513/512
| 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, reduced harmonic |
| Tenney height (log2 nd) | 18.0028 |
| Weil height (log2 max(n, d)) | 18.0056 |
| Wilson height (sopfr (nd)) | 46 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.30567 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.
Sagittal notation
In the Sagittal system, this comma (possibly tempered) is represented by the sagittal and is called the 19 schisma, or 19s for short, because the simplest interval it notates is 19/1 (equiv 19/16), as for example in D-F . The downward version is called 1/19s or 19s down and is represented by .