4921/4920

4921/4920, the volontisma, is a 41-limit superparticular comma of about 0.35 cents.

Interval information

Ratio	4921/4920
Factorization	2-3 × 3-1 × 5-1 × 7 × 19 × 37 × 41-1
Monzo	[-3 -1 -1 1 0 0 0 1 0 0 0 1 -1⟩
Size in cents	0.3518411¢
Name	volontisma
Color name	41u37o19ozg3 fowuthisonozogu 3rd
FJS name	[math]\displaystyle{ \text{d2}^{7,19,37}_{5,41} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	24.5292
Weil norm (log2 max(n, d))	24.5295
Wilson norm (sopfr(nd))	118
Comma size	unnoticeable
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Commatic relationships

This comma is the difference between the following superparticular pairs:

• 247/246 and 260/259
• 370/369 and 400/399
• 616/615 and 704/703
• 1026/1025 and 1296/1295
• 1805/1804 and 2850/2849

It can be factored into the following superparticular ratios:

• 5985/5984 and 27676/27675
• 6561/6560 and 19684/19683
• 9361/9360 and 10374/10373
• 9472/9471 and 10241/10240

Temperaments

Tempering out this comma in the full 41-limit leads to the rank-12 temperament volontismic. Using the 2.3.5.7.19.37.41 subgroup leads to the rank-6 temperament volontic.

Volontic

Subgroup: 2.3.5.7.19.37.41

Comma list: 4921/4920

Mapping:

[⟨	1	1	2	2	4	5	5	],
⟨	0	1	0	0	0	0	-1	],
⟨	0	0	1	0	0	0	-1	],
⟨	0	0	0	1	0	0	1	],
⟨	0	0	0	0	1	0	1	],
⟨	0	0	0	0	0	1	1	]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.965, ~5/4 = 386.335, ~7/4 = 968.795, ~19/16 = 297.442, ~37/32 = 251.238

Optimal ET sequence: 5h, 7dm, 7, 8d, 8dhhmm, 9, 10m, 12l, 12m, 19hm, 19, 22, 26, 27, 41lm, 50m, 53, 80, 99m, 130, 140, 149, 152m, 171, 202, 270, 311, 460, 472, 513, 783, 1296, 1323, 1376, 1578l, 1795, 1848, 2361l, 3144l, 4007, 4209hl, 4520hl, 4619, 4992hl, 5532hl, 6315hl, 6368hl

Badness (Sintel): 0.087

Etymology

This comma was named by Francium in 2025. It refers to 4921 Volonté, the asteroid, which in turn was named after Gian Maria Volonté, an Italian actor.

See also

• Unnoticeable comma
• List of superparticular intervals