3213/3211

Interval information

Ratio	3213/3211
Factorization	33 × 7 × 13-2 × 17 × 19-1
Monzo	[0 3 0 1 0 -2 1 -1⟩
Size in cents	1.077979¢
Name	cobaltomenisma
Color name	19u17o3uuz1 nusothuthuzo unison
FJS name	[math]\text{A1}^{7,17}_{13,13,19}[/math]
Special properties	reduced
Tenney height (log2 nd)	23.2985
Weil height (log2 max(n, d))	23.2994
Wilson height (sopfr(nd))	78
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.20995 bits
Comma size	unnoticeable
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3213/3211, the cobaltomenisma, is a 19-limit (also 3.7.13.17.19 subgroup) unnoticeable comma of about 1.1 cents.

Commatic relationships

This comma is the difference between the following pairs:

• 170/169 and 190/189
• 171/170 and 1701/1690
• 1216/1215 and 7616/7605

It can be factored into the following intervals:

• 1729/1728 and 793152/793117
• 2376/2375 and 14875/14872
• 2601/2600 and 4200/4199
• 3136/3135 and 75735/75712
• 4914/4913 and 83521/83486

Temperaments

Tempering out this comma in the full 19-limit leads tot he rank-7 temperament cobaltomenismic. Using the 3.7.13.17.19 subgroup leads to the rank-4 temperament cobaltomenite.

Adding the trichthonisma, the sextantonisma, the neovulturisma, the lehmerisma and the schismina leads to vasca.

Adding the breedsma, the sextantonisma, the neovulturisma, the neomirkwaisma and the neogrendelisma leads to surmarvelpyth.

Cobaltomenite

Subgroup: 3.7.13.17.19

Comma list: 3213/3211

Mapping:

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

Optimal tuning (CTE): ~3 = 1\1, ~7/3 = 1466.784, ~13/9 = 636.921, ~17/9 = 1100.861

Optimal ET sequence: b7, b8, b9, b21, b30, b41, b44g, b48, b53, b57, b78, b110, b119, b131, b176, b188, b197, b385, b582, b660, b1045, b2693f, b3078fh, b3353f, b3738fh, b4398fh, b4783ffh

Etymology

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

See also

• Unnoticeable comma