Viljevisma

Interval information

Ratio	2553/2552
Factorization	2-3 × 3 × 11-1 × 23 × 29-1 × 37
Monzo	[-3 1 0 0 -1 0 0 0 1 -1 0 1⟩
Size in cents	0.6782504¢
Name	viljevisma
Color name	37o29u23o1u2 thisotwenutwetholu 2nd
FJS name	[math]\text{d}{-2}^{23,37}_{11,29}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	22.6354
Weil height (log2 max(n, d))	22.636
Wilson height (sopfr(nd))	109
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.20412 bits
Comma size	unnoticeable
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2553/2552, the viljevisma, is a 37-limit superparticular comma of about 0.68 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 111/110 and 116/115
• 407/406 and 484/483
• 552/551 and 704/703
• 851/850 and 1276/1275
• 925/924 and 1450/1449

It can be factored into the following superparticular ratios:

• 2640/2639 and 77441/77440
• 2737/2736 and 37962/37961
• 3249/3248 and 11914/11913
• 3367/3366 and 10557/10556
• 3510/3509 and 9361/9360
• 3565/3564 and 8991/8990
• 3626/3625 and 8625/8624
• 3774/3773 and 7889/7888

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament viljevismic. Using the 2.3.11.23.29.37 subgroup leads to the rank-5 temperament viljevic.

Viljevismic

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37

Comma list: 2553/2552

Mapping:

[⟨	1	1	2	2	3	3	4	4	4	4	4	5	],
⟨	0	1	0	0	0	0	0	0	0	0	0	-1	],
⟨	0	0	1	0	0	0	0	0	0	0	0	0	],
⟨	0	0	0	1	0	0	0	0	0	0	0	0	],
⟨	0	0	0	0	1	0	0	0	0	0	0	1	],
⟨	0	0	0	0	0	1	0	0	0	0	0	0	],
⟨	0	0	0	0	0	0	1	0	0	0	0	0	],
⟨	0	0	0	0	0	0	0	1	0	0	0	0	],
⟨	0	0	0	0	0	0	0	0	1	0	0	-1	],
⟨	0	0	0	0	0	0	0	0	0	1	0	1	],
⟨	0	0	0	0	0	0	0	0	0	0	1	0	]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.935, ~5/4 = 386.314, ~7/4 = 968.826, ~11/8 = 551.413, ~13/8 = 840.528, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.112, ~29/16 = 1029.764, ~31/16 = 1145.036

Viljevic

Subgroup: 2.3.11.23.29.37

Comma list: 2553/2552

Mapping:

[⟨	1	1	3	4	4	5	],
⟨	0	1	0	0	0	-1	],
⟨	0	0	1	0	0	1	],
⟨	0	0	0	1	0	-1	],
⟨	0	0	0	0	1	1	]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.935, ~11/8 = 551.413, ~23/16 = 628.112, ~29/16 = 1029.764

Optimal ET sequence: 5i, 7ijj, 7, 10i, 12el, 14, 15, 17, 29, 31j, 46j, 48, 111, 128, 159, 176, 224, 248, 311, 359, 735, 783, 812, 860, 1171, 1219, 2614il, 2973il

Etymology

This comma was named by Francium in 2024. It refers to 2553 Viljev, which in turn was named after Mikhail Anatolyevich Vilyev, a Russian astronomer.

See also

• Unnoticeable comma
• List of superparticular intervals