57/56
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Ratio | 57/56 |
Factorization | 2^{-3} × 3 × 7^{-1} × 19 |
Monzo | [-3 1 0 -1 0 0 0 1⟩ |
Size in cents | 30.642111¢ |
Name | hendrix comma |
Color name | 19or1, noru 1sn, Noru comma |
FJS name | [math]\text{P1}^{19}_{7}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} nd) | 11.6402 |
Weil height (log_{2} max(n, d)) | 11.6658 |
Wilson height (sopfr (nd)) | 35 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.44034 bits |
Comma size | medium |
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 8:10:14:19 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.