575/574

Interval information

Ratio	575/574
Subgroup monzo	2.5.7.23.41 [-1 2 -1 1 -1⟩
Size in cents	3.013463¢
Name	renatisma
Color name	41u23oryy1 fowutwethoruyoyo unison
FJS name	[math]\displaystyle{ \text{d}{-2}^{5,5,23}_{7,41} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	18.3323
Weil height (log2 max(n, d))	18.3348
Wilson height (sopfr(nd))	83
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.28261 bits
Comma size	unnoticeable
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575/574, the renatisma, is a 41-limit superparticular interval superparticular comma of about 3.0 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 165/164 and 231/230
• 225/224 and 369/368
• 253/252 and 451/450

It can be factored into the following superparticular ratios:

• 576/575 and 330625/330624
• 589/588 and 24150/24149
• 616/615 and 8625/8624
• 621/620 and 7750/7749
• 625/624 and 7176/7175
• 736/735 and 2625/2624
• 780/779 and 2185/2184
• 897/896 and 1600/1599
• 925/924 and 1518/1517

Temperaments

Tempering out this comma in the full 41-limit leads to the rank-12 temperament renatismic. Using the 2.5.7.23.41 subgroup leads to the rank-4 temperament renatic.

Renatic

Subgroup: 2.5.7.23.41

Comma list: 575/574

Mapping:

[⟨	1	2	2	4	5	],
⟨	0	1	0	0	2	],
⟨	0	0	1	0	-1	],
⟨	0	0	0	1	1	]]

Optimal tuning (CTE): ~ 2 = 1\1, ~5/4 = 385.900, ~7/4 = 969.128, ~23/16 = 627.490

Optimal ET sequence: 4, 6, 10m, 15m, 18im, 19, 21, 25, 31, 56, 74m, 78, 84, 109, 249, 358, 432m, 541m, 650m

Badness (Sintel): 0.045

Etymology

This comma was named by Francium in 2025. It refers to 575 Renate, the asteroid. The name's origin is unknown, it may be inspired by the asteroid's provisional designation, containing the letters "RE".

See also

• Unnoticeable comma
• List of superparticular intervals