513/512: Difference between revisions

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m Normalising usage of Infobox Interval
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{{Infobox Interval
{{Infobox Interval
| Icon =
| Name = undevicesimal comma, undevicesimal schisma, Boethius' comma
| Ratio = 513/512
| Comma = yes
| Monzo = -9 3 0 0 0 0 0 1
| Cents = 3.37802
| Name = undevicesimal comma, <br>undevicesimal schisma, <br>Boethius' comma
| Color name =
| FJS name = P1<sup>19</sup>
| Sound =  
}}
}}


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* [[List of superparticular intervals]]
* [[List of superparticular intervals]]


[[Category:19-limit]]
[[Category:Superparticular]]
[[Category:Unnoticeable commas]]
[[Category:Boethius]]
[[Category:Boethius]]

Revision as of 16:11, 25 October 2022

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
FJS name [math]\displaystyle{ \text{P1}^{19} }[/math]
Special properties superparticular,
reduced,
reduced harmonic
Tenney norm (log2 nd) 18.0028
Weil norm (log2 max(n, d)) 18.0056
Wilson norm (sopfr(nd)) 46
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.

See also