User:BudjarnLambeth/Lightyear comma
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(Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])
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)