FloraC: Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

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Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

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	Comma list: 99/98, 121/120, 3125/3087		Comma list: 99/98, 121/120, 3125/3087

	~~Mapping:~~ {{~~mapping~~\| 1 -9 -12 -14 -9 \| 0 17 23 27 20 }}		{{Mapping\|legend=0\| 1 -9 -12 -14 -9 \| 0 17 23 27 20 }}

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	Comma list: 99/98, 121/120, 169/168, 275/273		Comma list: 99/98, 121/120, 169/168, 275/273

	~~Mapping:~~ {{~~mapping~~\| 1 -9 -12 -14 -9 -10 \| 0 17 23 27 20 22 }}		{{Mapping\|legend=0\| 1 -9 -12 -14 -9 -10 \| 0 17 23 27 20 22 }}

	Optimal tunings:		Optimal tunings:

FloraC: Birth

2026-09-20T05:03:19Z

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This is a collection of '''nuwell temperaments''', which [[tempering out|temper out]] the [[nuwell comma]] ({{monzo|legend=1| 1 5 1 -4 }}, [[ratio]]: 2430/2401). Its fundamental equivalence entails that [[7/6]] is sharpened so that it stacks four times to reach [[15/8]]. Most of these temperaments extend to the [[11-limit]] by equating [[11/8]][[~]][[15/11]] with (7/6)<sup>2</sup>, tempering out [[99/98]] and [[121/120]].

Temperaments discussed elsewhere are:
* [[Quasisuper]] (+64/63) → [[Archytas clan #Quasisuper|Archytas clan]]
* ''[[Oncle]]'' (+1029/1024) → [[Gamelismic clan #Oncle|Gamelismic clan]]
* ''[[Alphatrimot]]'' (+5120/5103) → [[Alphatricot family #Alphatrimot|Alphatricot family]]
* [[Squares]] (+81/80) → [[Meantone family #Squares|Meantone family]]
* ''[[Progression]]'' (+36/35) → [[Mint temperaments #Progression|Mint temperaments]]
* [[Orwell]] (+225/224) → [[Semicomma family #Orwell|Semicomma family]]
* ''[[Hamity]]'' (+4000/3969) → [[Amity family #Hamity|Amity family]]
* ''[[Nusecond]]'' (+126/125) → [[Starling temperaments #Nusecond|Starling temperaments]]
* ''[[Chromo]]'' (+875/864) → [[Keemic temperaments #Chromo|Keemic temperaments]]

Considered below is maja. For the [[rank-3 temperament]], see [[Miscellaneous 7-limit temperaments #Nuwell]].

== Maja ==
: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum #Maja (5-limit)]].''

Maja tempers out 3125/3087, the [[gariboh comma]], and 4375/4374, the [[ragisma]], in addition to the nuwell comma, and may be described as the {{nowrap| 8d & 53 }} temperament. It was named by [[Petr Pařízek]] in 2011 for [[~]][[13/10]] is a generator for the [[13-limit]] version and that ''M'' and ''J'' are the 13th letter and the 10th letter, respectively<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>. It is unrelated to either the [[interval quality|major]] quality or [[magic]] temperament. Note that in the data below, the generator is its [[octave complement]], such that seventeen of them [[octave reduction|octave reduced]] reach the [[3/2|perfect fifth]]. Its [[ploidacot]] is iota-17-cot.

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 2430/2401, 3125/3087

{{Mapping|legend=1| 1 -9 -12 -14 | 0 17 23 27 }}
: mapping generators: ~2, ~54/35

[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0230{{c}}, ~54/35 = 747.0972{{c}}
: [[error map]]: {{val| -0.077 -0.612 -2.157 +3.873 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~54/35 = 747.1084{{c}}
: error map: {{val| 0.000 -1.112 -2.820 +3.102 }}

{{Optimal ET sequence|legend=1| 8d, …, 45, 53 }}

[[Badness]] (Sintel): 2.26

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 99/98, 121/120, 3125/3087

Mapping: {{mapping| 1 -9 -12 -14 -9 | 0 17 23 27 20 }}

Optimal tunings:
* WE: ~2 = 1200.7417{{c}}, ~54/35 = 747.5622{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~54/35 = 747.2024{{c}}

{{Optimal ET sequence|legend=0| 8d, …, 45e, 53 }}

Badness (Sintel): 1.65

=== 13-limit ===
Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 121/120, 169/168, 275/273

Mapping: {{mapping| 1 -9 -12 -14 -9 -10 | 0 17 23 27 20 22 }}

Optimal tunings:
* WE: ~2 = 1200.8497{{c}}, ~20/13 = 747.6240{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 747.2212{{c}}

{{Optimal ET sequence|legend=0| 8d, …, 45ef, 53 }}

Badness (Sintel): 1.14

== References ==

[[Category:Nuwell temperaments| ]] 
[[Category:Temperament collections]]
[[Category:Catalogs of rank-2 temperaments]]

Nuwell temperaments - Revision history

FloraC: Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

FloraC: Birth