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
30.64211¢
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{nd}[/math])
~4.46264 bits
Comma size
medium
open this interval in xen-calc
| Interval information |
Noru comma
reduced
(Shannon, [math]\sqrt{nd}[/math])
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.