121125/121121

Interval information

Ratio	121125/121121
Factorization	3 × 53 × 7-1 × 11-3 × 13-1 × 17 × 19
Monzo	[0 1 3 -1 -3 -1 1 1⟩
Size in cents	0.05717276¢
Name	aubertisma
Color name	19o17o3u1u3ry31 nosothutrilu-arutriyo unison
FJS name	[math]\text{AA1}^{5,5,5,17,19}_{7,11,11,11,13}[/math]
Special properties	reduced
Tenney height (log2 nd)	33.7722
Weil height (log2 max(n, d))	33.7723
Wilson height (sopfr(nd))	107
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.19985 bits
Comma size	unnoticeable
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121125/121121, the aubertisma, is a 19-limit (also 3.5.7.11.13.17.19 subgroup) unnoticeable comma of about 0.057 cents.

Commatic relationships

This comma is the difference between the following intervals:

• 286/285 and 850/847
• 1275/1274 and 1331/1330
• 1540/1539 and 42500/42471
• 2376/2375 and 11016/11011
• 3136/3135 and 190400/190333
• 4200/4199 and 225000/224939
• 5929/5928 and 14875/14872
• 13377/13376 and 937125/937024
• 14400/14399 and 27456/27455

It can be factored into the following ratios:

• 89376/89375 and 1328125/13280960
• 165376/165375 and 8859375/8859136

Temperaments

Tempering out this comma in the full 19-limit leads to the rank-7 temperament aubertismic. Using the 3.5.7.11.13.17.19 subgroup leads to the rank-6 temperament aubertite.

Aubertite

Subgroup: 3.5.7.11.13.17.19

Comma list: 121125/121121

Mapping:

[⟨	1	1	1	2	2	2	3	],
[⟨	0	1	0	0	0	0	-3	],
[⟨	0	0	1	0	0	0	1	],
[⟨	0	0	0	1	0	0	3	],
[⟨	0	0	0	0	1	0	1	],
[⟨	0	0	0	0	0	1	-1	]]

Optimal tuning (CTE): ~3 = 1\1, ~5/3 = 884.354, ~7/3 = 1466.873, ~11/9 = 347.418, ~13/9 = 636.621, ~17/9 = 1101.041

Optimal ET sequence: b7h, b10f, b13gh, b14, b15h, b17h, b21, b22, b28, b32, b43, b53, b56, b71h, b75g, b78, b99, b114, b131, b209, b245, b368, b376, b454, b581, b591, b613, b669, b712, b914, b1045, b1512, b1757, b2579, b2710, b3170, b3379, b3624, b5136, b6925, b8891, b10549

Etymology

This comma was named by Francium in 2025. It refers to Aubertite, the mineral.

See also

• Unnoticeable comma