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 1sn, Lano comma |
| FJS name | [math]\text{P1}^{19}[/math] |
| Special properties | superparticular, reduced |
| Tenney height (log2 nd) | 18.0028 |
| Weil height (log2 max(n, d)) | 18.0056 |
| Wilson height (sopfr (nd)) | 46 |
| 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 an unnoticeable 19-limit (also 2.3.19 subgroup) comma. It is the amount by which 19/16 exceeds the Pythagorean minor third (32/27). 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.
Temperaments
- "Boethius" redirects here. For the medieval Roman platonist, see Wikipedia: Boethius.
By tempering out this comma in the 19-limit is defined the boethius temperament, or in the 2.3.19 subgroup, the boethian temperament. Both enables the boethius chords.