57/56

Interval information

Ratio	57/56
Factorization	2-3 × 3 × 7-1 × 19
Monzo	[-3 1 0 -1 0 0 0 1⟩
Size in cents	30.64211¢
Name	hendrix comma
FJS name	[math]\displaystyle{ \text{P1}^{19}_{7} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	11.6402
Weil height (log2 max(n, d))	11.6658
Wilson height (sopfr(nd))	35
Open this interval in xen-calc

57/56 is a superparticular interval of about 30.6¢ which makes the difference between 4/3 (about 498¢) and 19/14 (about 528.7¢) in 19-limit Just_intonation; it is also the difference between 19/16 and 7/6. It is also called the hendrix comma, since by tempering it out, one can build an 8:10:12:19 hendrix chord, which has steps of 5/4-7/5-4/3. Patent vals which temper out the hendrix comma include those from 9, 10, 12, 16, 21, 22 and 26 edo.

57/56 is a comma of the 2.3.7.19 subgroup, and on that subgroup, patent vals tempering it out include those from 9, 12, 14, 17 and 26. The comma defines a rank three temperament on this subgroup.

See: List of Superparticular Intervals