513/512: Difference between revisions

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Boethius was roman not greek
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== Temperaments ==
== Temperaments ==
: ''"Boethius" redirects here. For the ancient Greek platonist, see [[Wikipedia: Boethius]].''
: ''"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]].  
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]].  

Revision as of 13:30, 17 April 2024

Interval information
Ratio 513/512
Subgroup monzo 2.3.19 [-9 3 1
Size in cents 3.378019¢
Names undevicesimal comma,
undevicesimal schisma,
Boethius' comma
Color name L19o1, lano 1sn,
Lano comma
FJS name [math]\displaystyle{ \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
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.

See also