Very high accuracy temperaments: Difference between revisions

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Below are listed some very high accuracy temperaments ([[Tenney-Euclidean temperament measures|TE error]] ~~<~~ 0.005 cents/octave).

Below are listed some very high accuracy temperaments (Breed's [[Tenney-Euclidean temperament measures|TE error]] < 0.005 cents/octave).

= Rank-2 temperaments =

== Kwazy ==

Kwazy (118 &~~amp;~~ 612) tempers out the kwazy comma, {{monzo| -53 10 16 }}. 7-limit extensions of the kwazy temperament include [[~~Hemimage~~ temperaments #Bisupermajor|bisupermajor]] and [[~~Marvel temperaments~~ #~~Gwazy~~|~~gwazy~~]].

Kwazy ({{nowrap| 118 & 612 }}) tempers out the [[kwazy comma]], {{monzo| -53 10 16 }}. 7-limit extensions of the kwazy temperament include [[marvel temperaments #Gwazy|gwazy]], [[hemimage temperaments #Bisupermajor|bisupermajor]], and [[ragismic microtemperaments #Crazy|crazy]].

[[Subgroup]]: 2.3.5

[[Comma list]]: {{monzo| -53 10 16 }} ~~= 9010162353515625 / 9007199254740992~~

[[Comma list]]: {{monzo| -53 10 16 }}

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: mapping generators: ~94921875/67108864, ~1125/1024

[[Optimal tuning]] ([[CTE]]): ~94921875/67108864 = ~~1\2~~, ~1125/1024 = 162.~~7433~~

[[Optimal tuning]]s:

* [[CTE]]: ~94921875/67108864 = 600.000000, ~1125/1024 = 162.743279

* [[POTE]]: ~94921875/67108864 = 600.000000, ~1125/1024 = 162.742626

{{Optimal ET sequence|legend=1| 22, 74, 96, 118, 376, 494, 612, 1342, 3296, 4638, 7934 }}

[[Badness]]: 0.~~014091~~

[[Badness]] (Sintel): 0.331

== Astro ==

Astro temperament tempers out the astro comma, {{monzo| 91 -12 -31 }}. 7-limit extensions of the astro temperament include [[Horwell temperaments #Kastro|kastro]].

Astro temperament tempers out the [[astro comma]], {{monzo| 91 -12 -31 }}. 7-limit extensions of the astro temperament include [[Horwell temperaments #Kastro|kastro]].

[[Subgroup]]: 2.3.5

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: mapping generators: ~2, ~{{monzo| -38 5 13 }}

[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~{{monzo| -38 5 13 }} = 132.~~1949~~

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000000, ~{{monzo| -38 5 13 }} = 132.194857

* [[POTE]]: ~2 = 1200.000000, ~{{monzo| -38 5 13 }} = 132.194668

{{Optimal ET sequence|legend=1| 9, 109, 118, 699, 817, 935, 1053, 1171, 13934, 15105, 16276, 17447, 18618, 19789, 20960, 22131, 23302, 24473, 25644, 26815, 27986c }}

{{Optimal ET sequence|legend=1| 9, …, 109, 118, 699, 817, 935, 1053, 1171, 13934, 15105, 16276, 17447, 18618, 19789, 20960, 22131, 23302, 24473, 25644, 26815, 27986c }}

[[Badness]]: 0.~~062778~~

[[Badness]] (Sintel): 1.47

== Gaster ==

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: mapping generators: ~2, ~{{monzo| 19 -19 5 }}

[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~{{monzo| 19 -19 5 }} = 594.~~6345~~

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000000, ~{{monzo| 19 -19 5 }} = 594.634456

* [[POTE]]: ~2 = 1200.000000, ~{{monzo| 19 -19 5 }} = 594.634565

{{Optimal ET sequence|legend=1| 111, 224, 335, 559, 1342, 1901, 3243, 8387, 11630 }}

[[Badness]]: 0.~~088530~~

[[Badness]] (Sintel): 2.08

== Whoosh ==

Whoosh (152 &~~amp;~~ 289) tempers out the whoosh comma, {{monzo| 37 25 -33 }}. 7-limit extensions of the whoosh temperament include [[Porwell temperaments #Whoops|whoops]].

Whoosh ({{nowrap| 152 & 289 }}) tempers out the [[whoosh comma]], {{monzo| 37 25 -33 }}. 7-limit extensions of the whoosh temperament include [[Porwell temperaments #Whoops|whoops]].

[[Subgroup]]: 2.3.5

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: mapping generators: ~2, ~864/625

[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~864/625 = 560.546826

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000000, ~864/625 = 560.546952

* [[POTE]]: ~2 = 1200.000000, ~864/625 = 560.546826

{{Optimal ET sequence|legend=1| 15, 122, 137, 152, 289, 441, 730, 1171, 1901, 3072, 4243, 7315, 25017, 32332, 39647c }}

{{Optimal ET sequence|legend=1| 15, …, 122, 137, 152, 289, 441, 730, 1171, 1901, 3072, 4243, 7315, 25017, 32332, 39647c }}

[[Badness]]: 0.~~025653~~

[[Badness]] (Sintel): 0.602

== Monzismic ==

Monzismic (53 &~~amp;~~ 612) tempers out the [[monzisma]], {{monzo| 54 -37 2 }}. For its 7-limit extension, see [[Ragismic microtemperaments #Monzismic]].

Monzismic ({{nowrap| 53 & 612 }}) tempers out the [[monzisma]], {{monzo| 54 -37 2 }}. For its 7-limit extension, see [[Ragismic microtemperaments #Monzismic]].

[[Subgroup]]: 2.3.5

[[Comma list]]: {{monzo| 54 -37 2 }} ~~= 450359962737049600 / 450283905890997363~~

[[Comma list]]: {{monzo| 54 -37 2 }}

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: mapping generators: ~2, ~{{monzo| 27 -18 1 }}

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~{{monzo| 27 -18 1 }} = 950.~~9814~~

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000000, ~{{monzo| 27 -18 1 }} = 950.981427

* [[POTE]]: ~2 = 1200.000000, ~{{monzo| 27 -18 1 }} = 950.981594

{{Optimal ET sequence|legend=1| 53, 347, 400, 453, 506, 559, 612, 1171, 1783, 4737, 6520 }}

[[Badness]]: 0.~~010391~~

[[Badness]] (Sintel): 0.244

== Egads ==

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: mapping generators: ~2, ~6/5

[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~6/5 = 315.~~6479~~

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000000, ~6/5 = 315.647899

* [[POTE]]: ~2 = 1200.000000, ~6/5 = 315.647919

{{Optimal ET sequence|legend=1| 19, 365, 384, 403, 422, 441, 901, 1342, 1783, 3125, 4908, 45955, 50863, 55771, 60679, 65587, 70495, 75403, 80311, 85219, 90127 }}

{{Optimal ET sequence|legend=1| 19, …, 365, 384, 403, 422, 441, 901, 1342, 1783, 3125, 4908, 45955, 50863, 55771, 60679, 65587, 70495, 75403, 80311, 85219, 90127 }}

[[Badness]]: 0.~~041819~~

[[Badness]] (Sintel): 0.981

=== Hemiegads ===

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Mapping: {{mapping| 1 15 16 -16 | 0 -102 -104 143 }}

Optimal ~~tuning (~~CTE): ~2 = ~~1\1~~, ~36756909/33554432 = 157.~~8240~~

Optimal tunings:

* CTE: ~2 = 1200.000000, ~36756909/33554432 = 157.823952

* CWE: ~2 = 1200.000000, ~36756909/33554432 = 157.823954

{{Optimal ET sequence|legend=1| 38, 403, 441, 1802, 2243, 2684, 3125, 6691, 9816, 16507, 75844, 125365c }}

{{Optimal ET sequence|legend=0| 38, 403, 441, 1802, 2243, 2684, 3125, 6691, 9816, 16507, 75844, 125365c }}

Badness: 0.~~0124~~

Badness (Sintel): 0.313

== Fortune ==

Fortune tempers out the fortune comma, {{monzo| -107 47 14 }}. It can be described as 612 &~~amp;~~ 2513 temperament, which tempers out 78125000/78121827 (euzenius comma) in the 7-limit; 151263/151250, 21437500/21434787, and 369140625/369098752 in the 11-limit.

Fortune tempers out the [[fortune comma]], {{monzo| -107 47 14 }}. It can be described as {{nowrap| 612 & 2513 }} temperament, which tempers out 78125000/78121827 ([[euzenius comma]]) in the 7-limit; 151263/151250, 21437500/21434787, and 369140625/369098752 in the 11-limit.

