8277/8192
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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
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| Interval information |
reduced harmonic
(Shannon, [math]\sqrt{nd}[/math])
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)