10.751 -11.066 +5.762 }}

Line 669:

Line 691:

Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~6/5 = 337.~~749~~

* WE: ~2 = 1198.5480{{c}}, ~6/5 = 337.1557{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~6/5 = 337.~~564~~

* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 337.6000{{c}}

Line 684:

Line 706:

Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~6/5 = ~~337~~.~~793~~

* WE: ~2 = 1197.7111{{c}}, ~6/5 = 336.8391{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~6/5 = 337.~~483~~

* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 337.5336{{c}}

Line 699:

Line 721:

Optimal tunings:

* ~~CTE~~: ~2 = ~~1200~~.~~000~~, ~6/5 = ~~337~~.~~629~~

* WE: ~2 = 1197.7807{{c}}, ~6/5 = 336.8884{{c}}

* ~~POTE~~: ~2 = 1200.~~000~~, ~6/5 = 337.~~513~~

* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 337.5279{{c}}

Line 708:

Line 730:

[[Category:Archytas clan| ]]

[[Category:Temperament clans]]

[[Category:~~Rank~~ 2]]

[[Category:Catalogs of rank-2 temperaments]]

@@ Line 12: / Line 12: @@
 {{Mapping|legend=2| 1 0 6 | 0 1 -2 }}
-: sval mapping generators: ~2, ~3
 {{Mapping|legend=3| 1 0 0 6 | 0 1 0 -2 }}
+: mapping generators: ~2, ~3
-: [[gencom]]: [2 3; 64/63]
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000, ~3/2 = 709.595
+* [[WE]]: ~2 = 1196.9552{{c}}, ~3/2 = 707.5215{{c}}
-: [[error map]]: {{val| 0.000 +7.640 +11.984 }}
+: [[error map]]: {{val| -3.045 +2.522 +3.952 }}
-* [[POTE]]: ~2 = 1200.000, ~3/2 = 709.321
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 709.3901{{c}}
-: error map: {{val| 0.000 +7.366 +12.532 }}
+: error map: {{val| 0.000 +7.435 +12.394 }}
 {{Optimal ET sequence|legend=1| 2, 3, 5, 12, 17, 22, 137bdd, 159bddd, 181bbddd }}
@@ Line 34: / Line 31: @@
 ==== 7-limit extensions ====
 The second comma in the comma list defines which [[7-limit]] family member we are looking at:
-* [[#Schism|Schism]] adds 360/343, for an [[exotemperament]] well tuned around [[12edo]];
+* [[#Schism|Schism]] adds [[360/343]], for a tuning around [[12edo]];
-* Dominant adds [[36/35]], for a tuning flat of [[17edo|17c-edo]];
+* [[Meantone family #Dominant|Dominant]] adds [[36/35]], for a tuning between [[12edo]] and [[17edo|17c-edo]];
 * [[#Quasisuper|Quasisuper]] adds [[2430/2401]], for a tuning between 17c-edo and [[22edo]];
 * [[#Superpyth|Superpyth]] adds [[245/243]], for a tuning between 22edo and [[27edo]];
-* [[#Quasiultra|Quasiultra]] adds 33614/32805, for a tuning between 27edo and [[32edo]];
+* [[#Quasiultra|Quasiultra]] adds [[33614/32805]], for a tuning between 27edo and [[32edo]];
-* [[#Ultrapyth|Ultrapyth]] adds 6860/6561, for a tuning sharp of 32edo;
+* [[#Ultrapyth|Ultrapyth]] adds [[6860/6561]], for a tuning sharp of 32edo;
 * Mother adds [[16/15]], for an exotemperament well tuned around [[5edo]].
 These all use the same generators as archy.
-[[686/675]] gives beatles, splitting the fifth in two. [[8748/8575]] gives immunized, splitting the twelfth in two. [[50/49]] gives pajara with a semioctave period. [[392/375]] gives progress, splitting the twelfth in three. [[250/243]] gives porcupine, splitting the fourth in three. [[126/125]] gives augene with a 1/3-octave period. [[4375/4374]] gives modus, splitting the fifth in four. [[3125/3024]] gives brightstone. [[9604/9375]] gives fervor. [[3125/2916]] gives sixix. [[3125/3087]] gives passion. Those split the generator in five in various ways. [[28/27]] gives blacksmith with a 1/5-octave period. Finally, [[15625/15552]] gives catalan, splitting the twelfth in six.
