Magic comma: Difference between revisions

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{{Infobox Interval

~~| JI glyph =~~

| Ratio = 3125/3072

~~| Monzo = -10 -1 5~~

| Name = magic comma, small diesis

~~| Cents = 29.61357~~

| Name = magic comma, ~~ ~~small diesis

| Color name = Ly5-2, Laquinyo comma

| ~~FJS name =~~

| Comma = yes

~~| 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)5/3.

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, 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 ==

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* [[Small comma]]

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

~~[[Category:Small commas]]~~

~~[[Category:Medium commas]]~~

[[Category:Magic]]

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

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| JI glyph =
 | 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
-| FJS name =
+| Comma = yes
-| 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.
+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 ==
@@ Line 19: / Line 17: @@
 * [[Small comma]]
-[[Category:5-limit]]
-[[Category:Small commas]]
-[[Category:Medium commas]]
 [[Category:Magic]]
+[[Category:Commas named for their regular temperament properties]]