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
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6656/6655, the jacobin comma, is a 13-limit (also 2.5.11.13 subgroup) superparticular interval of about 0.26012 cents. 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.

Temperaments

By tempering it out, the jacobin temperament is defined. Perhaps most remarkably, 1789edo is an edo that supports the jacobin temperament. Simpler edos that support this temperament include 37, 72, 135, 159, 183, 194, 320. On the larger end, the list includes edos like 3395 and 3125. Although it is more rational to use JI-approximating edos like the above mentioned for this temperament, 1789edo has a unique position due to its number of steps being a hallmark year of the French Revolution.

See also

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