+[[25/24]] gives dichotic. [[686/675]] gives beatles. Those split the fifth in two. [[8748/8575]] gives immunized, splitting the twelfth in two. [[50/49]] gives pajara with a semioctave period. [[392/375]] gives progress, splitting the twelfth in three. [[250/243]] gives porcupine, splitting the fourth in three. [[126/125]] gives augene with a 1/3-octave period. [[4375/4374]] gives modus, splitting the fifth in four. [[3125/3024]] gives brightstone. [[9604/9375]] gives fervor. [[3125/2916]] gives sixix. [[3125/3087]] gives passion. Those split the generator in five in various ways. [[15625/15552]] gives catalan, splitting the twelfth in six. Finally, [[28/27]] gives blackwood and [[17496/16807]] gives [[gothic]], reducing the intervals of 3 and 7 to the same chain of 1/5- and 1/17-octave periods, respectively.
 Temperaments discussed elsewhere are:
@@ Line 50: / Line 47: @@
 * [[Dominant (temperament)|Dominant]] (+36/35) → [[Meantone family #Dominant|Meantone family]]
 * ''[[Medusa]]'' (+15/14) → [[Very low accuracy temperaments #Medusa|Very low accuracy temperaments]]
+* ''[[Dichotic]]'' (+25/24) → [[Dicot family #Dichotic|Dicot family]]
 * ''[[Immunized]]'' (+8748/8575) → [[Immunity family #Immunized|Immunity family]]
 * [[Pajara]] (+50/49) → [[Diaschismic family #Pajara|Diaschismic family]]
-* [[Augene]] (+126/125) → [[Augmented family #Augene|Augmented family]]
+* [[Augene]] (+126/125) → [[Augmented family #Septimal augmented (augene)|Augmented family]]
 * [[Porcupine]] (+250/243) → [[Porcupine family #Septimal porcupine|Porcupine family]]
-* ''[[Modus]]'' (+4375/4374) → [[Tetracot family #Modus|Tetracot family]]
+* [[Modus]] (+4375/4374) → [[Tetracot family #Modus|Tetracot family]]
 * ''[[Brightstone]]'' (+3125/3024) → [[Magic family #Brightstone|Magic family]]
 * ''[[Passion]]'' (+3125/3087) → [[Passion family #Septimal passion|Passion family]]
-* ''[[Blacksmith]]'' (+28/27) → [[Limmic temperaments #Blacksmith|Limmic temperaments]]
 * ''[[Catalan]]'' (+15625/15552) → [[Kleismic family #Catalan|Kleismic family]]
+* [[Blackwood]] (+28/27) → [[Blackwood family #Blackwood|Blackwood family]]
+* ''[[Gothic]]'' (+17496/16807) → [[17th-octave temperaments #Gothic|17th-octave temperaments]]
 Considered below are superpyth, quasisuper, ultrapyth, quasiultra, schism, beatles, progress, fervor, and sixix.
 ==== Subgroup extensions ====
-Omitting prime 5, archy can be extended to the 2.3.7.11 subgroup by identifying 11/8 as a diminished fourth (C–Gb). This is called supra, given right below. Discussed elsewhere is [[suhajira]] of the [[neutral clan #Suhajira|neutral clan]].
+Omitting prime 5, archy can be extended to the 2.3.7.11 subgroup by identifying 11/8 as a diminished fourth (C–G♭). This is called supra, given right below. Discussed elsewhere is [[suhajira]] of the [[rastmic clan #Suhajira|rastmic clan]].
 === Supra ===
@@ Line 70: / Line 69: @@
 Comma list: 64/63, 99/98
-Sval mapping: {{mapping| 1 0 6 13 | 0 1 -2 -6 }}
+Subgroup-val mapping: {{mapping| 1 0 6 13 | 0 1 -2 -6 }}
 Gencom mapping: {{mapping| 1 0 0 6 13 | 0 1 0 -2 -6 }}
-: gencom: [2 3; 64/63 99/98]
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~3/2 = 708.456
+* WE: ~2 = 1197.2650{{c}}, ~3/2 = 705.5803{{c}}
-* POTE: ~2 = 1200.000, ~3/2 = 707.192
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 707.4981{{c}}
 {{Optimal ET sequence|legend=0| 5, 12, 17, 39d, 56d }}
