3381/3380

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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 0.51212367¢
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:

It factors into the following superparticular pairs:

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 sequence6fhi, 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 sequence7dfi, 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