667/666

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667/666, the denisisma, is a 37-limit superparticular comma of about 2.6 cents.

Interval information
Ratio 667/666
Subgroup monzo 2.3.23.29.37 [-1 -2 1 1 -1
Size in cents 2.597501¢
Name denisisma
Color name 37u29o23o1
thisutwenotwetho unison
FJS name [math]\displaystyle{ \text{P1}^{23,29}_{37} }[/math]
Special properties superparticular,
reduced
Tenney norm (log2 nd) 18.7609
Weil norm (log2 max(n, d)) 18.7631
Wilson norm (sopfr(nd)) 97
Comma size unnoticeable
Open this interval in xen-calc

Commatic relationships

This comma is the difference between the following superparticular pairs:

It can be factored into the following superparticular ratios:

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament denisismic. Using the 2.3.23.29.37 subgroup leads to the rank-4 temperament denisic.

Denisic

Subgroup: 2.3.23.29.37

Comma list: 667/666

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.116, ~23/16 = 627.620, ~29/16 = 1028.823

Optimal ET sequence3, 5, 7i, 9ijl, 10, 12l, 17, 19, 22, 29, 48, 77, 99, 147, 176, 224, 323, 547, 706ij

Badness (Sintel): 0.036

Etymology

This comma was named by Francium in 2025. It refers to 667 Denise, the asteroid. The origin of the asteroid's name is unknown, it could be inspired by its provisional designation, containing the letters "DN".

See also