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

Latest revision as of 08:08, 3 November 2024

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.

Tempering out this comma leads to the magus and amigo temperaments.

@@ Line 2: / Line 2: @@
 | Ratio = 50331648/48828125
 | Monzo = 24 1 -11
-| Name = Magus comma
+| Name = magus comma
 | Color name = salegu 4th, sg<sup>11</sup>4
 | Comma = yes
 }}
-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>. Tempering it out leads to the [[Magus]] temperament.
+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),
+* a perfect fifth ([[3/2]]) and eleven [[5/4|classic major thirds (5/4)]], octave-reduced: 12/(5/4)<sup>11</sup>, and
+* the [[15/8|classic major seventh (15/8)]] and twelve classic major thirds, octave-reduced: 15/(5/4)<sup>12</sup>.
+== Temperaments ==
+Tempering out this comma leads to the [[magus]] and [[amigo]] temperaments.
+== See also ==
+* [[Würschmidt comma]]
+* [[Magic comma]]
+[[Category:Commas with unknown etymology]]