666/665

Interval information

Ratio	666/665
Factorization	2 × 32 × 5-1 × 7-1 × 19-1 × 37
Monzo	[1 2 -1 -1 0 0 0 -1 0 0 0 1⟩
Size in cents	2.601404¢
Name	beastisma
Color name	37o19urg1 thisonurugu unison
FJS name	[math]\displaystyle{ \text{m}{-2}^{37}_{5,7,19} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	18.7566
Weil height (log2 max(n, d))	18.7588
Wilson height (sopfr(nd))	76
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.26198 bits
Comma size	unnoticeable
S-expression	S36 × S37
Open this interval in xen-calc

666/665, the beastisma, is a 37-limit superparticular comma of about 2.6 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 36/35 and 38/37
• 96/95 and 112/111
• 111/110 and 133/132
• 148/147 and 190/189

It can be factored into the following superparticular ratios:

• 676/675 and 44955/44954
• 704/703 and 12321/12320
• 729/728 and 7696/7695
• 736/735 and 6993/6992
• 837/836 and 3256/3255
• 851/850 and 3060/3059
• 925/924 and 2376/2375
• 1036/1035 and 1863/1862
• 1184/1183 and 1521/1520
• 1296/1295 and 1369/1368
• 1331/1330 and 1332/1331

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament beastismic. Using the 2.3.5.7.19.37 subgroup leads to the rank-5 temperament beastic.

Beastic

Subgroup: 2.3.5.7.19.37

Comma list: 666/665

Mapping:

[⟨	1	1	2	2	4	5	],
⟨	0	1	0	0	0	-2	],
⟨	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 = 701.764, ~5/4 = 386.518, ~7/4 = 969.125, ~19/16 = 298.198

Optimal ET sequence: 5, 7dhll, 7d, 7l, 8d, 8dhhll, 9, 10h, 12, 19hl, 19, 22h, 26, 27, 41l, 50, 53, 72, 99, 130, 152, 202, 282, 301, 354, 583, 624l, 937dh

Badness (Sintel): 0.156

Etymology

This comma was named by Francium in 2025. 666 is referred as the number of the Beast.

See also

• Unnoticeable comma
• List of superparticular intervals