Magus comma: Difference between revisions

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

Revision as of 17:01, 29 May 2024

The Magus comma (ratio: 50331648/48828125, monzo: [24 1 -11⟩) is a medium 5-limit comma, which is the difference between a stack of four classic chromatic semitones (25/24) and three classic diatonic semitones (16/15), that is, (16/15)^3/(25/24)⁴. It is also the difference between three lesser dieses (128/125) and a classic chromatic semitone, or (128/125)^3/(25/24).

Tempering it out leads to the Magus temperament.

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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 (!28/125)]] and a classic chromatic semitone.
+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).
 Tempering it out leads to the [[Magus]] temperament.