Joshuavoisma

Interval information

Ratio	25025/25024
Factorization	2-6 × 52 × 7 × 11 × 13 × 17-1 × 23-1
Monzo	[-6 0 2 1 1 1 -1 0 -1⟩
Size in cents	0.06918156¢
Name	joshuavoisma
Color name	23u17u3o1ozyy-2 twethusutholozoyoyo negative 2nd
FJS name	[math]\displaystyle{ \text{P1}^{5,5,7,11,13}_{17,23} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	29.2221
Weil norm (log2 max(n, d))	29.2222
Wilson norm (sopfr(nd))	93
Comma size	unnoticeable
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25025/25024, the joshuavoisma, is a 23-limit superparticular comma of about 0.069 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 273/272 and 276/275
• 385/384 and 391/390
• 715/714 and 736/735
• 1225/1224 and 1288/1287
• 4225/4224 and 5083/5082
• 5985/5984 and 7866/7865

It can be factored into following superparticular commas:

• 27456/27455 and 282625/282624
• 28561/28560 and 202125/202124
• 31213/31212 and 126225/126224
• 37180/37179 and 76545/76544

Temperaments

Tempering out this comma in the full 23-limit leads to the rank-8 temperament joshuavoismic. Using the 2.5.7.11.13.17.23 subgroup leads to the rank-6 temperament joshuavoic.

Joshuavoismic

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 25025/25024

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.955, ~5/4 = 386.306, ~7/4 = 968.820, ~11/8 = 551.309, ~13/8 = 840.517, ~17/16 = 104.968, ~19/16 = 297.513

Optimal ET sequence: 6fhi, 7dghi, 8dgghhi, 9i, 10, 10h, 12e, 15f, 15g, 19eghi, 22i, 22fh, 24, 26i, 27egi, 31h, 31, 41fg, 41, 43, 46, 50, 58ghi, 62, 68, 72hi, 72i, 94, 118, 121i, 137, 140, 152fg, 183, 190g, 193, 217, 270, 311, 373g, 431, 487, 494, 494h, 525, 566g, 581, 718, 742i, 814, 935, 954h, 1106, ...

Joshuavoic

Subgroup: 2.5.7.11.13.17.23

Comma list: 25025/25024

Mapping:

[⟨	1	2	2	3	3	4	2	],
⟨	0	1	0	0	0	0	2	],
⟨	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, ~5/4 = 386.306, ~7/4 = 968.820, ~11/8 = 551.309, ~13/8 = 840.517, ~17/16 = 104.968

Optimal ET sequence: 4, 6eg, 6, 9i, 10eg, 10, 12fgi, 13i, 15f, 16, 26i, 28g, 31, 37i, 43, 46, 56, 66gi, 68, 72i, 74g, 78, 93, 109g, 121i, 124, 233, 261, 264, 307, 357, 385, 457, 581, 690, 764, 814, 1075, 1199, 1339, 1702, 1796, 1889, 1963, 2460, 2777, 2917, 4116, 7033

Etymology

The name joshuavoisma was named by Francium in 2024. It refers to 25025 Joshuavo, the asteroid.

See also

• Unnoticeable comma
• List of superparticular intervals