513/512
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| Ratio | 513/512 |
| Subgroup monzo | 2.3.19 [-9 3 1⟩ |
| Size in cents | 3.3780187¢ |
| Names | undevicesimal comma, undevicesimal schisma, Boethius' comma |
| Color name | L19o1, Lano comma |
| FJS name | [math]\text{P1}^{19}[/math] |
| Special properties | superparticular, reduced, reduced harmonic |
| Tenney height (log2 n⋅d) | 18.0028 |
| Weil height (max(n, d)) | 513 |
| Benedetti height (n⋅d) | 262656 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.44811 bits |
| Comma size | unnoticeable |
| open this interval in xen-calc | |
513/512, the undevicesimal comma, undevicesimal schisma or Boethius' comma, is a 19-limit (also 2.3.19 subgroup) unnoticeable comma. It is the amount by which 19/16 exceeds the Pythagorean minor third (32/27). By tempering it out is defined the boethius temperament, which enables the boethius chords. It is significant in Functional Just System and Helmholtz-Ellis notation as the formal comma to translate a Pythagorean interval to a nearby undevicesimal interval.