User:BudjarnLambeth/1000/979

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Interval information
Ratio 1000/979
Subgroup monzo 2.5.11.89 [3 3 -1 -1
Size in cents 36.74308¢
Name Canine comma
Color name 89u1uy31
FJS name [math]\displaystyle{ \text{A1}^{5,5,5}_{11,89} }[/math]
Special properties reduced
Tenney height (log2 nd) 19.9009
Weil height (log2 max(n, d)) 19.9316
Wilson height (sopfr(nd)) 121
Harmonic entropy
(Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])
~4.5144 bits
Comma size medium
Open this interval in xen-calc

1000/979, a.k.a. the canine comma, is tempered out by the Teefs temperament.

Tempering this comma on its own gives the canine temperament, a rank-3, 2.5.11.89 subgroup tuning.

Canine

Equal Temperament Mappings
2	5	11	89	
[ ⟨	9	21	31	59	]
⟨	6	14	21	39	]
⟨	7	16	24	45	] ⟩
 
Reduced Mapping
2	5	11	89	
[ ⟨	1	0	0	3	]
⟨	0	1	0	3	]
⟨	0	0	1	-1	] ⟩
 
TE Generator Tunings (cents)
⟨1199.0107, 2780.9802, 4155.2644]
 
TE Step Tunings (cents)
⟨32.41194, 92.72700, 50.13446]
 
TE Tuning Map (cents)
⟨1199.011, 2780.980, 4155.264, 7784.708]
 
TE Mistunings (cents)
⟨-0.989, -5.333, 3.946, 13.828]

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	0.025366
Adjusted Error	11.270504 cents
TE Error	1.740421 cents/octave
 
Unison Vector
[3, 3, -1, -1⟩ (1000:979)