@@ Line 87: / Line 84: @@
 ==== Supraphon ====
+This extension maps [[13/11]] to the minor third (C–E♭), [[12/11]][[~]][[14/13]] to the augmented unison (C–C♯), and [[13/12]] to the diminished third (C–E𝄫).
 Subgroup: 2.3.7.11.13
 Comma list: 64/63, 78/77, 99/98
-Sval mapping: {{mapping| 1 0 6 13 18 | 0 1 -2 -6 -9 }}
+Subgroup-val mapping: {{mapping| 1 0 6 13 18 | 0 1 -2 -6 -9 }}
 Gencom mapping: {{mapping| 1 0 0 6 13 18 | 0 1 0 -2 -6 -9 }}
-: gencom: [2 3; 64/63 78/77 99/98]
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~3/2 = 707.344
+* WE: ~2 = 1197.1909{{c}}, ~3/2 = 704.4836{{c}}
-* POTE: ~2 = 1200.000, ~3/2 = 706.137
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 706.4289{{c}}
 {{Optimal ET sequence|legend=0| 12f, 17 }}
@@ Line 111: / Line 108: @@
 : ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Superpyth (5-limit)]].''
-Superpyth, virtually the canonical extension, adds [[245/243]] and [[1728/1715]] to the comma list and can be described as {{nowrap| 22 & 27 }}. ~5/4 is found at +9 generator steps, as an augmented second (C–D#). 49edo remains an obvious tuning choice.
+Superpyth, virtually the canonical extension, adds [[245/243]] and [[1728/1715]] to the comma list and can be described as {{nowrap| [[22edo|22]] [[&]] [[27edo|27]] }}. ~[[5/4]] is found at +9 generator steps, as an augmented second (C–D♯). In the [[11-limit]] it finds the ~[[11/8]] at +16 generator steps, as a double-augmented second (C–D𝄪). [[49edo]] remains an obvious tuning choice in either case.
+Extending superpyth to the [[13-limit]] is more diffcult. Tridecimal superpyth finds the ~[[13/8]] at +13 generator steps, as a double-augmented fourth (C–F𝄪), for which 27edo can be recommended as a tuning since it is the only [[13-odd-limit]] [[diamond monotone]] tuning. The other extension, called uberpyth, is more flexible with its tunings, but unfortunately tends to tune the 13 very sharp.
 [[Subgroup]]: 2.3.5.7
@@ Line 120: / Line 119: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000, ~3/2 = 709.591
+* [[WE]]: ~2 = 1197.0549{{c}}, ~3/2 = 708.5478{{c}}
-: [[error map]]: {{val| 0.000 +7.636 +0.002 +11.993 }}
+: [[error map]]: {{val| -2.945 +3.648 -0.548 +2.298 }}
-* [[POTE]]: ~2 = 1200.000, ~3/2 = 710.291
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 710.1193{{c}}
-: error map: {{val| 0.000 +8.336 +6.305 +10.592 }}
+: error map: {{val| 0.000 +8.164 +4.760 +10.935 }}
 {{Optimal ET sequence|legend=1| 5, 17, 22, 27, 49, 174bbcddd }}
@@ Line 130: / Line 129: @@
 === 11-limit ===
-The canonical extension to the 13-limit finds the ~11/8 at +16 generator steps, as a double-augmented second (C–Dx) and finds the ~13/8 at +13 generator steps, as a double-augmented fourth (C–Fx).
 Subgroup: 2.3.5.7.11
@@ Line 139: / Line 136: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~3/2 = 709.514
+* WE: ~2 = 1197.0673{{c}}, ~3/2 = 708.4391{{c}}
-* POTE: ~2 = 1200.000, ~3/2 = 710.175
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 710.0129{{c}}
 {{Optimal ET sequence|legend=0| 22, 27e, 49 }}
@@ Line 154: / Line 151: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~3/2 = 709.836
+* WE: ~2 = 1197.3011{{c}}, ~3/2 = 708.8813{{c}}
-* POTE: ~2 = 1200.000, ~3/2 = 710.479
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 710.3219{{c}}
 {{Optimal ET sequence|legend=0| 22, 27e, 49, 76bcde }}
 Badness (Sintel): 1.02
+==== Uberpyth ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 64/63, 100/99, 144/143, 245/243
