Magic comma: Difference between revisions

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The '''magic comma''' or '''small diesis''' is the interval '''3125/3072''' of 29.614 [[cent]]s. It is the amount by which five major thirds ([[5/4]]) exceeds the twelfth, or "[[tritave]]"; in other words (5/4)^5/3. Tempering it out leads to [[Magic family #Five limit magic|5-limit magic temperament]].
{{Infobox Interval
| JI glyph =
| Ratio = 3125/3072
| Monzo = -10 -1 5
| Cents = 29.61357
| Name = magic comma, <br>small diesis
| Color name =
| FJS name =
| Sound =
}}
 
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]].


[[Category:5-limit]]
[[Category:5-limit]]

Revision as of 17:05, 8 November 2020

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. Tempering it out leads to 5-limit magic temperament.

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