1000/979

This page presents a novelty topic. It features ideas which are less likely to find practical applications in xenharmonic music. It may contain 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 feature idiosyncratic terms, notations, or conceptual frameworks.

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]\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]\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)