+Mapping: {{mapping| 1 0 -12 6 -22 26 | 0 1 9 -2 16 -14 }}
+Optimal tunings:
+* WE: ~2 = 1196.6666{{c}}, ~3/2 = 708.3602{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 710.2878{{c}}
+{{Optimal ET sequence|legend=0| 22f, 27e, 49f, 125bcddeeeff, 174bbcdddeeeeffff }}
+Badness (Sintel): 1.11
 ==== Thomas ====
@@ Line 169: / Line 181: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~16/13 = 354.759
+* WE: ~2 = 1197.4942{{c}}, ~16/13 = 354.2950{{c}}
-* POTE: ~2 = 1200.000, ~16/13 = 355.036
+* CWE: ~2 = 1200.0000{{c}}, ~16/13 = 354.9824{{c}}
 {{Optimal ET sequence|legend=0| 27e, 44, 71d, 98bde }}
@@ Line 177: / Line 189: @@
 === Suprapyth ===
-Suprapyth finds the ~11/8 at the diminished fifth (C–Gb), and finds the ~13/8 at the diminished seventh (C–Bbb).
+Suprapyth finds the ~11/8 at the diminished fifth (C–G♭), and finds the ~13/8 at the diminished seventh (C–B𝄫).
 Subgroup: 2.3.5.7.11
@@ Line 186: / Line 198: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~3/2 = 709.356
+* WE: ~2 = 1198.6960{{c}}, ~3/2 = 708.7235{{c}}
-* POTE: ~2 = 1200.000, ~3/2 = 709.495
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 709.4699{{c}}
 {{Optimal ET sequence|legend=0| 5, 17, 22 }}
@@ Line 201: / Line 213: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~3/2 = 708.702
+* WE: ~2 = 1199.9871{{c}}, ~3/2 = 708.6952{{c}}
-* POTE: ~2 = 1200.000, ~3/2 = 708.703
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 708.7028{{c}}
 {{Optimal ET sequence|legend=0| 5f, 17, 22 }}
@@ Line 209: / Line 221: @@
 == Quasisuper ==
-Quasisuper can be described as {{nowrap| 17c & 22 }}, with the ~5/4 mapped to -13 generator steps, as a double-diminished fifth (C–Gbb).
+{{Main|Quasisuper}}
+Quasisuper can be described as {{nowrap| 17c & 22 }}, with the ~5/4 mapped to -13 generator steps, as a double-diminished fifth (C–G𝄫). The 11-limit version, quasisupra, can be viewed as an extension of the excellent 2.3.7.11-subgroup 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
@@ Line 218: / Line 232: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000, ~3/2 = 708.769
+* [[WE]]: ~2 = 1196.9830{{c}}, ~3/2 = 706.4578{{c}}
-: [[error map]]: {{val| 0.000 +6.814 -0.310 +13.636 }}
+: [[error map]]: {{val| -3.017 +1.486 -0.435 +6.190 }}
-* [[POTE]]: ~2 = 1200.000, ~3/2 = 708.238
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 708.3716{{c}}
-: error map: {{val| 0.000 +6.283 +6.586 +14.697 }}
+: error map: {{val| 0.000 +6.417 +4.855 +14.431 }}
 {{Optimal ET sequence|legend=1| 17c, 22, 61d }}
@@ Line 228: / Line 242: @@
 === 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
@@ Line 237: / Line 249: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~3/2 = 708.713
+* WE: ~2 = 1197.5675{{c}}, ~3/2 = 706.7690{{c}}
-* POTE: ~2 = 1200.000, ~3/2 = 708.205
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 708.3200{{c}}
 {{Optimal ET sequence|legend=0| 17c, 22, 39d, 61d }}
@@ Line 252: / Line 264: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~3/2 = 708.411
+* WE: ~2 = 1198.2543{{c}}, ~3/2 = 706.9736{{c}}
-* POTE: ~2 = 1200.000, ~3/2 = 708.004
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 708.0936{{c}}
 {{Optimal ET sequence|legend=0| 17c, 22, 39d }}
@@ Line 267: / Line 279: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~3/2 = 709.043
+* WE: ~2 = 1198.8446{{c}}, ~3/2 = 708.3388{{c}}
-* POTE: ~2 = 1200.000, ~3/2 = 709.021
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 708.0252{{c}}
 {{Optimal ET sequence|legend=0| 22 }}
