Magus comma: Difference between revisions

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The '''Magus comma''' ([[ratio]]: 50331648/48828125, {{monzo|legend=1| 24 1 -11 }}) is a [[medium comma|medium]] [[5-limit]] [[comma]], which is the difference between a stack of four [[25/24|classic chromatic semitones (25/24)]] and three [[16/15|classic diatonic semitones (16/15)]], that is, (16/15)^3/(25/24)<sup>4</sup>. It is also the difference between three [[128/125|lesser dieses (128/125)]] and a classic chromatic semitone, or (128/125)^3/(25/24).
The '''Magus comma''' ([[ratio]]: 50331648/48828125, {{monzo|legend=1| 24 1 -11 }}) is a [[medium comma|medium]] [[5-limit]] [[comma]], which is the difference between:
 
* four [[25/24|classic chromatic semitones (25/24)]] and three [[16/15|classic diatonic semitones (16/15)]], (16/15)<sup>3</sup>/(25/24)<sup>4</sup>,
* three [[128/125|lesser dieses (128/125)]] and a classic chromatic semitone, (128/125)<sup>3</sup>/(25/24), and
* twelve [[5/4|classic major thirds (5/4)]] and a [[15/8|classic major seventh (15/8)]], 15/(5/4)<sup>12</sup> (octave-reduced).


Tempering it out leads to the [[Magus]] temperament.
Tempering it out leads to the [[Magus]] temperament.

Revision as of 17:44, 29 May 2024

Interval information
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]\displaystyle{ \text{6d4}_{5,5,5,5,5,5,5,5,5,5,5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 51.1262
Weil norm (log2 max(n, d)) 51.1699
Wilson norm (sopfr(nd)) 106
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:

Tempering it out leads to the Magus temperament.