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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. | ||
It's unique in the fact that in 12edo, instead of being tempered out, it's blown up to a whole semitone - six 5/4s make a minor | It's unique in the fact that in 12edo, instead of being tempered out, it's blown up to a whole semitone - six 5/4s make a minor thirteenth (20 steps), while 3/1 is a perfect tweltfth (19 steps). | ||
== Temperaments == | == Temperaments == | ||
Revision as of 21:37, 25 May 2022
| 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.
It's unique in the fact that in 12edo, instead of being tempered out, it's blown up to a whole semitone - six 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
- Magic family, where it is tempered out
- Small comma