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No-threes subgroup temperaments: Difference between revisions

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[[Badness]] (Sintel): 7.18 × 10<sup>3</sup>
[[Badness]] (Sintel): 7.18 × 10<sup>3</sup>
=== Tricesimoprimal miracloid ===
{{See also| Tricesimoprimal miracloid/Eliora's approach }}
{{Todo|inline=1| complete section | comment = Add missing data from 2.5.7 to 2.5.7.11.19.29. }}
Tricesimoprimal miracloid is described as the 52 & 1789 temperament in the 2.5.7.11.19.29.31 subgroup, with harmonics specifically selected for 52edo and 1789edo. Its generator is [[31/29]], which is also close to the secor. In terms of microtempering, a circle of 52 generators is essentially a barely noticeable [[well temperament]] for 52edo.
==== 2.5.7.11.19.29.31 subgroup ====
Subgroup: 2.5.7.11.19.29.31
Comma list: 10241/10240, 5858783/5856400, 4093705/4090624, 15109493/15089800, 102942875/102834688
Subgroup-val mapping: {{mapping| 1 -42 -2 -15 -12 -61 -61 | 0 461 50 192 169 685 686 }}
Optimal tunings:
* WE: ~2 = 1200.0079{{c}}, ~31/29 = 115.3723{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~31/29 = 115.3716{{c}}
{{Optimal ET sequence|legend=0| 52, 1737, 1789 }}
Badness (Sintel): 4.51


=== No-threes naiad (rank-3) ===
=== No-threes naiad (rank-3) ===
{{Todo|inline=1| review | comment = Devise the permanent name for this temperament; determine its status with respect to its extensions linked below. }}
{{See also| Wizardharry clan #Naiad | Werckismic temperaments #Seminaiad }}
{{See also| Wizardharry clan #Naiad | Werckismic temperaments #Seminaiad }}


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Temperaments discussed elsewhere include
Temperaments discussed elsewhere include
* Orgone → [[Orgonia #Orgone|Orgonia]]
* Orgone → [[Orgonia #Orgone|Orgonia]]
* Berylic → [[4th-octave temperaments #Berylic|4th-octave temperaments]]
* 21-23-commatic → [[21st-octave temperaments #21-23-commatic|21st-octave temperaments]]
* 21-23-commatic → [[21st-octave temperaments #21-23-commatic|21st-octave temperaments]]
* 31-17/13-commatic → [[31st-octave temperaments #31-17/13-commatic|31st-octave temperaments]]
* 31-17/13-commatic → [[31st-octave temperaments #31-17/13-commatic|31st-octave temperaments]]
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[[Badness]] (Sintel): 0.386
[[Badness]] (Sintel): 0.386
=== Arsenic ===
Arsenic was named by [[Xenllium]] in 2026 after the 33rd chemical element.
[[Subgroup]]: 2.11.13.17.19
[[Comma list]]: 2432/2431, 7086244/7054567, 33698267/33554432
{{Mapping|legend=2| 33 0 8 249 26 | 0 1 1 -1 1 }}
: mapping generators: ~247/242, ~11
[[Optimal tuning]]s:
* [[WE]]: ~247/242 = 36.3676{{c}}, ~11/8 = 550.4246{{c}}
* [[CWE]]: ~247/242 = 36.3636{{c}}, ~11/8 = 550.4187{{c}}
{{Optimal ET sequence|legend=1| 33, 165, 198, 231, 495h }}
[[Badness]] (Sintel): 2.30


=== Berylic ===
=== Berylic ===
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