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. [[28/27]] gives blackwood with a 1/5-octave period. Finally, [[15625/15552]] gives catalan, splitting the twelfth in six.

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~~]]

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

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

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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~~{{Multival|legend=1| 1 9 -2 12 -6 -30 }}~~

[[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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~~{{Multival|legend=1| 1 -13 -2 -23 -6 32 }}~~

[[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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~~{{Multival|legend=1| 1 14 -2 20 -6 -44 }}~~

[[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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~~{{Multival|legend=1| 1 -18 -2 -31 -6 46 }}~~

[[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 }}

~~{{Multival|legend=1| 1 -8 -2 -15 -6 18~~ }}

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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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~~{{Multival|legend=1| 2 -9 -4 -19 -12 16 }}~~

[[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 512:

Line 516:

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 527:

Line 531:

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 535:

Line 539:

== 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 544:

Line 551:

: mapping generators: ~2, ~10/7

~~{{Multival|legend=1| 3 -5 -6 -15 -18 0 }}~~

[[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 565:

Line 570:

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 580:

Line 585:

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 595:

Line 600:

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 604:

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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 609:

Line 616:

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

: mapping generators: ~2, ~7/5

: mapping generators: ~2, ~10/7

~~{{Multival|legend=1| 5 -9 -10 -26 -30 2 }}~~

[[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 630:

Line 635:

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 645:

Line 650:

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 659:

Line 664:

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 666:

Line 671:

~~{{Multival|legend=1| 5 6 -10 -2 -30 -40 }}~~

[[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 687:

Line 690:

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 702:

Line 705:

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 717:

Line 720:

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 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. [[28/27]] gives blackwood with a 1/5-octave period. Finally, [[15625/15552]] gives catalan, splitting the twelfth in six.
 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]]
+* [[Blackwood]] (+28/27) → [[Blackwood family #Blackwood|Blackwood family]]
 * ''[[Catalan]]'' (+15625/15552) → [[Kleismic family #Catalan|Kleismic family]]
 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 68: @@
 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 83: @@
 ==== 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 107: @@
 : ''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 118: / Line 116: @@
 {{Mapping|legend=1| 1 0 -12 6 | 0 1 9 -2 }}
-{{Multival|legend=1| 1 9 -2 12 -6 -30 }}
 [[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 132: / Line 128: @@
 === 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 141: / Line 135: @@
 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 156: / Line 150: @@
 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 171: / Line 180: @@
 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 179: / Line 188: @@
 === 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 188: / Line 197: @@
 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 203: / Line 212: @@
 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 211: / Line 220: @@
 == 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 229: @@
 {{Mapping|legend=1| 1 0 23 6 | 0 1 -13 -2 }}
-{{Multival|legend=1| 1 -13 -2 -23 -6 32 }}
 [[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 232: / Line 241: @@
 === 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 241: / Line 248: @@
 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 256: / Line 263: @@
 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 271: / Line 278: @@
 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 279: / Line 286: @@
 == 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 288: / Line 296: @@
 {{Mapping|legend=1| 1 0 -20 6 | 0 1 14 -2 }}
-{{Multival|legend=1| 1 14 -2 20 -6 -44 }}
 [[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 309: / Line 315: @@
 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 324: / Line 330: @@
 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 339: / Line 345: @@
 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 354: / Line 360: @@
 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 362: / Line 368: @@
 == 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 369: / Line 375: @@
 {{Mapping|legend=1| 1 0 31 6 | 0 1 -18 -2 }}
-{{Multival|legend=1| 1 -18 -2 -31 -6 46 }}
 [[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 385: / Line 389: @@
 {{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 394: / Line 398: @@
 [[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 }}
-{{Multival|legend=1| 1 -8 -2 -15 -6 18 }}
 {{Optimal ET sequence|legend=1| 5c, 7c, 12 }}
@@ Line 413: / Line 415: @@
 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 422: / Line 424: @@
 == 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 428: / Line 434: @@
 {{Mapping|legend=1| 1 1 5 4 | 0 2 -9 -4 }}
-{{Multival|legend=1| 2 -9 -4 -19 -12 16 }}
 [[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 452: / Line 456: @@
 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 467: / Line 471: @@
 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 482: / Line 486: @@
 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 497: / Line 501: @@
 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 512: / Line 516: @@
 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 527: / Line 531: @@
 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 535: / Line 539: @@
 == 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 544: / Line 551: @@
 : mapping generators: ~2, ~10/7
-{{Multival|legend=1| 3 -5 -6 -15 -18 0 }}
 [[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 565: / Line 570: @@
 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 580: / Line 585: @@
 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 595: / Line 600: @@
 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 604: / Line 609: @@
 == 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 609: / Line 616: @@
 [[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
-{{Multival|legend=1| 5 -9 -10 -26 -30 2 }}
 [[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 630: / Line 635: @@
 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 645: / Line 650: @@
 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 659: / Line 664: @@
 {{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 666: / Line 671: @@
 {{Mapping|legend=1| 1 3 4 0 | 0 -5 -6 10 }}
-{{Multival|legend=1| 5 6 -10 -2 -30 -40 }}
 [[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 687: / Line 690: @@
 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 702: / Line 705: @@
 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 717: / Line 720: @@
 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 }}