Aunusisma

Interval information

Ratio	1480/1479
Factorization	23 × 3-1 × 5 × 17-1 × 29-1 × 37
Monzo	[3 -1 1 0 0 0 -1 0 0 -1 0 1⟩
Size in cents	1.170148¢
Name	aunusisma
Color name	37o29u17uy1 thisotwenusuyo unison
FJS name	[math]\text{d}{-2}^{5,37}_{17,29}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	21.0618
Weil height (log2 max(n, d))	21.0628
Wilson height (sopfr(nd))	97
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.21187 bits
Comma size	unnoticeable
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1480/1479, the aunusisma, is a 37-limit superparticular ratio of about 1.2 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 222/221 and 261/260
• 320/319 and 408/407
• 407/406 and 561/560

It can be factored into the following superparticular intervals:

• 1520/1519 and 56203/56202
• 1540/1539 and 37962/37961
• 1596/1595 and 20350/20349
• 1625/1624 and 16576/16575
• 1665/1664 and 13312/13311
• 1702/1701 and 11340/11339
• 2109/2108 and 4960/4959
• 2176/2175 and 4625/4624
• 2500/2499 and 3626/3625
• 2553/2552 and 3520/3519
• 2640/2639 and 3367/3366

Temperaments

Tempering out this comma in the full 37-limit leads to the 11-rank temperament aunusismic. Using the 2.3.5.17.29.37 subgroup leads to the rank-5 temperament aunusic.

Aunusismic

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37

Comma list: 1480/1479

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.994, ~5/4 = 386.230, ~7/4 = 968.826, ~11/8 = 551.318, ~13/8 = 840.528, ~17/16 = 105.215, ~19/16 = 297.513, ~23/16 = 628.274, ~29/16 = 1029.944, ~31/16 = 1145.036

Aunusic

Subgroup: 2.3.5.17.29.37

Comma list: 1480/1479

Mapping:

[⟨	1	1	2	4	4	4	],
⟨	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 = 701.994, ~5/4 = 386.230, ~17/16 = 105.215, ~29/16 = 1029.944

Optimal ET sequence: 5g, 5gjl, 7g, 10j, 12l, 19gl, 19, 22, 34, 46j, 60l, 65, 84l, 99, 106, 159, 171, 205, 388, 559, 764j, 1277, 1482

Etymology

This comma was named by Francium in 2024. It refers to 1480 Aunus, the asteroid, which in turn was named after the Karelian town Olonets (Finnish: Aunus).

See also

• Unnoticeable comma
• List of superparticular intervals