[[Subgroup]]: 2.3.5

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: mapping generators: ~2, 7381125/4194304

Optimal tuning (CTE): ~2 = ~~1\1~~, ~8388608/7381125 = 221.~~5679~~

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000000, ~8388608/7381125 = 221.567861

* [[POTE]]: ~2 = 1200.000000, ~8388608/7381125 = 221.567899

{{Optimal ET sequence|legend=1| 65, 352, 417, 482, 547, 612, 1901, 2513, 5638, 8151, 18815, 45781, 64596, 110377, 174973bc }}

[[Badness]]: 0.~~027876~~

[[Badness]] (Sintel): 0.654

=== 7-limit ===

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Mapping: {{mapping| 1 13 -36 -263 | 0 -14 47 326 }}

Optimal ~~tuning (~~CTE): ~2 = ~~1\1~~, ~8388608/7381125 = 221.~~5680~~

Optimal tunings:

* CTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568013

* POTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568031

{{Optimal ET sequence|legend=1| 612, 1901, 2513, 3125, 6862, 9987, 13112, 36211, 49323 }}

{{Optimal ET sequence|legend=0| 612, 1901, 2513, 3125, 6862, 9987, 13112, 36211, 49323 }}

Badness: 0.~~023704~~

Badness (Sintel): 0.600

=== 11-limit ===

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Mapping: {{mapping| 1 13 -36 -263 -573 | 0 -14 47 326 707 }}

Optimal ~~tuning (~~CTE): ~2 = ~~1\1~~, ~8388608/7381125 = 221.~~5681~~

Optimal tunings:

* CTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568116

* POTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568139

{{Optimal ET sequence|legend=1| 612, 2513, 3125, 3737, 8086, 19909d }}

Badness: 0.~~036641~~

Badness (Sintel): 1.21

== Senior ==

Senior (171 &~~amp;~~ 1171) tempers out the senior comma, {{monzo| -17 62 -35 }}. 7-limit extensions of the senior temperament include [[Ragismic microtemperaments #Seniority|seniority]].

Senior ({{nowrap| 171 & 1171 }}) tempers out the [[senior comma]], {{monzo| -17 62 -35 }}. 7-limit extensions of the senior temperament include [[Ragismic microtemperaments #Seniority|seniority]].

[[Subgroup]]: 2.3.5

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: mapping generators: ~2, ~{{monzo| -6 23 -13 }}

[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~{{monzo| -6 23 -13 }} = 322.~~8013~~

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000000, ~{{monzo| -6 23 -13 }} = 322.801349

* [[POTE]]: ~2 = 1200.000000, ~{{monzo| -6 23 -13 }} = 322.801358

{{Optimal ET sequence|legend=1| 171, 658, 829, 1000, 1171, 2513, 6197, 39695, 45892, 52089, 58286, 64483, 70680 }}

{{Optimal ET sequence|legend=1| 26, …, 145, 171, 658, 829, 1000, 1171, 2513, 6197, 39695, 45892, 52089, 58286, 64483, 70680 }}

[[Badness]]: 0.~~021220~~

[[Badness]] (Sintel): 0.498

== Gross ==

Gross (118 &~~amp;~~ 1783) tempers out the gross comma, {{monzo| 144 -22 -47 }}, by which a stack of 22 [[3/1|3rd harmonics]] and 47 [[5/1|5th harmonics]] falls short of 144 (gross) octaves.

Gross ({{nowrap| 118 & 1783 }}) tempers out the gross comma, {{monzo| 144 -22 -47 }}, by which a stack of 22 [[3/1|3rd harmonics]] and 47 [[5/1|5th harmonics]] falls short of 144 (gross) octaves.

[[Subgroup]]: 2.3.5

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: mapping generators: ~2, ~{{monzo| -45 7 15 }}

[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~{{monzo| 46 -7 -15 }} = 91.~~5310~~

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000000, ~{{monzo| 46 -7 -15 }} = 91.530979

* [[POTE]]: ~2 = 1200.000000, ~{{monzo| 46 -7 -15 }} = 91.531001

{{Optimal ET sequence|legend=1| ~~13, 105,~~ 118, 957, 1075, 1193, 1311, 1429, 1547, 1665, 1783, 3684, 5467, 36486, 41953, 47420, 52887, 63821, 69288, 74755, 144043c, 218798c }}

{{Optimal ET sequence|legend=1| 118, 957, 1075, 1193, 1311, 1429, 1547, 1665, 1783, 3684, 5467, 36486, 41953, 47420, 52887, 63821, 69288, 74755, 144043c, 218798c }}

[[Badness]]: 0.~~046315~~

[[Badness]] (Sintel): 1.09

; Music

* ''Gross temperament EP'' (2023) by [[User:Francium|Francium]] – [https://open.spotify.com/album/02Fz6IIJ2x9k7bEvFylZ2A Spotify] | [https://francium223.bandcamp.com/album/gross-temperament-ep Bandcamp] | [https://youtube.com/playlist?list=PLLZE7hMjEXRZy_JWYbZxbsxPsXahiEJA2&si=RttlCFpkeN4Rl7Tj YouTube] – 2-piece extended play

== Quectismic ==

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: mapping generators: ~2, ~3

[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~3/2 = 701.~~9553~~

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000000, ~3/2 = 701.955310

* [[CWE]]: ~2 = 1200.000000, ~3/2 = 701.955310

{{Optimal ET sequence|legend=1| 306, 359c, 665, 2301, 2966, 3631, 4296, 46591, 50887, 55183, 59479, 63775, 68071, 72367, 76663, 80959, 85255, 89551 }}

[[Badness]]: 0.~~372~~

[[Badness]] (Sintel): 8.74

=== Nanoquectismic ===

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Mapping: {{mapping| 1 0 -554 109 | 0 1 351 -67 }}

Optimal ~~tuning (~~CTE): ~2 = ~~1\1~~, ~3/2 = 701.~~955~~

Optimal tunings:

* CTE: ~2 = 1200.000000, ~3/2 = 701.955371

* CWE: ~2 = 1200.000000, ~3/2 = 701.955457

Badness: 0.~~604~~

Badness (Sintel): 15.3

=== Conanoquectismic ===

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Mapping: {{mapping| 1 0 -554 -945 | 0 1 351 598 }}

Optimal ~~tuning (~~CTE): ~2 = ~~1\1~~, ~3/2 = 701.~~9548~~

Optimal tunings:

* CTE: ~2 = 1200.000000, ~3/2 = 701.954810

* CWE: ~2 = 1200.000000, ~3/2 = 701.954771

Badness: 2.17

Badness (Sintel): 55.0

== Counterquectismic ==

[[Subgroup]]: 2.3.5

[[Comma list]]: {{monzo| -500 314 1 }}

: mapping generators: ~2, ~3

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000000, ~3/2 = 701.954415

* [[CWE]]: ~2 = 1200.000000, ~3/2 = 701.954416

{{Optimal ET sequence|legend=1| 306c, 359, 665, 2354, 3019, 3684, 11717, 15401, 19085, 34486 }}

[[Badness]] (Sintel): 12.0

== Raider ==

[[Subgroup]]: 2.3.5

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: mapping generators: ~2, ~6561/4000

[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~8000/6561 = 343.~~2961~~

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000000, ~8000/6561 = 343.296094

* [[POTE]]: ~2 = 1200.000000, ~8000/6561 = 343.296098

{{Optimal ET sequence|legend=1| 388, 783, 1171, 1954, 3125, 4296, 5467, 7421, 9763, 14059, 18355, 22651, 26947, 31243, 35539, 66782, 102321, 137860 }}

[[Badness]]: 0.~~012867~~

[[Badness]] (Sintel): 0.302

== Pirate ==

[[Subgroup]]: 2.3.5

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: ~~mapping~~ generators: ~2, ~{{monzo| -23 -4 13 }}

: Mapping generators: ~2, ~{{monzo| -23 -4 13 }}

[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~{{monzo| 24 4 -13 }} = 185.~~7542~~

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000000, ~{{monzo| 24 4 -13 }} = 185.754186

* [[POTE]]: ~2 = 1200.000000, ~{{monzo| 24 4 -13 }} = 185.754179

{{Optimal ET sequence|legend=1| 84, 239, 323, 730, 1783, 2513, 4296, 15401, 19697, 23993, 52282, 76275, 128557, 204832 … }}

[[Badness]]: 0.~~005656~~

[[Badness]] (Sintel): 0.133

== Atomic ==

Atomic extensions discussed elsewhere include [[minutes]] and [[~~The Flashmob~~ #Hafnium|hafnium]].

Atomic observes the [[schisma]], and the 3/2 is one schisma sharp of its [[12edo]] value. In atomic, since twelve fifths are sharp of seven octaves by twelve schismas, the [[Pythagorean comma]] is twelve schismas, and hence [[81/80]], the Didymus comma, is eleven schismas. In fact eleven schismas is sharp of 81/80, and twelve schismas of the Pythaorean comma, by the microscopic interval of the atom, which atomic tempers out. Extremely accurate.

Atomic extensions discussed elsewhere include [[minutes]] and [[72nd-octave temperaments#Hafnium|hafnium]].

