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

It can be seen as the difference between 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

Its S-expression is (S76)(S441)÷(S77)(S324)

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

Etymology

The name tredekisma comes from tredek, which is one step of 270edo, which is an excellent 2.3.5.7.11.13.19 subgroup system that tempers it out.