User:BudjarnLambeth/8277/8192: Difference between revisions

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Documented recently named comma
 
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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.)}}
{{Infobox Interval
{{Infobox Interval
| Name = Lime comma
| Name = Lilly pilly comma
| Ratio = 8277/8192
| Color name = 89o31o-2
| Comma = yes
| Comma = yes
}}
}}


729/712, a.k.a. the Lime comma, is tempered out by the [[Batch 89 temperaments#Lylla|Lylla]] temperament.
'''8277/8192''', a.k.a. the '''lilly pilly comma''', is tempered out by the [[Batch 89 temperaments#Lylla|Lylla]] temperament.
 
Tempering this comma ''on its own'' gives the lilly pilly temperament, a [[rank-3]], 2.3.31.89 [[subgroup]] tuning.
 
== Lilly pilly ==
<pre>
Equal Temperament Mappings
2 3 31 89
[ ⟨ 24 38 119 155 ]
⟨ 17 27 84 110 ]
⟨ 19 30 94 123 ] ⟩
Reduced Mapping
2 3 31 89
[ ⟨ 1 0 0 13 ]
⟨ 0 1 0 -1 ]
⟨ 0 0 1 -1 ] ⟩
TE Generator Tunings (cents)
⟨1200.9762, 1901.7664, 5943.1926]
TE Step Tunings (cents)
⟨15.53945, 24.39904, 21.74978]
TE Tuning Map (cents)
⟨1200.976, 1901.766, 5943.193, 7767.731]
TE Mistunings (cents)
⟨0.976, -0.189, -1.843, -3.149]
 
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 0.037924
Adjusted Error 3.750764 cents
TE Error 0.579203 cents/octave
Unison Vector
[-13, 1, 1, 1⟩ (8277:8192)
</pre>
 
[[Category:Commas named after mythology or literature]]