Magus comma
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| Ratio | 50331648/48828125 |
| Factorization | 224 × 3 × 5-11 |
| Monzo | [24 1 -11⟩ |
| Size in cents | 52.504148¢ |
| 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 | |
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 it out leads to the Magus and Amigo temperaments.