Meranisma

Interval information

Ratio	3553/3552
Factorization	2-5 × 3-1 × 11 × 17 × 19 × 37-1
Monzo	[-5 -1 0 0 1 0 1 1 0 0 0 -1⟩
Size in cents	0.4873284¢
Name	meranisma
Color name	37u19o17o1o1 thisunosolo unison
FJS name	[math]\text{d2}^{11,17,19}_{37}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	23.5892
Weil height (log2 max(n, d))	23.5896
Wilson height (sopfr(nd))	97
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.2013 bits
Comma size	unnoticeable
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3553/3552, the meranisma, is a 37-limit superparticular comma of about 0.49 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 209/208 and 222/221
• 297/296 and 324/323
• 741/740 and 936/935
• 969/968 and 1332/1331
• 1444/1443 and 2432/2431
• 1666/1665 and 3136/3135

It can be factored into the following superparticular ratios:

• 3565/3564 and 1055241/1055240
• 3876/3875 and 42625/42624
• 4256/4255 and 21505/21504
• 5440/5439 and 10241/10240
• 5797/5796 and 9177/9176
• 7105/7104 and 7106/7105

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament meranismic. Using the 2.3.11.17.19.37 subgroup leads to the rank-5 temperament meranic.

Meranismic

Subgroup: 2.3.5.7.11.13.17.19.23.29

Comma list: 3553/3552

Mapping:

[⟨	1	1	2	2	3	3	4	4	4	4	4	5	],
⟨	0	1	0	0	0	0	0	0	0	0	0	-1	],
⟨	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	1	],
⟨	0	0	0	0	0	1	0	0	0	0	0	0	],
⟨	0	0	0	0	0	0	1	0	0	0	0	1	],
⟨	0	0	0	0	0	0	0	1	0	0	0	1	],
⟨	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 = 701.971, ~5/4 = 386.314, ~7/4 = 968.826, ~11/8 = 551.242, ~13/8 = 840.528, ~17/16 = 104.849, ~19/16 = 297.398, ~23/16 = 628.274, ~29/16 = 1029.577, ~31/16 = 1145.036

Meranic

Subgroup: 2.3.11.17.19.37

Comma list: 3553/3552

Mapping:

[⟨	1	1	3	4	4	5	],
⟨	0	1	0	0	0	-1	],
⟨	0	0	1	0	0	1	],
⟨	0	0	0	1	0	1	],
⟨	0	0	0	0	1	1	]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.971, ~11/8 = 551.242, ~17/16 = 104.849, ~19/16 = 297.398

Optimal ET sequence: 5ll, 5g, 7ghll, 7g, 8, 9, 10, 10hl, 12el, 14l, 17l, 17g, 22l, 22h, 24, 89, 104, 113, 128, 137, 152, 157, 159, 169l, 181, 183, 205, 207, 231, 311, 335, 388, 400, 412, 436, 525, 581, 605, 629, 836, 860, 1465, 1489, 2325, 3390, 3814gh, 4226egh, 4250egh, 5715egh

Etymology

This comma was named by Francium in 2024. It refers to 3553 Mera, the asteroid, which in turn was named after Maera, a daughter of Praetus.

See also

• Unnoticeable comma
• List of superparticular intervals