[[Subgroup]]: 2.3.5

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: mapping generators: ~{{monzo| -67 35 5 }}, ~3

[[Optimal tuning]] ([[CTE]]): ~{{monzo| -67 35 5 }} = ~~1\12~~, ~3/2 = 701.~~9552~~ (or ~32805/32768 = 1.~~9552~~)

[[Optimal tuning]]s:

* [[CTE]]: ~{{monzo| -67 35 5 }} = 100.000000, ~3/2 = 701.955176 (~32805/32768 = 1.955176)

* [[POTE]]: ~{{monzo| -67 35 5 }} = 100.000000, ~3/2 = 701.955162 (~32805/32768 = 1.955162)

{{Optimal ET sequence|legend=1| 12, …, 576, 588, 600, 612, 2460, 3072, 3684, 4296, 12276, 16572, 20868, 25164, 46032 }}

[[Badness]]: 0.~~003803~~

[[Badness]] (Sintel): 0.0892

=== 7-limit ===

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Mapping: {{mapping| 12 0 161 338 | 0 1 -7 -16 }}

Optimal ~~tuning~~ (~~CTE~~): ~30375/28672 = ~~1\12~~, ~3/2 = 701.~~9499~~ (or ~32805/32768 = 1.~~9499~~)

Optimal tunings:

* CTE: ~30375/28672 = 100.000000, ~3/2 = 701.949917 (or ~32805/32768 = 1.949917)

* POTE: ~30375/28672 = 100.000000, ~3/2 = 701.949608 (or ~32805/32768 = 1.949608)

{{Optimal ET sequence|legend=1| 12, …, 600, 612, 1236, 1848, 4308, 10464, 14772, 25236c, 40008ccd }}

{{Optimal ET sequence|legend=0| 12, …, 600, 612, 1236, 1848, 4308, 10464, 14772, 25236c, 40008ccd }}

Badness: 0.~~045818~~

Badness (Sintel): 1.16

=== 11-limit ===

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Mapping: {{mapping| 12 0 161 338 517 | 0 1 -7 -16 -25 }}

Optimal ~~tuning~~ (~~CTE~~): ~30375/28672 = ~~1\12~~, ~3/2 = 701.~~9485~~ (or ~32805/32768 = 1.~~9485~~)

Optimal tunings:

* CTE: ~30375/28672 = 100.000000, ~3/2 = 701.948456 (or ~32805/32768 = 1.948456)

* POTE: ~30375/28672 = 100.000000, ~3/2 = 701.947988 (or ~32805/32768 = 1.947988)

Badness: 0.~~016029~~

Badness (Sintel): 0.530

== ~~Niobium~~ ==

== Revopentic (2.3.7) ==

~~Niobium can be viewed as the 41st-octave counterpart of atomic.~~

[[Subgroup]]: 2.3.5

Subgroup: 2.3.7

[[Comma list]]: ~~{{monzo| -875 492 41 }}~~

Comma list: 11399736556781568/11398895185373143

: mapping generators: ~~~{{monzo| -64 36 3 }}~~, ~3

: mapping generators: ~2, ~24576/16807

[[Optimal tuning]] ([[CTE]]): ~~~{{monzo| -64 36 3 }}~~ = ~~1\41~~, ~3/2 = ~~701~~.~~9536~~

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000000, ~24576/16807 = 657.791865

* [[CWE]]: ~2 = 1200.000000, ~24576/16807 = 657.791796

{{Optimal ET sequence|legend=1| 41, …, ~~2378~~, ~~2419~~, ~~2460~~, ~~4961~~, ~~7421~~, ~~17302~~, ~~24723~~, ~~66748~~, ~~91471~~, ~~116194~~ }}

{{Optimal ET sequence|legend=1| 31, 73, 104, 135, 436, 571, 706, 1277, 8233, 9510, 10787, 12064, 13341, 14618, 15895, 33067, 48962, 113819d, 162781d, … }}

[[Badness]]: 5.57

[[Badness]] (Sintel): 0.0704

== Revopent ==

=== Revopent ===

~~Described~~ as the 1848 & 3125 temperament~~, revopent is named because the year 1848 is known for revolutions while 3125 is 5 to the 5~~.

Revopent can be described as the {{nowrap| 1848 & 3125 }} temperament.

Subgroup: 2.3.5.7

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Mapping: {{mapping| 1 12 -155 5 | 0 -19 287 -4 }}

Optimal ~~tuning (~~CTE): ~24576/16807 = 657.~~792~~

Optimal tunings:

* CTE: ~2 = 1200.000000, ~24576/16807 = 657.792032

* CWE: ~2 = 1200.000000, ~24576/16807 = 657.792032

{{Optimal ET sequence|legend=1| 135, 436c, 571, 1277, 1848, 3125, 8098, 11223, 25571, 36794, 121605d }}

{{Optimal ET sequence|legend=0| 135, 436c, 571, 1277, 1848, 3125, 8098, 11223, 25571, 36794, 121605d }}

Badness: 0.~~263~~

Badness (Sintel): 0.665

== ~~Francium~~ ==

== Nanic ==

~~Francium tempers out the [[euzenius comma]] and the 87-126/125 comma in the 7-limit, hereby dividing the octave into 87 parts.~~

Subgroup: 2.3.5.7

[[Subgroup]]: 2.3.7

Comma list: ~~78125000/78121827,~~ {{monzo| ~~152~~ -~~112~~ -~~41 43~~ }}

[[Comma list]]: {{monzo| 109 -67 -1 }}

~~Mapping:~~ {{~~mapping~~| 87 1 ~~-106 -406~~ | 0 ~~4 9 19~~ }}

: mapping generators: ~~~126/125~~, ~~~{{monzo| 37 -25 -12 11 }}~~

: sval mapping generators: ~2, ~3

Optimal tuning (CTE): ~~~126~~/~~125~~ = ~~1\87~~, ~~~{{monzo| 37 -25 -12 11 }}~~ = ~~472~~.~~043~~

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000000, ~3/2 = 701.957820

* [[POTE]]: ~2 = 1200.000000, ~3/2 = 701.957784

{{Optimal ET sequence|legend=1| ~~783~~, …, ~~8178~~, ~~8961~~, ~~9744~~, ~~10527~~, ~~20271~~, ~~30798~~ }}

{{Optimal ET sequence|legend=1| 53, 200, 253, 306, 665, 971, 1277, 6691, 7968, 9245, 10522, 11799, 13076, 40505, 53581, 66657, 79733 }}

Badness: 0.~~762~~

[[Badness]] (Sintel): 0.474

==~~= 11-limit =~~==

== Icarus ==

~~Subgroup: 2.3.5~~.7.11

This temperament is named after a very distant star. Curiously, the names of two even more distant stars coincide with named temperaments, those being [[godzilla]] and [[mothra]].

~~Comma list~~: ~~78125000/78121827, 199297406/199290375, {{monzo| 74 -17 -~~5 ~~-4 -~~7 }}

[[Subgroup]]: 3.5.7

~~Mapping~~: {{~~mapping~~| ~~87 1~~ -~~106~~ -~~406 1225 | 0 4 9 19 -27~~ }}

[[Comma list]]: {{monzo| -32 -64 71 }}

~~: mapping generators: ~126/125, ~~~{{~~monzo~~| 35 ~~1 -6~~ -3 -4 }}

Optimal tuning (CTE): ~~~126/125~~ = ~~1\87~~, ~{{monzo| ~~35 1 -6~~ -3 -4 }} = ~~472~~.~~043~~

[[Optimal tuning]]s:

* [[CTE]]: ~3 = 1901.955, ~{{monzo| 5 9 -10 }} = 898.340

* [[CWE]]: ~3 = 1901.955, ~{{monzo| 5 9 -10 }} = 898.340

{{Optimal ET sequence|~~legend=1~~| ~~783~~, ~~8178~~, ~~8961~~, ~~9744~~, ~~28449de~~, ~~38193bcde~~, ~~47937bcdee }}~~

~~Badness: 0.352~~

[[Badness]] (Sintel): 0.00493

~~== Nanic ==~~

~~{{See also| Nanisma }}~~

[[~~Subgroup]]: 2.3.7~~

~~[[Comma list]]: {{monzo| 109 -67 -1 }}~~

~~{{Mapping|legend=1| 1 0 109 | 0 1 -67 }}~~

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

~~[[Optimal tuning~~]] (~~[[POTE]]~~)~~: ~3/2 = 701.9578~~

~~{{Optimal ET sequence|legend=1| 53, 200, 253, 306, 665, 971, 1277, 6691, 7968, 9245, 10522, 11799, 13076, 40505, 53581, 66657, 79733 }}~~

~~[[Badness]]~~: 0.~~0138~~

= Rank-3 temperaments =

== Sasaquinbizo-atriyo (171 &~~amp;~~ 1106 &~~amp;~~ 3566) ==

== Sasaquinbizo-atriyo (171 & 1106 & 3566) ==

[[Subgroup]]: 2.3.5.7

[[Comma list]]: {{monzo| 3 -24 3 10 }} = 282475249000/282429536481

[[Comma list]]: {{monzo| 3 -24 3 10 }} (282475249000/282429536481)

