Nuwell temperaments: Difference between revisions
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This | This page collects '''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]]. | ||
For the [[rank-3 temperament]], see [[Miscellaneous 7-limit temperaments #Nuwell]]. | |||
Temperaments discussed elsewhere are: | Temperaments discussed elsewhere are: | ||
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* ''[[Chromo]]'' (+875/864) → [[Keemic temperaments #Chromo|Keemic temperaments]] | * ''[[Chromo]]'' (+875/864) → [[Keemic temperaments #Chromo|Keemic temperaments]] | ||
Considered below is maja | Considered below is maja. | ||
== Maja == | == Maja == | ||
Latest revision as of 20:58, 9 November 2026
This page collects nuwell temperaments, which temper out the nuwell comma (monzo: [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)2, tempering out 99/98 and 121/120.
For the rank-3 temperament, see Miscellaneous 7-limit temperaments #Nuwell.
Temperaments discussed elsewhere are:
- Quasisuper (+64/63) → Archytas clan
- Oncle (+1029/1024) → Gamelismic clan
- Alphatrimot (+5120/5103) → Alphatricot family
- Squares (+81/80) → Meantone family
- Progression (+36/35) → Mint temperaments
- Hedgehog (+50/49) → Stearnsmic clan
- Orwell (+225/224) → Semicomma family
- Hamity (+4000/3969) → Amity family
- Nusecond (+126/125) → Starling temperaments
- Chromo (+875/864) → Keemic temperaments
Considered below is maja.
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 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[1]. It is unrelated to either the major quality or magic temperament. Note that in the data below, the generator is its octave complement, such that seventeen of them octave reduced reach the perfect fifth. Its ploidacot is iota-17-cot.
Subgroup: 2.3.5.7
Comma list: 2430/2401, 3125/3087
Mapping: [⟨1 -9 -12 -14], ⟨0 17 23 27]]
- mapping generators: ~2, ~54/35
- WE: ~2 = 1200.0230 ¢, ~54/35 = 747.0972 ¢
- error map: ⟨-0.077 -0.612 -2.157 +3.873]
- CWE: ~2 = 1200.0000 ¢, ~54/35 = 747.1084 ¢
- error map: ⟨0.000 -1.112 -2.820 +3.102]
Optimal ET sequence: 8d, …, 45, 53
Badness (Sintel): 2.26
11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 121/120, 3125/3087
Mapping: [⟨1 -9 -12 -14 -9], ⟨0 17 23 27 20]]
Optimal tunings:
- WE: ~2 = 1200.7417 ¢, ~54/35 = 747.5622 ¢
- CWE: ~2 = 1200.0000 ¢, ~54/35 = 747.2024 ¢
Optimal ET sequence: 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: [⟨1 -9 -12 -14 -9 -10], ⟨0 17 23 27 20 22]]
Optimal tunings:
- WE: ~2 = 1200.8497 ¢, ~20/13 = 747.6240 ¢
- CWE: ~2 = 1200.0000 ¢, ~20/13 = 747.2212 ¢
Optimal ET sequence: 8d, …, 45ef, 53
Badness (Sintel): 1.14