Magic comma
(Redirected from 3125/3072)
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| Ratio | 3125/3072 |
| Factorization | 2-10 × 3-1 × 55 |
| Monzo | [-10 -1 5⟩ |
| Size in cents | 29.613568¢ |
| Names | magic comma, small diesis |
| Color name | Ly5-2, Laquinyo comma |
| FJS name | [math]\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 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.39008 bits |
| Comma size | small |
| 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, 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 tweltfth (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