Jouvisma

Interval information

Ratio	77441/77440
Factorization	2-7 × 5-1 × 7 × 11-2 × 13 × 23 × 37
Monzo	[-7 0 -1 1 -2 1 0 0 1 0 0 1⟩
Size in cents	0.022355667¢
Name	jouvisma
Color name	37o23o3o1uuzg3 thisotwethotholuluzogu 3rd
FJS name	[math]\text{P1}^{7,13,23,37}_{5,11,11}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	32.4816
Weil height (log2 max(n, d))	32.4816
Wilson height (sopfr(nd))	121
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.19983 bits
Comma size	unnoticeable
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77441/77440, the jouvisma, is a 37-limit superparticular comma of about 0.022 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 481/480 and 484/483
• 3367/3366 and 3520/3519
• 9361/9360 and 10648/10647

It can be factored into following superparticular commas:

• 82621/82620 and 1235169/1235168
• 123201/123200 and 208495/208494

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament jouvismic. Using the 2.5.7.11.13.23.37 subgroup leads to the rank-6 temperament jouvic.

Jouvismic

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37

Comma list: 77441/77440

Mapping:

[⟨	1	1	2	2	3	3	4	4	4	4	4	6	],
⟨	0	1	0	0	0	0	0	0	0	0	0	0	],
⟨	0	0	1	0	0	0	0	0	0	0	0	1	],
⟨	0	0	0	1	0	0	0	0	0	0	0	-1	],
⟨	0	0	0	0	1	0	0	0	0	0	0	2	],
⟨	0	0	0	0	0	1	0	0	0	0	0	-1	],
⟨	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	0	],
⟨	0	0	0	0	0	0	0	0	0	0	1	0	]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.955, ~5/4 = 386.315, ~7/4 = 968.824, ~11/8 = 551.322, ~13/8 = 840.525, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.271, ~29/16 = 1029.577, ~31/16 = 1145.036

Jouvic

Subgroup: 2.5.7.11.13.23.37

Comma list: 77441/77440

Mapping:

[⟨	1	2	2	3	3	4	6	],
⟨	0	1	0	0	0	0	1	],
⟨	0	0	1	0	0	0	-1	],
⟨	0	0	0	1	0	0	2	],
⟨	0	0	0	0	1	0	-1	],
⟨	0	0	0	0	0	1	-1	]]

Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 386.315, ~7/4 = 968.824, ~11/8 = 551.322, ~13/8 = 840.525, ~23/16 = 628.271

Optimal ET sequence: 4, 6l, 8cefl, 8d, 9, 12f, 13, 15, 16, 21l, 25f, 29, 31, 37, 47, 58i, 60el, 62, 63, 72, 78, 80, 84, 103l, 109, 124, 187, 224, 233, 311, 348, 373, 457, 497, 515, 544, 560, 581, 655, 684, 764, 888, 1448, 1469, 1572, 2153, 2196, 2336, 2460, 2544, 3432, 3992, 4116, 7033, 7548, 7921, 9120, 9577, 10465

Etymology

This comma was named by Francium in 2024. It refers to 77441 Jouve, the asteroid, which in turn was named after Jacques Jouve, a person, who was involved in the construction of the Observatory of Saint-Veran.

See also

• Unnoticeable comma
• List of superparticular intervals