7936/7921

This page presents a novelty topic. It may contain ideas which are less likely to find practical applications in xenharmonic music, or numbers that are impractically large, exceedingly complex, or chosen arbitrarily. Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks.

Interval information

Ratio	7936/7921
Subgroup monzo	2.31.89 [8 1 -2⟩
Size in cents	3.275338¢
Name	Lily comma
Color name	89uu31o1
FJS name	[math]\text{d1}^{31}_{89,89}[/math]
Special properties	reduced
Tenney height (log2 nd)	25.9057
Weil height (log2 max(n, d))	25.9084
Wilson height (sopfr(nd))	225
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.29943 bits
Comma size	unnoticeable
open this interval in xen-calc

7936/7921, a.k.a. the lily comma, is tempered out by the Lylla temperament.

Tempering this comma on its own gives the lily temperament, a rank-2, 2.31.89 subgroup tuning.

Lily

Equal Temperament Mappings
2	31	89	
[ ⟨	21	104	136	]
⟨	23	114	149	] ⟩
 
Reduced Mapping
2	31	89	
[ ⟨	1	4	6	]
⟨	0	2	1	] ⟩
 
TE Generator Tunings (cents)
⟨1199.8978, 572.5654]
 
TE Step Tunings (cents)
⟨29.87046, 24.89644]
 
TE Tuning Map (cents)
⟨1199.898, 5944.722, 7771.952]
 
TE Mistunings (cents)
⟨-0.102, -0.314, 1.072]

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	0.166333
Adjusted Error	0.764933 cents
TE Error	0.118123 cents/octave
 
Unison Vector
[8, 1, -2⟩ (7936:7921)