User:BudjarnLambeth/Lightyear comma: Difference between revisions
Documented recently named comma |
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{{editable user page|Do not remove anything, but feel free to add stuff (e.g. music, instruments, modes, subsets, tables, diagrams, any other observations.)}} | |||
{{Infobox Interval | {{Infobox Interval | ||
| Name = Lightyear comma | | Name = Lightyear comma | ||
| Color name = 89u<sup>3</sup>31o<sup>3</sup>-2 | |||
| Ratio = 714984/704969 | |||
| Comma = yes | | 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 | |||
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) | |||
</pre> | |||
[[Category:Commas named after mythology or literature]] | |||