Magic comma: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Arseniiv (talk | contribs)
m infoboxified
+sectioning; +link
Line 10: Line 10:
}}
}}


The '''magic comma''' or '''small diesis''' is the interval '''3125/3072'''. It is the amount by which five major thirds ([[5/4]]) exceeds the twelfth, or [[tritave]]; in other words (5/4)<sup>5</sup>/3. Tempering it out leads to [[Magic family #Five limit magic|5-limit magic temperament]].
The '''magic comma''' or '''small diesis''' is the interval '''3125/3072'''. It is the amount by which five major thirds ([[5/4]]) exceeds the twelfth, or ''[[tritave]]''; in other words (5/4)<sup>5</sup>/3.  
 
== Temperaments ==
Tempering it out leads to [[Magic family #Five limit magic|5-limit magic temperament]].
 
== See also ==
* [[Magic family]], where it is tempered out
* [[Small comma]]


[[Category:5-limit]]
[[Category:5-limit]]
Line 16: Line 23:
[[Category:Medium comma]]
[[Category:Medium comma]]
[[Category:Magic]]
[[Category:Magic]]
[[Category:Todo:expand]]

Revision as of 13:28, 17 April 2021

Interval information
Ratio 3125/3072
Factorization 2-10 × 3-1 × 55
Monzo [-10 -1 5
Size in cents 29.61357¢
Names magic comma,
small diesis
FJS name [math]\displaystyle{ \text{dd}{-2}^{5,5,5,5,5} }[/math]
Special properties reduced
Tenney height (log2 nd) 23.1946
Weil height (log2 max(n, d)) 23.2193
Wilson height (sopfr(nd)) 48
Open this interval in xen-calc

The magic comma or small diesis is the interval 3125/3072. It is the amount by which five major thirds (5/4) exceeds the twelfth, or tritave; in other words (5/4)5/3.

Temperaments

Tempering it out leads to 5-limit magic temperament.

See also