User:BudjarnLambeth/2883/2848: Difference between revisions
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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 = | | Name = Lilac comma | ||
| Ratio = 2883/2848 | |||
| Comma = yes | | Comma = yes | ||
| Color name = 89u31oo-2 | |||
}} | }} | ||
2883/2848, a.k.a. the | '''2883/2848''', a.k.a. the '''lilac comma''', is tempered out by the [[Batch_89_temperaments#Lylla|Lylla]] temperament. | ||
Tempering this comma ''on its own'' gives the lilac temperament, a [[rank-3]], 2.3.31.89 [[subgroup]] tuning. | |||
== Lilac == | |||
<pre> | |||
Equal Temperament Mappings | |||
2 3 31 89 | |||
[ ⟨ 19 30 94 123 ] | |||
⟨ 5 8 25 33 ] | |||
⟨ 17 27 84 110 ] ⟩ | |||
Reduced Mapping | |||
2 3 31 89 | |||
[ ⟨ 1 0 0 -5 ] | |||
⟨ 0 1 0 1 ] | |||
⟨ 0 0 1 2 ] ⟩ | |||
TE Generator Tunings (cents) | |||
⟨1200.6308, 1901.6381, 5938.8430] | |||
TE Step Tunings (cents) | |||
⟨32.54482, 8.45154, 31.76597] | |||
TE Tuning Map (cents) | |||
⟨1200.631, 1901.638, 5938.843, 7776.170] | |||
TE Mistunings (cents) | |||
⟨0.631, -0.317, -6.193, 5.290] | |||
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 0.031827 | |||
Adjusted Error 5.288352 cents | |||
TE Error 0.816641 cents/octave | |||
Unison Vector | |||
[-5, 1, 2, -1⟩ (2883:2848) | |||
</pre> | |||
[[Category:Commas named after mythology or literature]] | |||