User:BudjarnLambeth/Lightyear comma: Difference between revisions

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 {{novelty}}
+{{editable user page|Do not remove anything, but feel free to add stuff (e.g. music, instruments, modes, subsets, tables, diagrams, any other observations.)}}
-/704969, a.k.a. the Lightyear comma, is tempered out by the [[Batch 89 temperaments#Lylla|Lylla]] temperament.
-Tempering this comma ''on its own'' gives the Lightyear temperament, a 2.3.31.89 [[subgroup]] tuning.
 {{Infobox Interval
 | Name = Lightyear comma
 | Color name = 89u<sup>3</sup>31o<sup>3</sup>-2
+| Ratio = 714984/704969
 | Comma = yes
 }}
+'''714984/704969''', a.k.a. the '''lightyear comma''', is tempered out by the [[Batch 89 temperaments#Lylla|Lylla]] temperament.
+Tempering this comma ''on its own'' gives the lightyear temperament, a [[rank-3]], 2.3.31.89 [[subgroup]] tuning.
+== Lightyear ==
+<pre>
+Equal Temperament Mappings
+	3	31	89
+[ ⟨	34	54	169	221	]
+⟨	17	27	84	110	]
+⟨	19	30	94	123	] ⟩
+Reduced Mapping
+	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)
+</pre>
+[[Category:Commas named after mythology or literature]]