[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9624, ~6561/3430 = 1122.9387

{{Optimal ET sequence|legend=1| 171, 764, 935, 1106, 1277, 2118, 2289, 2460, 3224, 3395, 3566, 26068, 26239, 29634, 29805, 33200, 33371, 36937, 40503, 44069 }}

[[Badness]]: 0.~~281 × 10-3~~

[[Badness]] (Sintel): 1.24

== Saquadtrizo-asepgu (171 &~~amp;~~ 2019 &~~amp;~~ 3566) ==

== Saquadtrizo-asepgu (171 & 2019 & 3566) ==

[[Subgroup]]: 2.3.5.7

[[Comma list]]: {{monzo| 0 -11 -7 12 }} = 13841287201/13839609375

[[Comma list]]: {{monzo| 0 -11 -7 12 }} (13841287201/13839609375)

~~{{Mapping|legend~~=~~1| 1 0 0 0 | 0 1 7 5 | 0 0 12 7 }}~~

[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9584, ~16807/10125 = 877.2825

{{Optimal ET sequence|legend=1| 171, 814, 985, 1034, 1205, 1376, 1547, 1718, 1848, 2019, 3224, 3395, 3566, 8980, 9151, 12717, 47131, 50697, 59848d, 63414d, 76131d }}

[[Badness]]: 0.~~135 × 10-3~~

[[Badness]] (Sintel): 0.595

== Laquinzo-aquadquadgu (171 &~~amp;~~ 441 &~~amp;~~ 4973) ==

== Laquinzo-aquadquadgu (171 & 441 & 4973) ==

[[Subgroup]]: 2.3.5.7

[[Comma list]]: {{monzo| -7 19 -16 5 }} = 19534128475869/19531250000000

[[Comma list]]: {{monzo| -7 19 -16 5 }} (19534128475869/19531250000000)

[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9501, ~250/189 = 484.2956

{{Optimal ET sequence|legend=1| 171, 441, 612, 2696, 2795, 2867, 2966, 3137, 3308, 3407, 3479, 3578, 3749, 3920, 4091, 4190, 4361, 4532, 4703, 4802, 4973, 5144, 10117, 10558, 15531, 15702, 52079, 62637, 67781, 78339 }}

[[Badness]]: 0.~~297 × 10-3~~

[[Badness]] (Sintel): 1.31

== Laleruyo (171 &~~amp;~~ 1547 &~~amp;~~ 3125) ==

== Laleruyo (171 & 1547 & 3125) ==

[[Subgroup]]: 2.3.5.7

[[Comma list]]: {{monzo| -1 4 11 -11 }} = 3955078125/3954653486

[[Comma list]]: {{monzo| -1 4 11 -11 }} (3955078125/3954653486)

[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~375/343 = 154.3678, ~5/4 = 386.3070

{{Optimal ET sequence|legend=1| 171, 863, 894, 1034, 1065, 1205, 1236, 1376, 1407, 1547, 1578, 1718, 2612, 2783, 2954, 3125, 12329, 15454, 18579, 21704, 40283, 61987 }}

[[Badness]]: 0.~~114 × 10-3~~

[[Badness]] (Sintel): 0.501

== Starscape or Latritriru-ayo ==

Line 444:

Line 510:

[[Comma list]]: 645700815/645657712

[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9514, ~9/7 = 435.0709

{{Optimal ET sequence|legend=1| 171, 742, 764, 935, 1106, 1277, 1677, 1848, 2019, 2783, 2954, 3125, 8098, 11223, 25571, 33840, 36794, 45063, 48188, 59411, 70634 }}

[[Badness]]: 0.~~545 × 10-3~~

[[Badness]] (Sintel): 0.240

== Sepbizo-asegu (171 &~~amp;~~ 3566 &~~amp;~~ 4973) ==

== Sepbizo-asegu (171 & 3566 & 4973) ==

[[Subgroup]]: 2.3.5.7

[[Comma list]]: {{monzo| -3 2 -17 14 }} = 6104007655641/6103515625000

[[Comma list]]: {{monzo| -3 2 -17 14 }} (6104007655641/6103515625000)

[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9548, ~31250/16807 = 1073.8021

{{Optimal ET sequence|legend=1| 171, 894, 1065, 1236, 1407, 1578, 3053, 3224, 3395, 3566, 5144, 8368, 8539, 8710, 17249, 20815, 29525, 38064, 67589, 105653 }}

[[Badness]]: 0.~~223 × 10-3~~

[[Badness]] (Sintel): 0.982

== Euzenius or Sabiruquinyo ==

Line 468:

Line 538:

[[Comma list]]: 78125000/78121827

[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~6250/5103 = 350.9787, ~5/4 = 386.3099

{{Optimal ET sequence|legend=1| 171, 441, 612, 1730, 1901, 2072, 2171, 2342, 2513, 2684, 2783, 2954, 3125, 6520, 6691, 9816, 16336, 16507, 23027, 26152, 32843, 42659, 58995, 68811, 101654 }}

[[Badness]]: 0.~~205 × 10-3~~

[[Badness]] (Sintel): 0.0902

== Nommismic or Quinla-zoyoyo ==

Line 483:

Line 555:

[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~3/2 = 701.9516, ~5/4 = 386.3132

[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9516, ~5/4 = 386.3132

{{Optimal ET sequence|legend=1| 612, 1236, 1277, 1848, 2513, 3125, 6862, 8098, 8710, 11835, 14960, 26795, 195663b, }} …

[[Badness]]: 0.~~366 × 10-3~~

[[Badness]] (Sintel): 1.62

== Satwethezo-atritribigu (171 &~~amp;~~ 1547 &~~amp;~~ 4973) ==

== Satwethezo-atritribigu (171 & 1547 & 4973) ==

[[Subgroup]]: 2.3.5.7

[[Comma list]]: {{monzo| 1 -15 -18 23 }}

[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9551, ~56953125/40353607 = 596.5022

{{Optimal ET sequence|legend=1| 171, 863, 1034, 1205, 1376, 1547, 1718, 3255, 3426, 3597, 4460, 4631, 4802, 4973, 5144, 6520, 6691, 11664, 18355, 48374, 48545, 66900, 145464, }} …

[[Badness]]: 0.~~114 × 10-3~~

[[Badness]] (Sintel): 0.505

== Trisa-quinbiru-agu ~~(441 & 1848 & 3125)~~ ==

== Technologismic or Trisa-quinbiru-agu ==

[[Subgroup]]: 2.3.5.7

[[Comma list]]: {{monzo| 51 -13 -1 -10 }}

[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9553, ~63/32 = 1172.7374

{{Optimal ET sequence|legend=1| 441, 966, 1277, 1407, 1718, 1848, 2684, 3125, 6691, 9816, 11664, 14789, 18355, 33144, 51499, 124478, 175977, }} …

[[Badness]]: 0.~~263 × 10-3~~

[[Badness]] (Sintel): 0.116

== Quinbisa-quinbizo-alegu (1848 &~~amp;~~ 11664 &~~amp;~~ 21480) ==

== Quinbisa-quinbizo-alegu (1848 & 11664 & 21480) ==

[[Subgroup]]: 2.3.5.7

[[Comma list]]: {{monzo| 110 -71 -11 10 }}

[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.955, ~32805/28672 = 233.128

{{Optimal ET sequence|legend=1| 1848, 3737, 5585, 6079, 7927, 9816, 11664, 21480, 33144, 54624, 70025, 81689, 103169, }} …

[[Badness]]: 0.~~122 × 10-3~~

[[Badness]] (Sintel): 0.538

[[Category:Temperament collections]]

[[Category:Pages with mostly numerical content]]

