3510/3509

Interval information
Ratio	3510/3509
Factorization	2 × 33 × 5 × 11-2 × 13 × 29-1
Monzo	[1 3 1 0 -2 1 0 0 0 -1⟩
Size in cents	0.4932993 ¢
Name	veederisma
Color name	29u3o1uuy1 ; twenutholuluyo unison
FJS name	[math]\displaystyle{ \text{A1}^{5,13}_{11,11,29} }[/math]
Special properties	superparticular,; reduced
Tenney norm (log2 nd)	23.5541
Weil norm (log2 max(n, d))	23.5545
Wilson norm (sopfr(nd))	80
Comma size	unnoticeable
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3510/3509, the veederisma, is a 29-limit superparticular comma of about 0.49 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

It can be factored into the following superparticular commas:

Temperaments

Tempering out this comma in the full 29-limit leads to the rank-9 temperament veederismic. Using the 2.3.5.11.13.29 subgroup leads to the rank-5 temperament veederic.

Veederismic

Subgroup: 2.3.5.7.11.13.17.19.23.29

Comma list: 3510/3509

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.922, ~5/4 = 386.290, ~7/4 = 968.826, ~11/8 = 551.422, ~13/8 = 840.468, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.274

Veederic

Subgroup: 2.3.5.11.13.29

Comma list: 3510/3509

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.922, ~5/4 = 386.290, ~11/8 = 551.422, ~13/8 = 840.468

Optimal ET sequence: 7fjj, 7, 14cfjj, 15f, 15jj, 16j, 17c, 22, 24, 31, 34, 41, 53j, 58, 65, 80, 87, 145j, 159, 183, 224, 270, 311, 407, 494, 901, 1395, 2296, 3749e, 4243ej, 5144ej, 6045ej, 6539ej

Etymology

The veederisma was named by Francium in 2024. It refers to 3510 Veeder, the asteroid. Which was in turn named after an American astronomer.