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 16:33, 1 June 2024

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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), and
the classic major seventh (15/8) and twelve classic major thirds (5/4), octave-reduced: 15/(5/4)¹².

Tempering it out leads to the Magus and Amigo temperaments.

@@ Line 12: / Line 12: @@
 * 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
-* an octave-reduced stack of twelve [[5/4|classic major thirds (5/4)]] and a [[15/8|classic major seventh (15/8)]]: 15/(5/4)<sup>12</sup>.
+* the [[15/8|classic major seventh (15/8)]] and twelve [[5/4|classic major thirds (5/4)]], octave-reduced: 15/(5/4)<sup>12</sup>.
 Tempering it out leads to the [[Magus]] and [[Amigo]] temperaments.