@@ Line 1: / Line 1: @@
-Below are listed some very high accuracy temperaments ([[Tenney-Euclidean temperament measures|TE error]] &lt; 0.005 cents/octave).
+{{Technical data page}}
+Below are listed some very high accuracy temperaments (Breed's [[Tenney-Euclidean temperament measures|TE error]] < 0.005 cents/octave).
 = Rank-2 temperaments =
 == Kwazy ==
-Kwazy (118 &amp; 612) tempers out the kwazy comma, {{monzo| -53 10 16 }}. 7-limit extensions of the kwazy temperament include [[Hemimage temperaments #Bisupermajor|bisupermajor]] and [[Marvel temperaments #Gwazy|gwazy]].
+Kwazy ({{nowrap| 118 & 612 }}) tempers out the [[kwazy comma]], {{monzo| -53 10 16 }}. 7-limit extensions of the kwazy temperament include [[marvel temperaments #Gwazy|gwazy]],  [[hemimage temperaments #Bisupermajor|bisupermajor]], and [[ragismic microtemperaments #Crazy|crazy]].
 [[Subgroup]]: 2.3.5
-[[Comma list]]: {{monzo| -53 10 16 }} = 9010162353515625 / 9007199254740992
+[[Comma list]]: {{monzo| -53 10 16 }}
 {{Mapping|legend=1| 2 1 6 | 0 8 -5 }}
@@ Line 13: / Line 14: @@
 : mapping generators: ~94921875/67108864, ~1125/1024
-[[Optimal tuning]] ([[CTE]]): ~94921875/67108864 = 1\2, ~1125/1024 = 162.7433
+[[Optimal tuning]]s:
+* [[CTE]]: ~94921875/67108864 = 600.000000, ~1125/1024 = 162.743279
+* [[POTE]]: ~94921875/67108864 = 600.000000, ~1125/1024 = 162.742626
 {{Optimal ET sequence|legend=1| 22, 74, 96, 118, 376, 494, 612, 1342, 3296, 4638, 7934 }}
-[[Badness]]: 0.014091
+[[Badness]] (Sintel): 0.331
 == Astro ==
-Astro temperament tempers out the astro comma, {{monzo| 91 -12 -31 }}. 7-limit extensions of the astro temperament include [[Horwell temperaments #Kastro|kastro]].
+Astro temperament tempers out the [[astro comma]], {{monzo| 91 -12 -31 }}. 7-limit extensions of the astro temperament include [[Horwell temperaments #Kastro|kastro]].
 [[Subgroup]]: 2.3.5
@@ Line 30: / Line 33: @@
 : mapping generators: ~2, ~{{monzo| -38 5 13 }}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~{{monzo| -38 5 13 }} = 132.1949
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~{{monzo| -38 5 13 }} = 132.194857
+* [[POTE]]: ~2 = 1200.000000, ~{{monzo| -38 5 13 }} = 132.194668
-{{Optimal ET sequence|legend=1| 9, 109, 118, 699, 817, 935, 1053, 1171, 13934, 15105, 16276, 17447, 18618, 19789, 20960, 22131, 23302, 24473, 25644, 26815, 27986c }}
+{{Optimal ET sequence|legend=1| 9, …, 109, 118, 699, 817, 935, 1053, 1171, 13934, 15105, 16276, 17447, 18618, 19789, 20960, 22131, 23302, 24473, 25644, 26815, 27986c }}
-[[Badness]]: 0.062778
+[[Badness]] (Sintel): 1.47
 == Gaster ==
@@ Line 48: / Line 53: @@
 : mapping generators: ~2, ~{{monzo| 19 -19 5 }}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~{{monzo| 19 -19 5 }} = 594.6345
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~{{monzo| 19 -19 5 }} = 594.634456
+* [[POTE]]: ~2 = 1200.000000, ~{{monzo| 19 -19 5 }} = 594.634565
 {{Optimal ET sequence|legend=1| 111, 224, 335, 559, 1342, 1901, 3243, 8387, 11630 }}
-[[Badness]]: 0.088530
+[[Badness]] (Sintel): 2.08
 == Whoosh ==
-Whoosh (152 &amp; 289) tempers out the whoosh comma, {{monzo| 37 25 -33 }}. 7-limit extensions of the whoosh temperament include [[Porwell temperaments #Whoops|whoops]].
+Whoosh ({{nowrap| 152 & 289 }}) tempers out the [[whoosh comma]], {{monzo| 37 25 -33 }}. 7-limit extensions of the whoosh temperament include [[Porwell temperaments #Whoops|whoops]].
 [[Subgroup]]: 2.3.5
@@ Line 65: / Line 72: @@
 : mapping generators: ~2, ~864/625
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~864/625 = 560.546826
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~864/625 = 560.546952
+* [[POTE]]: ~2 = 1200.000000, ~864/625 = 560.546826
-{{Optimal ET sequence|legend=1| 15, 122, 137, 152, 289, 441, 730, 1171, 1901, 3072, 4243, 7315, 25017, 32332, 39647c }}
+{{Optimal ET sequence|legend=1| 15, …, 122, 137, 152, 289, 441, 730, 1171, 1901, 3072, 4243, 7315, 25017, 32332, 39647c }}
-[[Badness]]: 0.025653
+[[Badness]] (Sintel): 0.602
 == Monzismic ==
-Monzismic (53 &amp; 612) tempers out the [[monzisma]], {{monzo| 54 -37 2 }}. For its 7-limit extension, see [[Ragismic microtemperaments #Monzismic]].
+Monzismic ({{nowrap| 53 & 612 }}) tempers out the [[monzisma]], {{monzo| 54 -37 2 }}. For its 7-limit extension, see [[Ragismic microtemperaments #Monzismic]].
 [[Subgroup]]: 2.3.5
-[[Comma list]]: {{monzo| 54 -37 2 }} = 450359962737049600 / 450283905890997363
+[[Comma list]]: {{monzo| 54 -37 2 }}
 {{Mapping|legend=1| 1 0 -27 | 0 2 37 }}
@@ Line 82: / Line 91: @@
 : mapping generators: ~2, ~{{monzo| 27 -18 1 }}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~{{monzo| 27 -18 1 }} = 950.9814
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~{{monzo| 27 -18 1 }} = 950.981427
+* [[POTE]]: ~2 = 1200.000000, ~{{monzo| 27 -18 1 }} = 950.981594
 {{Optimal ET sequence|legend=1| 53, 347, 400, 453, 506, 559, 612, 1171, 1783, 4737, 6520 }}
-[[Badness]]: 0.010391
+[[Badness]] (Sintel): 0.244
 == Egads ==
@@ Line 97: / Line 108: @@
 : mapping generators: ~2, ~6/5
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~6/5 = 315.6479
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~6/5 = 315.647899
+* [[POTE]]: ~2 = 1200.000000, ~6/5 = 315.647919
-{{Optimal ET sequence|legend=1| 19, 365, 384, 403, 422, 441, 901, 1342, 1783, 3125, 4908, 45955, 50863, 55771, 60679, 65587, 70495, 75403, 80311, 85219, 90127 }}
+{{Optimal ET sequence|legend=1| 19, …, 365, 384, 403, 422, 441, 901, 1342, 1783, 3125, 4908, 45955, 50863, 55771, 60679, 65587, 70495, 75403, 80311, 85219, 90127 }}
-[[Badness]]: 0.041819
+[[Badness]] (Sintel): 0.981
 === Hemiegads ===
@@ Line 110: / Line 123: @@
 Mapping: {{mapping| 1 15 16 -16 | 0 -102 -104 143 }}
-Optimal tuning (CTE): ~2 = 1\1, ~36756909/33554432 = 157.8240
+Optimal tunings:
+* CTE: ~2 = 1200.000000, ~36756909/33554432 = 157.823952
+* CWE: ~2 = 1200.000000, ~36756909/33554432 = 157.823954
-{{Optimal ET sequence|legend=1| 38, 403, 441, 1802, 2243, 2684, 3125, 6691, 9816, 16507, 75844, 125365c }}
+{{Optimal ET sequence|legend=0| 38, 403, 441, 1802, 2243, 2684, 3125, 6691, 9816, 16507, 75844, 125365c }}
-Badness: 0.0124
+Badness (Sintel): 0.313
 == Fortune ==
-Fortune tempers out the fortune comma, {{monzo| -107 47 14 }}. It can be described as 612 &amp; 2513 temperament, which tempers out 78125000/78121827 (euzenius comma) in the 7-limit; 151263/151250, 21437500/21434787, and 369140625/369098752 in the 11-limit.
+Fortune tempers out the [[fortune comma]], {{monzo| -107 47 14 }}. It can be described as {{nowrap| 612 & 2513 }} temperament, which tempers out 78125000/78121827 ([[euzenius comma]]) in the 7-limit; 151263/151250, 21437500/21434787, and 369140625/369098752 in the 11-limit.
 [[Subgroup]]: 2.3.5
@@ Line 127: / Line 142: @@
 : mapping generators: ~2, 7381125/4194304
