User:BudjarnLambeth/Lightyear comma

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Interval information

Ratio	714984/704969
Subgroup monzo	2.3.31.89 [3 1 3 -3⟩
Size in cents	24.42137 ¢
Name	Lightyear comma
Color name	89u331o3-2
FJS name	[math]\displaystyle{ \text{M}{-2}^{31,31,31}_{89,89,89} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	38.8748
Weil norm (log2 max(n, d))	38.8951
Wilson norm (sopfr(nd))	369
Comma size	small
Open this interval in xen-calc

714984/704969, a.k.a. the lightyear comma, is tempered out by the Lylla temperament.

Tempering this comma on its own gives the lightyear temperament, a rank-3, 2.3.31.89 subgroup tuning.

Lightyear

Equal Temperament Mappings
2	3	31	89	
[ ⟨	34	54	169	221	]
⟨	17	27	84	110	]
⟨	19	30	94	123	] ⟩
 
Reduced Mapping
2	3	31	89	
[ ⟨	1	0	0	1	]
⟨	0	3	0	1	]
⟨	0	0	1	1	] ⟩
 
TE Generator Tunings (cents)
⟨1199.8799, 633.9515, 5942.0869]
 
TE Step Tunings (cents)
⟨10.71063, 24.85800, 21.74381]
 
TE Tuning Map (cents)
⟨1199.880, 1901.854, 5942.087, 7775.918]
 
TE Mistunings (cents)
⟨-0.120, -0.101, -2.949, 5.038]

These calculations use inharmonic TE. Subgroup TE will not work because the basis is not a subgroup of the rational numbers or has a redundant entry or something else is wrong.
 
Complexity	0.060706
Adjusted Error	3.202037 cents
TE Error	0.494467 cents/octave
 
Unison Vector
[3, 1, 3, -3⟩ (714984:704969)