Vuillafansisma

Interval information

Ratio	25840/25839
Factorization	24 × 3-4 × 5 × 11-1 × 17 × 19 × 29-1
Monzo	[4 -4 1 0 -1 0 1 1 0 -1⟩
Size in cents	0.06699952¢
Name	vuillafansisma
Color name	29u19o17o1uy2 twenunosoluyo 2nd
FJS name	[math]\text{m2}^{5,17,19}_{11,29}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	29.3146
Weil height (log2 max(n, d))	29.3146
Wilson height (sopfr(nd))	101
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.19986 bits
Comma size	unnoticeable
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25840/25839, the vuillafansisma is a 29-limit superparticular comma of about 0.067 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 595/594 and 609/608
• 760/759 and 783/782
• 1216/1215 and 1276/1275
• 2080/2079 and 2262/2261
• 12376/12375 and 23751/23750

It can be factored into following superparticular commas:

• 27000/26999 and 601426/601425
• 28900/28899 and 244036/244035
• 30625/30624 and 165376/165375
• 30856/30855 and 158950/158949

Temperaments

Tempering out this comma in the full 29-limit leads to the rank-9 temperament vuillafansismic. Using the 2.3.5.11.17.19.29 subgroup leads to the rank-6 temperament vuillafansic.

Vuillafansismic

Subgroup: 2.3.5.7.11.13.17.19.23.29

Comma list: 25840/25839

Mapping:

[⟨	1	1	2	2	3	3	4	4	4	7	],
⟨	0	1	0	0	0	0	0	0	0	-4	],
⟨	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	-1	],
⟨	0	0	0	0	0	1	0	0	0	0	],
⟨	0	0	0	0	0	0	1	0	0	1	],
⟨	0	0	0	0	0	0	0	1	0	1	],
⟨	0	0	0	0	0	0	0	0	1	0	]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.961, ~5/4 = 386.311, ~7/4 = 968.826, ~11/8 = 551.325, ~13/8 = 840.528, ~17/16 = 104.946, ~19/16 = 297.503, ~23/16 = 628.274

Vuillafansic

Subgroup: 2.3.5.11.17.19.29

Comma list: 25840/25839

Mapping:

[⟨	1	1	2	3	4	4	7	],
⟨	0	1	0	0	0	0	-4	],
⟨	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 = 701.961, ~5/4 = 386.311, ~11/8 = 551.325, ~17/16 = 104.946, ~19/16 = 297.503

Optimal ET sequence: 5eghj, 7ghjj, 7g, 10ej, 12eh, 12, 15g, 19egh, 22j, 22h, 24, 34h, 39gj, 41, 46hj, 50, 53g, 65, 87, 99e, 118, 183, 205, 270, 349gh, 354, 388, 422, 472, 487, 559, 653, 677, 836, 1323, 1395, 1513, 1783, 2000, 2836, 3395, 4231, 4619, 5178, 6014, 8014

Etymology

The vuillafansisma was named by Francium in 2024. It refers to the postal code of Vuillafans, France.

See also

• Unnoticeable comma
• List of superparticular intervals