@@ Line 275: / Line 287: @@
 == Ultrapyth ==
-{{main|Ultrapyth}}
+{{Main| Ultrapyth }}
+: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Ultrapyth (5-limit)]].''
-Ultrapyth can be viewed as an extension of the excellent 2.3.7.13/5 [[the Biosphere #Oceanfront|oceanfront]] temperament, mapping the ~5/4 to +14 fifths as a double-augmented unison (C–Cx).
+Ultrapyth can be viewed as an extension of the excellent 2.3.7.13/5 [[the Biosphere #Oceanfront|oceanfront]] temperament, mapping the ~5/4 to +14 fifths as a double-augmented unison (C–C𝄪).
 [[Subgroup]]: 2.3.5.7
@@ Line 286: / Line 299: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000, ~3/2 = 713.218
+* [[WE]]: ~2 = 1197.2673{{c}}, ~3/2 = 712.0258{{c}}
-: [[error map]]: {{val| 0.000 +11.263 -1.264 +4.738 }}
+: [[error map]]: {{val| -2.733 +7.338 -1.557 -3.808 }}
-* [[POTE]]: ~2 = 1200.000, ~3/2 = 713.651
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 713.5430{{c}}
-: error map: {{val| 0.000 +11.696 +4.800 +3.872 }}
+: error map: {{val| 0.000 +11.588 +3.288 +4.088 }}
 {{Optimal ET sequence|legend=1| 5, 27c, 32, 37 }}
@@ Line 303: / Line 316: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~3/2 = 713.282
+* WE: ~2 = 1198.0290{{c}}, ~3/2 = 712.2235{{c}}
-* POTE: ~2 = 1200.000, ~3/2 = 713.395
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 713.3754{{c}}
 {{Optimal ET sequence|legend=0| 5, 32, 37 }}
@@ Line 318: / Line 331: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~3/2 = 713.309
+* WE: ~2 = 1198.1911{{c}}, ~3/2 = 712.4243{{c}}
-* POTE: ~2 = 1200.000, ~3/2 = 713.500
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 713.4684{{c}}
 {{Optimal ET sequence|legend=0| 5, 32, 37 }}
@@ Line 333: / Line 346: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~3/2 = 713.395
+* WE: ~2 = 1197.2230{{c}}, ~3/2 = 712.1393{{c}}
-* POTE: ~2 = 1200.000, ~3/2 = 713.791
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 713.6928{{c}}
 {{Optimal ET sequence|legend=0| 5e, 32e, 37, 79bce }}
@@ Line 348: / Line 361: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~3/2 = 713.708
+* WE: ~2 = 1197.2739{{c}}, ~3/2 = 712.1893{{c}}
-* POTE: ~2 = 1200.000, ~3/2 = 713.811
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 713.7079{{c}}
 {{Optimal ET sequence|legend=0| 5e, 32e, 37, 79bcef }}
@@ Line 356: / Line 369: @@
 == Quasiultra ==
-Quasiultra is to ultrapyth what quasisuper is to superpyth. It is the {{nowrap| 27 & 32 }} temperament, mapping the ~5/4 to -18 fifths as a double diminished sixth (C–Abbb).
+Quasiultra is to ultrapyth what quasisuper is to superpyth. It is the {{nowrap| 27 & 32 }} temperament, mapping the ~5/4 to -18 fifths as a double diminished sixth (C–A𝄫♭).
 [[Subgroup]]: 2.3.5.7
@@ Line 365: / Line 378: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000, ~3/2 = 711.838
+* [[WE]]: ~2 = 1196.9257{{c}}, ~3/2 = 709.6211{{c}}
 : [[error map]]: {{val| 0.000 +9.883 +0.608 +7.499 }}
-* [[CWE]]: ~2 = 1200.000, ~3/2 = 711.543
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 711.5429{{c}}
 : error map: {{val| 0.000 +9.588 +5.914 +8.088 }}
@@ Line 377: / Line 390: @@
 {{See also| Schismatic family #Schism }}
-Schism tempers out the [[schisma]], mapping the ~5/4 to -8 fifths as a diminished fourth (C–Fb) as does any schismic temperament. 12edo is recommendable tuning, though 29edo (29d val), 41edo (41d val), and 53edo (53dd val) can be used.