-Optimal tuning (CTE): ~2 = 1\1, ~8388608/7381125 = 221.5679
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~8388608/7381125 = 221.567861
+* [[POTE]]: ~2 = 1200.000000, ~8388608/7381125 = 221.567899
 {{Optimal ET sequence|legend=1| 65, 352, 417, 482, 547, 612, 1901, 2513, 5638, 8151, 18815, 45781, 64596, 110377, 174973bc }}
-[[Badness]]: 0.027876
+[[Badness]] (Sintel): 0.654
 === 7-limit ===
@@ Line 140: / Line 157: @@
 Mapping: {{mapping| 1 13 -36 -263 | 0 -14 47 326 }}
-Optimal tuning (CTE): ~2 = 1\1, ~8388608/7381125 = 221.5680
+Optimal tunings:
+* CTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568013
+* POTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568031
-{{Optimal ET sequence|legend=1| 612, 1901, 2513, 3125, 6862, 9987, 13112, 36211, 49323 }}
+{{Optimal ET sequence|legend=0| 612, 1901, 2513, 3125, 6862, 9987, 13112, 36211, 49323 }}
-Badness: 0.023704
+Badness (Sintel): 0.600
 === 11-limit ===
@@ Line 153: / Line 172: @@
 Mapping: {{mapping| 1 13 -36 -263 -573 | 0 -14 47 326 707 }}
-Optimal tuning (CTE): ~2 = 1\1, ~8388608/7381125 = 221.5681
+Optimal tunings:
+* CTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568116
+* POTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568139
 {{Optimal ET sequence|legend=1| 612, 2513, 3125, 3737, 8086, 19909d }}
-Badness: 0.036641
+Badness (Sintel): 1.21
 == Senior ==
-Senior (171 &amp; 1171) tempers out the senior comma, {{monzo| -17 62 -35 }}. 7-limit extensions of the senior temperament include [[Ragismic microtemperaments #Seniority|seniority]].
+Senior ({{nowrap| 171 & 1171 }}) tempers out the [[senior comma]], {{monzo| -17 62 -35 }}. 7-limit extensions of the senior temperament include [[Ragismic microtemperaments #Seniority|seniority]].
 [[Subgroup]]: 2.3.5
@@ Line 170: / Line 191: @@
 : mapping generators: ~2, ~{{monzo| -6 23 -13 }}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~{{monzo| -6 23 -13 }} = 322.8013
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~{{monzo| -6 23 -13 }} = 322.801349
+* [[POTE]]: ~2 = 1200.000000, ~{{monzo| -6 23 -13 }} = 322.801358
-{{Optimal ET sequence|legend=1| 171, 658, 829, 1000, 1171, 2513, 6197, 39695, 45892, 52089, 58286, 64483, 70680 }}
+{{Optimal ET sequence|legend=1| 26, …, 145, 171, 658, 829, 1000, 1171, 2513, 6197, 39695, 45892, 52089, 58286, 64483, 70680 }}
-[[Badness]]: 0.021220
+[[Badness]] (Sintel): 0.498
 == Gross ==
-Gross (118 &amp; 1783) tempers out the gross comma, {{monzo| 144 -22 -47 }}, by which a stack of 22 [[3/1|3rd harmonics]] and 47 [[5/1|5th harmonics]] falls short of 144 (gross) octaves.
+Gross ({{nowrap| 118 & 1783 }}) tempers out the gross comma, {{monzo| 144 -22 -47 }}, by which a stack of 22 [[3/1|3rd harmonics]] and 47 [[5/1|5th harmonics]] falls short of 144 (gross) octaves.
 [[Subgroup]]: 2.3.5
@@ Line 187: / Line 210: @@
 : mapping generators: ~2, ~{{monzo| -45 7 15 }}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~{{monzo| 46 -7 -15 }} = 91.5310
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~{{monzo| 46 -7 -15 }} = 91.530979
+* [[POTE]]: ~2 = 1200.000000, ~{{monzo| 46 -7 -15 }} = 91.531001
-{{Optimal ET sequence|legend=1| 13, 105, 118, 957, 1075, 1193, 1311, 1429, 1547, 1665, 1783, 3684, 5467, 36486, 41953, 47420, 52887, 63821, 69288, 74755, 144043c, 218798c }}
+{{Optimal ET sequence|legend=1| 118, 957, 1075, 1193, 1311, 1429, 1547, 1665, 1783, 3684, 5467, 36486, 41953, 47420, 52887, 63821, 69288, 74755, 144043c, 218798c }}
-[[Badness]]: 0.046315
+[[Badness]] (Sintel): 1.09
+; Music
+* ''Gross temperament EP'' (2023) by [[User:Francium|Francium]] – [https://open.spotify.com/album/02Fz6IIJ2x9k7bEvFylZ2A Spotify] | [https://francium223.bandcamp.com/album/gross-temperament-ep Bandcamp] | [https://youtube.com/playlist?list=PLLZE7hMjEXRZy_JWYbZxbsxPsXahiEJA2&si=RttlCFpkeN4Rl7Tj YouTube] – 2-piece extended play
 == Quectismic ==
@@ Line 204: / Line 232: @@
 : mapping generators: ~2, ~3
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9553
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~3/2 = 701.955310
+* [[CWE]]: ~2 = 1200.000000, ~3/2 = 701.955310
 {{Optimal ET sequence|legend=1| 306, 359c, 665, 2301, 2966, 3631, 4296, 46591, 50887, 55183, 59479, 63775, 68071, 72367, 76663, 80959, 85255, 89551 }}
-[[Badness]]: 0.372
+[[Badness]] (Sintel): 8.74
 === Nanoquectismic ===
@@ Line 217: / Line 247: @@
 Mapping: {{mapping| 1 0 -554 109 | 0 1 351 -67 }}
-Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.955
+Optimal tunings:
+* CTE: ~2 = 1200.000000, ~3/2 = 701.955371
+* CWE: ~2 = 1200.000000, ~3/2 = 701.955457
 {{Optimal ET sequence|legend=1| 306, 665, 1636, 2301, 2966 }}
-Badness: 0.604
+Badness (Sintel): 15.3
 === Conanoquectismic ===
@@ Line 230: / Line 262: @@
 Mapping: {{mapping| 1 0 -554 -945 | 0 1 351 598 }}
-Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.9548
+Optimal tunings:
+* CTE: ~2 = 1200.000000, ~3/2 = 701.954810
+* CWE: ~2 = 1200.000000, ~3/2 = 701.954771
 {{Optimal ET sequence|legend=1| 306d, 359cd, 665 }}
-Badness: 2.17
+Badness (Sintel): 55.0
+== Counterquectismic ==
+{{See also| Counterquectisma }}
+[[Subgroup]]: 2.3.5
+[[Comma list]]: {{monzo| -500 314 1 }}
+{{Mapping|legend=1| 1 0 500 | 0 1 -314 }}
+: mapping generators: ~2, ~3
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~3/2 = 701.954415
+* [[CWE]]: ~2 = 1200.000000, ~3/2 = 701.954416
+{{Optimal ET sequence|legend=1| 306c, 359, 665, 2354, 3019, 3684, 11717, 15401, 19085, 34486 }}
+[[Badness]] (Sintel): 12.0
 == Raider ==
-{{See also| Syntonic-chromatic equivalence continuum }}
+{{See also| Syntonic–chromatic equivalence continuum }}
 [[Subgroup]]: 2.3.5
@@ Line 247: / Line 300: @@
 : mapping generators: ~2, ~6561/4000
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~8000/6561 = 343.2961
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~8000/6561 = 343.296094
+* [[POTE]]: ~2 = 1200.000000, ~8000/6561 = 343.296098
 {{Optimal ET sequence|legend=1| 388, 783, 1171, 1954, 3125, 4296, 5467, 7421, 9763, 14059, 18355, 22651, 26947, 31243, 35539, 66782, 102321, 137860 }}
-[[Badness]]: 0.012867
+[[Badness]] (Sintel): 0.302
 == Pirate ==
+{{See also| Hemfiness temperaments #Piracy }}
 [[Subgroup]]: 2.3.5
@@ Line 260: / Line 317: @@
 {{Mapping|legend=1| 1 43 15 | 0 -49 -15 }}
-: mapping generators: ~2, ~{{monzo| -23 -4 13 }}
+: Mapping generators: ~2, ~{{monzo| -23 -4 13 }}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~{{monzo| 24 4 -13 }} = 185.7542
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~{{monzo| 24 4 -13 }} = 185.754186
+* [[POTE]]: ~2 = 1200.000000, ~{{monzo| 24 4 -13 }} = 185.754179
 {{Optimal ET sequence|legend=1| 84, 239, 323, 730, 1783, 2513, 4296, 15401, 19697, 23993, 52282, 76275, 128557, 204832 … }}
-[[Badness]]: 0.005656
+[[Badness]] (Sintel): 0.133
 == Atomic ==
 {{See also | Kirnberger's atom }}
