Magic comma: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 3125/3072 | | Ratio = 3125/3072 | ||
| Name = magic comma, small diesis | |||
| Name = magic comma, | |||
| Color name = Ly<sup>5</sup>-2, Laquinyo comma | | 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 '''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 == | == Temperaments == | ||
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* [[Small comma]] | * [[Small comma]] | ||
[[Category:Magic]] | [[Category:Magic]] | ||
[[Category:Commas named for their regular temperament properties]] | |||
Latest revision as of 22:24, 19 March 2025
| Interval information |
small diesis
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
Tempering it out leads to 5-limit magic temperament.
See also
- Magic family, where it is tempered out
- Small comma