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 19:38, 7 October 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:
+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>,
@@ Line 15: / Line 15: @@
 == Temperaments ==
-Tempering it out leads to the [[Magus]] and [[Amigo]] temperaments.
+Tempering out this comma leads to the [[magus]] and [[amigo]] temperaments.
 == See also ==
 * [[Würschmidt comma]]
 * [[Magic comma]]