+Schism tempers out the [[schisma]], mapping the ~5/4 to -8 fifths as a diminished fourth (C–F♭) as does any schismic temperament. 12edo is recommendable tuning, though 29edo (29d val), 41edo (41d val), and 53edo (53dd val) can be used.
 [[Subgroup]]: 2.3.5.7
@@ Line 386: / Line 399: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000, ~3/2 = 702.270
+* [[WE]]: ~2 = 1197.3598{{c}}, ~3/2 = 700.0126{{c}}
-: [[error map]]: {{val| 0.000 +0.315 -4.471 +26.635 }}
+: [[error map]]: {{val| -2.640 -4.583 -4.896 +20.588 }}
-* [[POTE]]: ~2 = 1200.000, ~3/2 = 701.556
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7376{{c}}
-: error map: {{val| 0.000 -0.399 +1.237 +28.062 }}
+: error map: {{val| 0.000 -0.217 -0.214 +27.699 }}
 {{Optimal ET sequence|legend=1| 5c, 7c, 12 }}
@@ Line 403: / Line 416: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~3/2 = 703.383
+* WE: ~2 = 1196.1607{{c}}, ~3/2 = 699.8897{{c}}
-* POTE: ~2 = 1200.000, ~3/2 = 702.136
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.4385{{c}}
 {{Optimal ET sequence|legend=0| 5c, 7ce, 12, 29de }}
@@ Line 412: / Line 425: @@
 == Beatles ==
 : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Beatles]].''
+Beatles tempers out 686/675, which may also be characterized by saying it tempers out [[2401/2400]]. It may be described as the {{nowrap| 10 & 17c }} temperament. It splits the fifth into two neutral-third generators of 49/40~60/49; its [[ploidacot]] is dicot. 5/4 may be found at -9 generator steps, as a semidiminished fourth (C–Fd). 27edo is an obvious tuning, though 17c-edo and 37edo are among the possibilities.
+Beatles extends easily to the no-11 13-limit, as the generator can be interpreted as ~16/13, tempering out 91/90, 169/168, and 196/195.
 [[Subgroup]]: 2.3.5.7
@@ Line 420: / Line 437: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000, ~49/40 = 356.634
+* [[WE]]: ~2 = 1196.6244{{c}}, ~49/40 = 354.9029{{c}}
-: [[error map]]: {{val| 0.000 +11.312 +3.984 +4.640 }}
+: [[error map]]: {{val| -3.376 +4.475 +2.682 -1.940 }}
-* [[POTE]]: ~2 = 1200.000, ~49/40 = 355.904
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 356.0819{{c}}
-: error map: {{val| 0.000 +9.853 +10.549 +7.558 }}
+: error map: {{val| 0.000 +10.209 +8.949 +6.847 }}
 {{Optimal ET sequence|legend=1| 10, 17c, 27, 64b, 91bcd, 118bccd }}
@@ Line 440: / Line 457: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~49/40 = 356.719
+* WE: ~2 = 1196.7001{{c}}, ~49/40 = 355.1606{{c}}
-* POTE: ~2 = 1200.000, ~49/40 = 356.140
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 356.2795{{c}}
 {{Optimal ET sequence|legend=0| 10e, 17cee, 27e, 64be, 91bcdee }}
@@ Line 455: / Line 472: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~16/13 = 356.722
+* WE: ~2 = 1197.2504{{c}}, ~16/13 = 355.4132{{c}}
-* POTE: ~2 = 1200.000, ~16/13 = 356.229
+* CWE: ~2 = 1200.0000{{c}}, ~16/13 = 356.3273{{c}}
 {{Optimal ET sequence|legend=0| 10e, 27e, 37, 64be }}
@@ Line 470: / Line 487: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~11/9 = 355.992
+* WE: ~2 = 1195.4102{{c}}, ~11/9 = 354.0597{{c}}
-* POTE: ~2 = 1200.000, ~11/9 = 355.419
+* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 355.5207{{c}}
 {{Optimal ET sequence|legend=0| 10, 17c, 27e }}
@@ Line 485: / Line 502: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~11/9 = 356.004
+* WE: ~2 = 1195.9943{{c}}, ~11/9 = 354.2695{{c}}
-* POTE: ~2 = 1200.000, ~11/9 = 355.456
+* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 355.5398{{c}}
 {{Optimal ET sequence|legend=0| 10, 17c, 27e }}
