Magic comma: Difference between revisions

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TallKite (talk | contribs)
autopatrolled, Sysops
3,990 edits
small correction - it's not unique that a small comma maps to 100¢ in 12-edo.
Plumtree (talk | contribs)
autopatrolled
1,976 edits
m Normalising usage of Infobox Interval
Line 1: Line 1:
{{Infobox Interval
{{Infobox Interval
| JI glyph =
| Ratio = 3125/3072
| Ratio = 3125/3072
| Monzo = -10 -1 5
| Name = magic comma, small diesis
| Cents = 29.61357
| Name = magic comma, <br>small diesis
| Color name = Ly<sup>5</sup>-2, Laquinyo comma
| Color name = Ly<sup>5</sup>-2, Laquinyo comma
| FJS name =
| Comma = yes
| Sound =  
}}
}}


Line 21: Line 17:
* [[Small comma]]
* [[Small comma]]


[[Category:5-limit]]
[[Category:Small commas]]
[[Category:Medium commas]]
[[Category:Magic]]
[[Category:Magic]]

Revision as of 17:44, 25 October 2022

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
Color name Ly5-2, Laquinyo comma
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
Comma size small
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.

In 12edo, instead of being tempered out, it's blown up to a whole semitone - five 5/4s make a minor thirteenth (20 steps), while 3/1 is a perfect tweltfth (19 steps).

Temperaments

Tempering it out leads to 5-limit magic temperament.

See also

Retrieved from "https://en.xen.wiki/index.php?title=Magic_comma&oldid=98444"