-Atomic extensions discussed elsewhere include [[minutes]] and [[The Flashmob #Hafnium|hafnium]].
+Atomic observes the [[schisma]], and the 3/2 is one schisma sharp of its [[12edo]] value. In atomic, since twelve fifths are sharp of seven octaves by twelve schismas, the [[Pythagorean comma]] is twelve schismas, and hence [[81/80]], the Didymus comma, is eleven schismas. In fact eleven schismas is sharp of 81/80, and twelve schismas of the Pythaorean comma, by the microscopic interval of the atom, which atomic tempers out. Extremely accurate.
+Atomic extensions discussed elsewhere include [[minutes]] and [[72nd-octave temperaments#Hafnium|hafnium]].
 [[Subgroup]]: 2.3.5
@@ Line 281: / Line 342: @@
 : mapping generators: ~{{monzo| -67 35 5 }}, ~3
-[[Optimal tuning]] ([[CTE]]): ~{{monzo| -67 35 5 }} = 1\12, ~3/2 = 701.9552 (or ~32805/32768 = 1.9552)
+[[Optimal tuning]]s:
+* [[CTE]]: ~{{monzo| -67 35 5 }} = 100.000000, ~3/2 = 701.955176 (~32805/32768 = 1.955176)
+* [[POTE]]: ~{{monzo| -67 35 5 }} = 100.000000, ~3/2 = 701.955162 (~32805/32768 = 1.955162)
 {{Optimal ET sequence|legend=1| 12, …, 576, 588, 600, 612, 2460, 3072, 3684, 4296, 12276, 16572, 20868, 25164, 46032 }}
-[[Badness]]: 0.003803
+[[Badness]] (Sintel): 0.0892
 === 7-limit ===
@@ Line 294: / Line 357: @@
 Mapping: {{mapping| 12 0 161 338 | 0 1 -7 -16 }}
-Optimal tuning (CTE): ~30375/28672 = 1\12, ~3/2 = 701.9499 (or ~32805/32768 = 1.9499)
+Optimal tunings:
+* CTE: ~30375/28672 = 100.000000, ~3/2 = 701.949917 (or ~32805/32768 = 1.949917)
+* POTE: ~30375/28672 = 100.000000, ~3/2 = 701.949608 (or ~32805/32768 = 1.949608)
-{{Optimal ET sequence|legend=1| 12, …, 600, 612, 1236, 1848, 4308, 10464, 14772, 25236c, 40008ccd }}
+{{Optimal ET sequence|legend=0| 12, …, 600, 612, 1236, 1848, 4308, 10464, 14772, 25236c, 40008ccd }}
-Badness: 0.045818
+Badness (Sintel): 1.16
 === 11-limit ===
@@ Line 307: / Line 372: @@
 Mapping: {{mapping| 12 0 161 338 517 | 0 1 -7 -16 -25 }}
-Optimal tuning (CTE): ~30375/28672 = 1\12, ~3/2 = 701.9485 (or ~32805/32768 = 1.9485)
+Optimal tunings:
+* CTE: ~30375/28672 = 100.000000, ~3/2 = 701.948456 (or ~32805/32768 = 1.948456)
+* POTE: ~30375/28672 = 100.000000, ~3/2 = 701.947988 (or ~32805/32768 = 1.947988)
-{{Optimal ET sequence|legend=1| 12, …, 600e, 612, 1236, 1848 }}
+{{Optimal ET sequence|legend=0| 12, …, 600e, 612, 1236, 1848 }}
-Badness: 0.016029
+Badness (Sintel): 0.530
-== Niobium ==
+== Revopentic (2.3.7) ==
-Niobium can be viewed as the 41st-octave counterpart of atomic.
+{{See also| Revopentisma }}
-[[Subgroup]]: 2.3.5
+Subgroup: 2.3.7
-[[Comma list]]: {{monzo| -875 492 41 }}
+Comma list: 11399736556781568/11398895185373143
-{{Mapping|legend=1| 41 0 875 | 0 1 -12 }}
+{{Mapping|legend=2| 1 12 5 | 0 -19 -4 }}
-: mapping generators: ~{{monzo| -64 36 3 }}, ~3
+: mapping generators: ~2, ~24576/16807
-[[Optimal tuning]] ([[CTE]]): ~{{monzo| -64 36 3 }} = 1\41, ~3/2 = 701.9536
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~24576/16807 = 657.791865
+* [[CWE]]: ~2 = 1200.000000, ~24576/16807 = 657.791796
-{{Optimal ET sequence|legend=1| 41, …, 2378, 2419, 2460, 4961, 7421, 17302, 24723, 66748, 91471, 116194 }}
+{{Optimal ET sequence|legend=1| 31, 73, 104, 135, 436, 571, 706, 1277, 8233, 9510, 10787, 12064, 13341, 14618, 15895, 33067, 48962, 113819d, 162781d, … }}
-[[Badness]]: 5.57
+[[Badness]] (Sintel): 0.0704
-== Revopent ==
+=== Revopent ===
-Described as the 1848 & 3125 temperament, revopent is named because the year 1848 is known for revolutions while 3125 is 5 to the 5.
+Revopent can be described as the {{nowrap| 1848 & 3125 }} temperament.
 Subgroup: 2.3.5.7
@@ Line 339: / Line 408: @@
 Mapping: {{mapping| 1 12 -155 5 | 0 -19 287 -4 }}
-Optimal tuning (CTE): ~24576/16807 = 657.792
+Optimal tunings:
+* CTE: ~2 = 1200.000000, ~24576/16807 = 657.792032
+* CWE: ~2 = 1200.000000, ~24576/16807 = 657.792032
-{{Optimal ET sequence|legend=1| 135, 436c, 571, 1277, 1848, 3125, 8098, 11223, 25571, 36794, 121605d }}
+{{Optimal ET sequence|legend=0| 135, 436c, 571, 1277, 1848, 3125, 8098, 11223, 25571, 36794, 121605d }}
-Badness: 0.263
+Badness (Sintel): 0.665
-== Francium ==
+== Nanic ==
-Francium tempers out the [[euzenius comma]] and the 87-126/125 comma in the 7-limit, hereby dividing the octave into 87 parts.
+{{See also| Nanisma }}
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.7
-Comma list: 78125000/78121827, {{monzo| 152 -112 -41 43 }}
+[[Comma list]]: {{monzo| 109 -67 -1 }}
-Mapping: {{mapping| 87 1 -106 -406 | 0 4 9 19 }}
+{{Mapping|legend=2| 1 0 109 | 0 1 -67 }}
-: mapping generators: ~126/125, ~{{monzo| 37 -25 -12 11 }}
+: sval mapping generators: ~2, ~3
-Optimal tuning (CTE): ~126/125 = 1\87, ~{{monzo| 37 -25 -12 11 }} = 472.043
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~3/2 = 701.957820
+* [[POTE]]: ~2 = 1200.000000, ~3/2 = 701.957784
-{{Optimal ET sequence|legend=1| 783, …, 8178, 8961, 9744, 10527, 20271, 30798 }}
+{{Optimal ET sequence|legend=1| 53, 200, 253, 306, 665, 971, 1277, 6691, 7968, 9245, 10522, 11799, 13076, 40505, 53581, 66657, 79733 }}
-Badness: 0.762
+[[Badness]] (Sintel): 0.474
-=== 11-limit ===
+== Icarus ==
-Subgroup: 2.3.5.7.11
+This temperament is named after a very distant star. Curiously, the names of two even more distant stars coincide with named temperaments, those being [[godzilla]] and [[mothra]].
-Comma list: 78125000/78121827, 199297406/199290375, {{monzo| 74 -17 -5 -4 -7 }}
+[[Subgroup]]: 3.5.7
-Mapping: {{mapping| 87 1 -106 -406 1225 | 0 4 9 19 -27 }}
+[[Comma list]]: {{monzo| -32 -64 71 }}
-: mapping generators: ~126/125, ~{{monzo| 35 1 -6 -3 -4 }}
+{{Mapping|legend=1| 1 35 32 | 0 -71 -64 }}
-Optimal tuning (CTE): ~126/125 = 1\87, ~{{monzo| 35 1 -6 -3 -4 }} = 472.043
+[[Optimal tuning]]s:
+* [[CTE]]: ~3 = 1901.955, ~{{monzo| 5 9 -10 }} = 898.340
+* [[CWE]]: ~3 = 1901.955, ~{{monzo| 5 9 -10 }} = 898.340
-{{Optimal ET sequence|legend=1| 783, 8178, 8961, 9744, 28449de, 38193bcde, 47937bcdee }}
+[[Optimal ET sequence]]: [[163edt|b163cd]], [[199edt|b199c]], [[235edt|b235]], [[271edt|b271]], [[4643edt|b4643]], [[4914edt|b4914]], …, [[8708edt|b8708]], [[8979edt|b8979]], [[18229edt|b18229]], [[27208edt|b27208]], [[99853edt|b99853]], [[127061edt|b127061]], [[154269edt|b154269]], [[181477edt|b181477]], [[208685edt|b208685]], [[390162edt|b390162]]
-Badness: 0.352
+[[Badness]] (Sintel): 0.00493
-== Nanic ==
-{{See also| Nanisma }}
-[[Subgroup]]: 2.3.7
-[[Comma list]]: {{monzo| 109 -67 -1 }}
-{{Mapping|legend=1| 1 0 109 | 0 1 -67 }}
-: sval mapping generators: ~2, ~3
-[[Optimal tuning]] ([[POTE]]): ~3/2 = 701.9578
-{{Optimal ET sequence|legend=1| 53, 200, 253, 306, 665, 971, 1277, 6691, 7968, 9245, 10522, 11799, 13076, 40505, 53581, 66657, 79733 }}
-[[Badness]]: 0.0138
 = Rank-3 temperaments =
-== Sasaquinbizo-atriyo (171 &amp; 1106 &amp; 3566) ==
