3627/3626

3627/3626, the sayersisma, is a 37-limit superparticular comma of about 0.48 cents.

Interval information

Ratio	3627/3626
Subgroup monzo	2.3.7.13.31.37 [-1 2 -2 1 1 -1⟩
Size in cents	0.4773843 ¢
Name	sayersisma
Color name	37u31o3orr-3 thisuthiwothoruru negative 3rd
FJS name	[math]\displaystyle{ \text{m}{-2}^{13,31}_{7,7,37} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	23.6487
Weil norm (log2 max(n, d))	23.6491
Wilson norm (sopfr(nd))	103
Comma size	unnoticeable
Open this interval in xen-calc

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 186/185 and 196/195
• 260/259 and 280/279
• 589/588 and 703/702
• 741/740 and 931/930
• 806/805 and 1036/1035
• 1296/1295 and 2016/2015

It can be factored into the following superparticular ratios:

• 3774/3773 and 93093/93092
• 4901/4900 and 13950/13949
• 5440/5439 and 10881/10880

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament sayersismic. Using the 2.3.7.13.31.37 subgroup leads to the rank-5 temperament sayersic.

Sayersic

Subgroup: 2.3.7.13.31.37

Comma list: 3627/3626

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.933, ~7/4 = 968.896, ~13/8 = 840.467, ~31/16 = 1144.926

Optimal ET sequence: 5f, 7, 8d, 9kl, 10k, 12fk, 14fl, 14, 17l, 17k, 19, 26, 27, 36l, 53, 63, 67, 75, 77, 94, 130, 224, 301, 328, 383, 458, 477, 607, 1308, 1542, 1636, 2243, 5951l

Badness (Sintel): 0.046

Etymology

This comma was named by Francium in 2025. It refers to 3627 Sayers, the asteroid, which in turn was named after Dorothy L. Sayers, a British author.

See also

• Unnoticeable comma
• List of superparticular intervals