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 (log2 nd) | 11.6402 |
| Weil height (log2 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.