+== Sasaquinbizo-atriyo (171 & 1106 & 3566) ==
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: {{monzo| 3 -24 3 10 }} = 282475249000/282429536481
+[[Comma list]]: {{monzo| 3 -24 3 10 }} (282475249000/282429536481)
 {{Mapping|legend=1| 1 0 9 -3 | 0 1 8 0 | 0 0 10 -3 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9624, ~6561/3430 = 1122.9387
 {{Optimal ET sequence|legend=1| 171, 764, 935, 1106, 1277, 2118, 2289, 2460, 3224, 3395, 3566, 26068, 26239, 29634, 29805, 33200, 33371, 36937, 40503, 44069 }}
-[[Badness]]: 0.281 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 1.24
-== Saquadtrizo-asepgu (171 &amp; 2019 &amp; 3566) ==
+== Saquadtrizo-asepgu (171 & 2019 & 3566) ==
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: {{monzo| 0 -11 -7 12 }} = 13841287201/13839609375
+[[Comma list]]: {{monzo| 0 -11 -7 12 }} (13841287201/13839609375)
+{{Mapping|legend=1| 1 0 0 0 | 0 1 7 5 | 0 0 -12 -7 }}
-{{Mapping|legend=1| 1 0 0 0 | 0 1 7 5 | 0 0 12 7 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9584, ~16807/10125 = 877.2825
 {{Optimal ET sequence|legend=1| 171, 814, 985, 1034, 1205, 1376, 1547, 1718, 1848, 2019, 3224, 3395, 3566, 8980, 9151, 12717, 47131, 50697, 59848d, 63414d, 76131d }}
-[[Badness]]: 0.135 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.595
-== Laquinzo-aquadquadgu (171 &amp; 441 &amp; 4973) ==
+== Laquinzo-aquadquadgu (171 & 441 & 4973) ==
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: {{monzo| -7 19 -16 5 }} = 19534128475869/19531250000000
+[[Comma list]]: {{monzo| -7 19 -16 5 }} (19534128475869/19531250000000)
 {{Mapping|legend=1| 1 0 3 11 | 0 1 4 9 | 0 0 5 16 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9501, ~250/189 = 484.2956
 {{Optimal ET sequence|legend=1| 171, 441, 612, 2696, 2795, 2867, 2966, 3137, 3308, 3407, 3479, 3578, 3749, 3920, 4091, 4190, 4361, 4532, 4703, 4802, 4973, 5144, 10117, 10558, 15531, 15702, 52079, 62637, 67781, 78339 }}
-[[Badness]]: 0.297 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 1.31
-== Laleruyo (171 &amp; 1547 &amp; 3125) ==
+== Laleruyo (171 & 1547 & 3125) ==
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: {{monzo| -1 4 11 -11 }} = 3955078125/3954653486
+[[Comma list]]: {{monzo| -1 4 11 -11 }} (3955078125/3954653486)
-{{Mapping|legend=1| 1 3 0 1 | 0 11 0 4 | 0 0 1 1 }}
+{{Mapping|legend=1| 1 3 0 1 | 0 -11 0 -4 | 0 0 1 1 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~375/343 = 154.3678, ~5/4 = 386.3070
 {{Optimal ET sequence|legend=1| 171, 863, 894, 1034, 1065, 1205, 1236, 1376, 1407, 1547, 1578, 1718, 2612, 2783, 2954, 3125, 12329, 15454, 18579, 21704, 40283, 61987 }}
-[[Badness]]: 0.114 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.501
 == Starscape or Latritriru-ayo ==
@@ Line 444: / Line 510: @@
 [[Comma list]]: 645700815/645657712
-{{Mapping|legend=1| 1 0 4 0 | 0 1 1 2 | 0 0 9 1 }}
+{{Mapping|legend=1| 1 0 4 0 | 0 1 1 2 | 0 0 -9 -1 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9514, ~9/7 = 435.0709
 {{Optimal ET sequence|legend=1| 171, 742, 764, 935, 1106, 1277, 1677, 1848, 2019, 2783, 2954, 3125, 8098, 11223, 25571, 33840, 36794, 45063, 48188, 59411, 70634 }}
-[[Badness]]: 0.545 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.240
-== Sepbizo-asegu (171 &amp; 3566 &amp; 4973) ==
+== Sepbizo-asegu (171 & 3566 & 4973) ==
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: {{monzo| -3 2 -17 14 }} = 6104007655641/6103515625000
+[[Comma list]]: {{monzo| -3 2 -17 14 }} (6104007655641/6103515625000)
-{{Mapping|legend=1| 1 0 13 16 | 0 1 10 12 | 0 0 14 17 }}
+{{Mapping|legend=1| 1 0 13 16 | 0 1 10 12 | 0 0 -14 -17 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9548, ~31250/16807 = 1073.8021
 {{Optimal ET sequence|legend=1| 171, 894, 1065, 1236, 1407, 1578, 3053, 3224, 3395, 3566, 5144, 8368, 8539, 8710, 17249, 20815, 29525, 38064, 67589, 105653 }}
-[[Badness]]: 0.223 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.982
 == Euzenius or Sabiruquinyo ==
@@ Line 468: / Line 538: @@
 [[Comma list]]: 78125000/78121827
-{{Mapping|legend=1| 1 0 0 -5 | 0 2 0 -13 | 0 0 1 5 }}
+{{Mapping|legend=1| 1 1 0 -5 | 0 2 0 -13 | 0 0 1 5 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~6250/5103 = 350.9787, ~5/4 = 386.3099
 {{Optimal ET sequence|legend=1| 171, 441, 612, 1730, 1901, 2072, 2171, 2342, 2513, 2684, 2783, 2954, 3125, 6520, 6691, 9816, 16336, 16507, 23027, 26152, 32843, 42659, 58995, 68811, 101654 }}
-[[Badness]]: 0.205 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.0902
 == Nommismic or Quinla-zoyoyo ==
@@ Line 483: / Line 555: @@
 {{Mapping|legend=1| 1 0 0 55 | 0 1 0 -30 | 0 0 1 -2 }}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9516, ~5/4 = 386.3132
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9516, ~5/4 = 386.3132
 {{Optimal ET sequence|legend=1| 612, 1236, 1277, 1848, 2513, 3125, 6862, 8098, 8710, 11835, 14960, 26795, 195663b, }} …
-[[Badness]]: 0.366 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 1.62
-== Satwethezo-atritribigu (171 &amp; 1547 &amp; 4973)  ==
+== Satwethezo-atritribigu (171 & 1547 & 4973)  ==
 [[Subgroup]]: 2.3.5.7
 [[Comma list]]: {{monzo| 1 -15 -18 23 }}
-{{Mapping|legend=1| 1 0 9 7 | 0 1 3 3 | 0 0 23 18 }}
+{{Mapping|legend=1| 1 0 9 7 | 0 1 3 3 | 0 0 -23 -18 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9551, ~56953125/40353607 = 596.5022
 {{Optimal ET sequence|legend=1| 171, 863, 1034, 1205, 1376, 1547, 1718, 3255, 3426, 3597, 4460, 4631, 4802, 4973, 5144, 6520, 6691, 11664, 18355, 48374, 48545, 66900, 145464, }} …
-[[Badness]]: 0.114 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.505
-== Trisa-quinbiru-agu (441 &amp; 1848 &amp; 3125) ==
+== Technologismic or Trisa-quinbiru-agu ==
 [[Subgroup]]: 2.3.5.7
 [[Comma list]]: {{monzo| 51 -13 -1 -10 }}
-{{Mapping|legend=1| 1 0 1 5 | 0 1 7 -2 | 0 0 10 -1 }}
+{{Mapping|legend=1| 1 0 1 5 | 0 1 7 -2 | 0 0 -10 1 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9553, ~63/32 = 1172.7374
 {{Optimal ET sequence|legend=1| 441, 966, 1277, 1407, 1718, 1848, 2684, 3125, 6691, 9816, 11664, 14789, 18355, 33144, 51499, 124478, 175977, }} …
-[[Badness]]: 0.263 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.116
-== Quinbisa-quinbizo-alegu (1848 &amp; 11664 &amp; 21480) ==
+== Quinbisa-quinbizo-alegu (1848 & 11664 & 21480) ==
 [[Subgroup]]: 2.3.5.7
 [[Comma list]]: {{monzo| 110 -71 -11 10 }}
-{{Mapping|legend=1| 1 0 0 -11 | 0 1 -1 6 | 0 0 10 11 }}
+{{Mapping|legend=1| 1 0 0 -11 | 0 1 9 17 | 0 0 -10 -11 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.955, ~32805/28672 = 233.128
 {{Optimal ET sequence|legend=1| 1848, 3737, 5585, 6079, 7927, 9816, 11664, 21480, 33144, 54624, 70025, 81689, 103169, }} …
-[[Badness]]: 0.122 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.538
 [[Category:Temperament collections]]
+[[Category:Pages with mostly numerical content]]