3381/3380

Interval information

Ratio	3381/3380
Factorization	2-2 × 3 × 5-1 × 72 × 13-2 × 23
Monzo	[-2 1 -1 2 0 -2 0 0 1⟩
Size in cents	0.5121237¢
Name	mikkolisma
Color name	23o3uuzzg2, twethothuthuzozogu 2nd
FJS name	[math]\text{A1}^{7,7,23}_{5,13,13}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	23.446
Weil height (log2 max(n, d))	23.4465
Wilson height (sopfr(nd))	75
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.20067 bits
Comma size	unnoticeable
open this interval in xen-calc

3381/3380, the mikkolisma, is a 23-limit superparticular comma of about 0.51 cents. It is the amount by which a stack consisting of 23/21 and two 14/13's succeed 80/63.

Commatic relationships

This comma is the difference between following superparticular pairs:

• 196/195 and 208/207
• 441/440 and 507/506
• 833/832 and 1105/1104
• 2646/2645 and 12168/12167

It factors into the following superparticular pairs:

• 3888/3887 and 25921/25920
• 3969/3968 and 22816/22815
• 5292/5291 and 9361/9360

Temperaments

Tempering out the comma leads to the rank-8 temperament mikkolismic. Using the 2.3.5.7.13.23 subgroup leads to the rank-5 temperament mikkolic.

Mikkolismic

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 3381/3380

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.944, ~5/4 = 386.338, ~7/4 = 968.756, ~11/8 = 551.318, ~13/8 = 840.650, ~17/16 = 104.955, ~19/16 = 297.513

Optimal ET sequence: 6fhi, 7deefghi, 7dfghi, 8d, 9, 10e, 10, 10h, 12fi, 16h, 16, 17cg, 17cgh, 19egh, 19, 22fh, 26i, 29g, 38df, 39dfgi, 41i, 46, 58hi, 62, 68, 72hi, 72i, 84, 87, 94, 111, 130, 140, 152fg, 159, 198, 198g, 217, 243e, 270, 282, 311, 373g, 422, 525, 581, 742i, 814, 954h, 1106, 1282, 1323, 1395, 1677e, 1696, 1768gi, 1920, 2874hi, 3202, 3513, 5011di, 6293di

Mikkolic

Subgroup: 2.3.5.7.13.23

Comma list: 3381/3380

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.944, ~5/4 = 386.338, ~7/4 = 968.756, ~13/8 = 840.650

Optimal ET sequence: 7dfi, 8d, 9, 10, 12fi, 16, 17c, 19, 27, 29, 36, 39dfi, 41i, 45fi, 46, 58i, 68, 84, 103, 111, 113, 130, 198, 224, 243, 311, 373, 441, 1012, 1106, 1236, 1395, 1677, 1920, 2118, 2361, 2631, 3072, 4327

Etymology

The name mikkolisma was named by Francium in 2024. It refers to 3381 Mikkola, the asteroid. Which was in turn named after a Finnish astronomer. Xenllium proposed the name seminaiadvice comma in 2023.

See also

• Unnoticeable comma
• List of superparticular intervals