11859211/11859210

Interval information
Ratio	11859211/11859210
Factorization	2-1 × 3-4 × 5-1 × 7 × 11-4 × 13 × 194
Monzo	[-1 -4 -1 1 -4 1 0 4⟩
Size in cents	0.0001459822¢
Name	tredekisma
Color name	quadno-athoquadlu-azogu 4th, 19o^43o1u^4zg4, Quadno-athoquadlu-azogu comma,
FJS name	[math]\displaystyle{ \text{ddd4}^{7,13,19,19,19,19}_{5,11,11,11,11} }[/math]
Special properties	superparticular,; reduced
Tenney norm (log2 nd)	46.999
Weil norm (log2 max(n, d))	46.999
Wilson norm (sopfr(nd))	159
Comma size	unnoticeable
	Open this interval in xen-calc

11859211/11859210, the tredekisma, is the smallest superparticular ratio in the 19-limit and 23-limit.

It can be seen as the differencebetween a stack of a 25/16 plus a minisma plus a Saquadnu comma, and a diminished fifth plus two Axirabian limmas:

(25/16)(4096/4095)(131072/130321)÷(1024/729)(128/121)^2

Temperaments

Only being 0.00014 cents, it is an insanely, unfathomably narrow comma; hundreds of times narrower than well known atomic commas like the Chalmersia and the Kirnberger's atom. As such, tempering out or fudging this either way are aurally identical to JI to human ears. It is notably tempered out in 270edo thanks to its very well approximated 2.3.5.7.11.13.19, hence its name; also tempered out in other edos like 94, 118, 152, 364, among others.

Tredekic

Subgroup: 2.3.5.7.11.13.19

[⟨	1	0	0	0	0	1	0	],
⟨	0	1	0	0	0	0	1	],
⟨	0	0	1	0	0	1	0	],
⟨	0	0	0	1	0	3	-1	],
⟨	0	0	0	0	1	0	1	],
⟨	0	0	0	0	0	-4	1	]]

mapping generators: ~2, ~3, ~5, ~7, ~11, ~133/33

Optimal tunings: TBA

Optimal ET sequence: TBA

Badness (Sintel): TBA

Tredekismic

Subgroup: 2.3.5.7.11.13.17.19

[⟨	1	0	0	0	0	1	0	0	],
⟨	0	1	0	0	0	0	0	1	],
⟨	0	0	1	0	0	1	0	0	],
⟨	0	0	0	1	0	3	0	-1	],
⟨	0	0	0	0	1	0	0	1	],
⟨	0	0	0	0	0	-4	0	1	],
⟨	0	0	0	0	0	0	1	0	]]

mapping generators: ~2, ~3, ~5, ~7, ~11, ~17, ~133/33

Optimal tunings: TBA

Optimal ET sequence: TBA

Badness (Sintel): TBA