31/1
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| Ratio | 31/1 |
| Subgroup monzo | 31 [1⟩ |
| Size in cents | 5945.0356¢ |
| Name | 31st harmonic |
| FJS name | [math]\text{M35}^{31}[/math] |
| Special properties | harmonic |
| Tenney height (log2 nd) | 4.9542 |
| Weil height (log2 max(n, d)) | 9.90839 |
| Wilson height (sopfr (nd)) | 31 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.94389 bits |
| open this interval in xen-calc | |
31/1, the 31st harmonic, is the harmonic past 30/1 and before 32/1. It is about four octaves and eleven semitones in size. Used in harmony, it sounds particularly wide: if the base note is F1, the higher note will be about E6. That is for all practical purposes beyond the range of choral music. It is however, the basis of 31-limit harmony, as many 31-limit intervals can be expressed as the difference between this and another harmonic.
See also
- 31/16 – its octave-reduced form