@@ Line 500: / Line 517: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~49/40 = 356.694
+* WE: ~2 = 1197.9660{{c}}, ~49/40 = 356.1056{{c}}
-* POTE: ~2 = 1200.000, ~49/40 = 356.710
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 356.7075{{c}}
 {{Optimal ET sequence|legend=0| 10, 27, 37 }}
@@ Line 515: / Line 532: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~16/13 = 356.700
+* WE: ~2 = 1198.1741{{c}}, ~16/13 = 356.1582{{c}}
-* POTE: ~2 = 1200.000, ~16/13 = 356.701
+* CWE: ~2 = 1200.0000{{c}}, ~16/13 = 356.7008{{c}}
 {{Optimal ET sequence|legend=0| 10, 27, 37 }}
@@ Line 523: / Line 540: @@
 == Progress ==
+{{Distinguish| Progression }}
 : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Progress]].''
+Progress tempers out 392/375 and may be described as {{nowrap| 15 & 17c }}. It splits the perfect twelfth into three generators of ~10/7; its ploidacot is alpha-tricot. 32c-edo gives an obvious tuning.
 [[Subgroup]]: 2.3.5.7
@@ Line 534: / Line 554: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000, ~10/7 = 638.782
+* [[WE]]: ~2 = 1195.1377{{c}}, ~10/7 = 635.2932{{c}}
-: [[error map]]: {{val| 0.000 +14.391 +19.777 -1.518 }}
+: [[error map]]: {{val| -4.862 +3.925 +12.908 -9.759 }}
-* [[POTE]]: ~2 = 1200.000, ~10/7 = 637.878
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 638.0791{{c}}
-: error map: {{val| 0.000 +11.679 +24.297 +3.907 }}
+: error map: {{val| 0.000 +12.282 +23.291 +2.700 }}
 {{Optimal ET sequence|legend=1| 2, 13, 15, 32c }}
@@ Line 551: / Line 571: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~10/7 = 638.846
+* WE: ~2 = 1195.4920{{c}}, ~10/7 = 635.5183{{c}}
-* POTE: ~2 = 1200.000, ~10/7 = 637.915
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 638.0884{{c}}
 {{Optimal ET sequence|legend=0| 2, 13, 15, 32c, 47bc }}
@@ Line 566: / Line 586: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~10/7 = 637.871
+* WE: ~2 = 1195.0786{{c}}, ~10/7 = 635.0197{{c}}
-* POTE: ~2 = 1200.000, ~10/7 = 637.635
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 637.6691{{c}}
 {{Optimal ET sequence|legend=0| 15, 17c, 32cf }}
@@ Line 581: / Line 601: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~10/7 = 637.797
+* WE: ~2 = 1196.0245{{c}}, ~10/7 = 634.6516{{c}}
-* POTE: ~2 = 1200.000, ~10/7 = 636.761
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 636.9528{{c}}
 {{Optimal ET sequence|legend=0| 2f, 15f, 17c }}
@@ Line 590: / Line 610: @@
 == Fervor ==
 : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Fervor]].''
+Fervor tempers out 9704/9375 and may be described as {{nowrap| 25 & 27 }}. It splits the 6th harmonic into five generators of ~10/7; its ploidacot is beta-pentacot. 27edo is about as accurate as it can be tuned.
 [[Subgroup]]: 2.3.5.7
@@ Line 595: / Line 617: @@
 [[Comma list]]: 64/63, 9604/9375
-{{Mapping|legend=1| 1 4 -2 -2 | 0 -5 9 10 }}
+{{Mapping|legend=1| 1 -1 7 8 | 0 5 -9 -10 }}
-: mapping generators: ~2, ~7/5
+: mapping generators: ~2, ~10/7
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000, ~7/5 = 577.353
+* [[WE]]: ~2 = 1196.2742{{c}}, ~10/7 = 620.2918{{c}}
-: [[error map]]: {{val| 0.000 +11.278 +9.867 +4.709 }}
+: [[error map]]: {{val| -3.726 +3.230 +4.980 -1.550 }}
-* [[POTE]]: ~2 = 1200.000, ~7/5 = 577.776
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 622.3179{{c}}
-: error map: {{val| 0.000 +9.163 +13.673 +8.937 }}
+: error map: {{val| 0.000 +9.634 +12.826 +7.996 }}
 {{Optimal ET sequence|legend=1| 2, 25, 27 }}
@@ Line 614: / Line 636: @@
