Shchedrinisma

Interval information

Ratio	4625/4624
Subgroup monzo	2.5.17.37 [-4 3 -2 1⟩
Size in cents	0.3743613¢
Name	shchedrinisma
Color name	37o17uuy3-2 thisosusutriyo negative 2nd
FJS name	[math]\text{ddd}{-3}^{5,5,5,37}_{17,17}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	24.3502
Weil height (log2 max(n, d))	24.3505
Wilson height (sopfr(nd))	94
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.20041 bits
Comma size	unnoticeable
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4625/4624, the shchedrinisma, is a 37-limit superparticular comma of about 0.37 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 375/374 and 408/407
• 925/924 and 1156/1155
• 1665/1664 and 2601/2600

It can be factored into following superparticular commas:

• 4693/4692 and 319125/319124
• 4761/4760 and 161875/161874
• 5985/5984 and 20350/20349
• 6325/6324 and 17205/17204

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament shchedrinismic. Using the 2.5.17.37 subgroup leads to the rank-3 temperament shchedrinic.

Shchedrinismic

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37

Comma list: 4625/4624

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.955, ~5/4 = 386.271, ~7/4 = 968.826, ~11/8 = 551.318, ~13/8 = 840.528, ~17/16 = 105.043, ~19/16 = 297.513, ~23/16 = 628.274, ~29/16 = 1029.577, ~31/16 = 1145.036

Shchedrinic

Subgroup: 2.5.17.37

Comma list: 4625/4624

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 386.271, ~17/16 = 105.043

Optimal ET sequence: 4, 5g, 6l, 7g, 9, 16, 22, 25, 34, 56, 81, 90, 115, 205, 320, 3315, 3635, 3955, 4275, 4595, 4915, 5235, 5555l, 5875l, 6195l, 6754l, 7074l, 7394l, 7714l

Etymology

The shchedrinisma was named by Francium in 2024. It refers to 4625 Shchedrin, the asteroid. Which was in turn named after a Russian composer.

See also

• Unnoticeable comma
• List of superparticular intervals