6656/6655
Ratio | 6656/6655 |
Factorization | 2^{9} × 5^{-1} × 11^{-3} × 13 |
Monzo | [9 0 -1 0 -3 1⟩ |
Size in cents | 0.26012081¢ |
Name | jacobin comma |
Color name | Thotrilu-agu comma |
FJS name | [math]\text{m2}^{13}_{5,11,11,11}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} nd) | 25.4007 |
Weil height (log_{2} max(n, d)) | 25.4009 |
Wilson height (sopfr (nd)) | 69 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.39778 bits |
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
Optimal GPV sequence: 9, 15, 22, 26, 31f, 37, 39df, 41, 46, 63, 72, 87, 111, 152f, 183, 198, 224, 270, 494, 764, 1012, 1084, 1236, 1506, 2814, 2901, 3125, 3395, 8026e, 8296e, 11421e, 11691e, 12927e, 13421e, 16322ee, 16816ee