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

| Ratio = 3125/3072

| Name = magic comma, small diesis

| Color name = Ly<sup>5</sup>-2, Laquinyo comma

| Comma = yes

}}

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, the amount by which two chromatic semitones of 25/24 exceed a diatonic semitone of 16/15, and the amount by which 25/24 exceeds the lesser diesis of [[128/125]].

In 12edo, instead of being tempered out, it is inflated to a whole semitone—five 5/4s make a minor thirteenth (20 steps), while 3/1 is a perfect twelfth (19 steps). Similarly, 25/24 and 16/15 are both mapped to one semitone, making a stack of two 25/24s one semitone larger than 16/15, and 25/24 is mapped to one step while 128/125 is tempered out.

== 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:Small comma]]~~

~~[[Category:Medium comma]]~~

[[Category:Magic]]

[[Category:Commas named for their regular temperament properties]]

[[Category:~~Todo:expand~~]]

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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
+| Ratio = 3125/3072
+| Name = magic comma, small diesis
+| Color name = Ly<sup>5</sup>-2, Laquinyo comma
+| Comma = yes
+}}
+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, the amount by which two chromatic semitones of 25/24 exceed a diatonic semitone of 16/15, and the amount by which 25/24 exceeds the lesser diesis of [[128/125]].
+In 12edo, instead of being tempered out, it is inflated to a whole semitone—five 5/4s make a minor thirteenth (20 steps), while 3/1 is a perfect twelfth (19 steps). Similarly, 25/24 and 16/15 are both mapped to one semitone, making a stack of two 25/24s one semitone larger than 16/15, and 25/24 is mapped to one step while 128/125 is tempered out.
+== 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:Small comma]]
-[[Category:Medium comma]]
 [[Category:Magic]]
+[[Category:Commas named for their regular temperament properties]]
-[[Category:Todo:expand]]