Magus comma
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Ratio
50331648/48828125
Factorization
224 × 3 × 5-11
Monzo
[24 1 -11⟩
Size in cents
52.50415¢
Name
magus comma
Color name
salegu 4th, sg114
FJS name
[math]\text{6d4}_{5,5,5,5,5,5,5,5,5,5,5}[/math]
Special properties
reduced
Tenney height (log2 nd)
51.1262
Weil height (log2 max(n, d))
51.1699
Wilson height (sopfr(nd))
106
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.45241 bits
Comma size
medium
open this interval in xen-calc
| Interval information |
(Shannon, [math]\sqrt{nd}[/math])
The magus comma (ratio: 50331648/48828125, monzo: [24 1 -11⟩) is a medium 5-limit comma, which is the difference between:
- four classic chromatic semitones (25/24) and three classic diatonic semitones (16/15): (16/15)3/(25/24)4,
- three lesser dieses (128/125) and a classic chromatic semitone: (128/125)3/(25/24),
- a perfect fifth (3/2) and eleven classic major thirds (5/4), octave-reduced: 12/(5/4)11, and
- the classic major seventh (15/8) and twelve classic major thirds, octave-reduced: 15/(5/4)12.
Temperaments
Tempering out this comma leads to the magus and amigo temperaments.