6656/6655

Interval information

Ratio	6656/6655
Factorization	29 × 5-1 × 11-3 × 13
Monzo	[9 0 -1 0 -3 1⟩
Size in cents	0.2601208¢
Name	jacobin comma
Color name	thotrilu-agu comma
FJS name	[math]\displaystyle{ \text{m2}^{13}_{5,11,11,11} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	25.4007
Weil height (log2 max(n, d))	25.4009
Wilson height (sopfr(nd))	69
Comma size	unnoticeable
Open this interval in xen-calc

6656/6655, the jacobin comma, apparently named by Gene Ward Smith in 2014, is a 13-limit (also 2.5.11.13 subgroup) superparticular interval of about 0.26 ¢. It is the difference between a stack of three 11/8 superfourths and one 13/10 naiadic plus an octave. In terms of commas, it is the difference between 364/363 and 385/384, between 2080/2079 and 3025/3024 as well as between 4096/4095 and 10648/10647. In the 17-limit, it factors neatly into 12376/12375 × 14400/14399.

Temperaments

By tempering it out, the jacobin temperament is defined. Perhaps most remarkably, 1789edo is an edo that supports the jacobin temperament. You may find a list of good JI-approximating edos that support this temperament below. Although it is more rational to use such edos for this temperament, 1789edo has a unique position due to its number of steps being a hallmark year of the French Revolution.

Subgroup: 2.3.5.7.11.13

Mapping:
[⟨1 0 0 0 0 -9],
⟨0 1 0 0 0 0],
⟨0 0 1 0 0 1],
⟨0 0 0 1 0 0],
⟨0 0 0 0 1 3]]

Mapping generators: ~2, ~3, ~5, ~7, ~11

See also

• 13-limit
• Unnoticeable comma
• List of superparticular intervals