 Comma list: 56/55, 64/63, 1350/1331
-Mapping: {{mapping| 1 4 -2 -2 3 | 0 -5 9 10 1 }}
+Mapping: {{mapping| 1 -1 7 8 4 | 0 5 -9 -10 -1 }}
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~7/5 = 577.296
+* WE: ~2 = 1195.4148{{c}}, ~10/7 = 619.7729{{c}}
-* POTE: ~2 = 1200.000, ~7/5 = 577.850
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 622.2525{{c}}
 {{Optimal ET sequence|legend=0| 2, 25e, 27e }}
@@ Line 629: / Line 651: @@
 Comma list: 56/55, 64/63, 78/77, 507/500
-Mapping: {{mapping| 1 4 -2 -2 3 -4 | 0 -5 9 10 1 16 }}
+Mapping: {{mapping| 1 -1 7 8 4 12 | 0 5 -9 -10 -1 -16 }}
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~7/5 = 577.374
+* WE: ~2 = 1195.6284{{c}}, ~10/7 = 619.6738{{c}}
-* POTE: ~2 = 1200.000, ~7/5 = 578.060
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 622.0631{{c}}
 {{Optimal ET sequence|legend=0| 2f, 27e }}
@@ Line 643: / Line 665: @@
 {{See also| Dual-fifth temperaments #Dual-3 Sixix }}
-Sixix is related to the [[kleismic family]] in a way similar to the one between [[meantone]] and [[mavila]]. In both cases the generator is nominally a 6/5 and the complexity to generate major and minor chords is the same, but in sixix it is tuned extremely sharply, to the point where the 3rd and 5th harmonics are reached by going down instead of up, inverting the logic of chord construction.
+Sixix tempers out 3125/2916 and may be described as {{nowrap| 25 & 32 }}. It is related to the [[kleismic family]] in a way similar to the one between [[meantone]] and [[mavila]]. In both cases the generator is nominally a 6/5 and the complexity to generate major and minor chords is the same, but in sixix it is tuned extremely sharply, to the point where the 3rd and 5th harmonics are reached by going down instead of up, inverting the logic of chord construction. Its ploidacot is gamma-pentacot.
 [[Subgroup]]: 2.3.5.7
@@ Line 652: / Line 674: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000, ~6/5 = 337.519
+* [[WE]]: ~2 = 1198.9028{{c}}, ~6/5 = 337.1334{{c}}
-: [[error map]]: {{val| 0.000 +10.449 -11.429 +6.366 }}
+: [[error map]]: {{val| -1.097 +9.086 -13.503 +2.508 }}
-* [[POTE]]: ~2 = 1200.000, ~6/5 = 337.442
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 337.4588{{c}}
-: error map: {{val| 0.000 +10.835 -10.965 +5.594 }}
+: error map: {{val| 0.000 +10.751 -11.066 +5.762 }}
 {{Optimal ET sequence|legend=1| 7, 18d, 25, 32 }}
@@ Line 669: / Line 691: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~6/5 = 337.749
+* WE: ~2 = 1198.5480{{c}}, ~6/5 = 337.1557{{c}}
-* POTE: ~2 = 1200.000, ~6/5 = 337.564
+* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 337.6000{{c}}
 {{Optimal ET sequence|legend=0| 7, 25e, 32 }}
@@ Line 684: / Line 706: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~6/5 = 337.793
+* WE: ~2 = 1197.7111{{c}}, ~6/5 = 336.8391{{c}}
-* POTE: ~2 = 1200.000, ~6/5 = 337.483
+* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 337.5336{{c}}
 {{Optimal ET sequence|legend=0| 7, 25e, 32f }}
@@ Line 699: / Line 721: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~6/5 = 337.629
+* WE: ~2 = 1197.7807{{c}}, ~6/5 = 336.8884{{c}}
-* POTE: ~2 = 1200.000, ~6/5 = 337.513
+* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 337.5279{{c}}
 {{Optimal ET sequence|legend=0| 7, 25e, 32f }}
@@ Line 708: / Line 730: @@
 [[Category:Archytas clan| ]] <!-- main article -->
 [[Category:Temperament clans]]
-[[Category:Rank 2]]
+[[Category:Catalogs of rank-2 temperaments]]