729/712

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Interval information

Ratio	729/712
Subgroup monzo	2.3.89 [-3 6 -1⟩
Size in cents	40.84989¢
Name	Oxidizer comma
Color name	L89u1
FJS name	[math]\text{P1}_{89}[/math]
Special properties	reduced
Tenney height (log2 nd)	18.9855
Weil height (log2 max(n, d))	19.0196
Wilson height (sopfr(nd))	113
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.51747 bits
Comma size	medium
open this interval in xen-calc

729/712, a.k.a. the oxidizer comma, is tempered out by the Rocket temperament.

Tempering this comma on its own gives the oxidizer temperament, a rank-2, 2.3.89 subgroup tuning.

Oxidizer

Equal Temperament Mappings
2	3	89	
[ ⟨	7	11	45	]
⟨	5	8	33	] ⟩
 
Reduced Mapping
2	3	89	
[ ⟨	1	2	9	]
⟨	0	-1	-6	] ⟩
 
TE Generator Tunings (cents)
⟨1200.8669, 504.1340]
 
TE Step Tunings (cents)
⟨118.93652, 73.66225]
 
TE Tuning Map (cents)
⟨1200.867, 1897.600, 7782.997]
 
TE Mistunings (cents)
⟨0.867, -4.355, 12.117]

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	0.386145
Adjusted Error	12.845148 cents
TE Error	1.983582 cents/octave
 
Unison Vector
[-3, 6, -1⟩ (729:712)