8277/8192

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Interval information

Ratio	8277/8192
Subgroup monzo	2.3.31.89 [-13 1 1 1⟩
Size in cents	17.87069¢
Name	Lilly pilly comma
Color name	89o31o-2
FJS name	[math]\text{d}{-2}^{31,89}[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	26.0149
Weil height (log2 max(n, d))	26.0298
Wilson height (sopfr(nd))	149
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~3.45171 bits
Comma size	small
open this interval in xen-calc

8277/8192, a.k.a. the lilly pilly comma, is tempered out by the Lylla temperament.

Tempering this comma on its own gives the lilly pilly temperament, a rank-3, 2.3.31.89 subgroup tuning.

Lilly pilly

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)