364/363: Difference between revisions

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The '''gentle comma''', '''364/363''', is a [[13-limit]] no-5 [[comma]] measuring about 4.8 cents. It is the amount by which an undecimal major third [[14/11]] and a tridecimal minor third [[13/11]] exceed a just perfect fifth [[3/2]].  
The '''gentle comma''', '''364/363''', is a [[13-limit]] no-5 [[comma]] measuring about 4.8 cents. It is the amount by which an undecimal major third [[14/11]] and a tridecimal minor third [[13/11]] exceed a just perfect fifth [[3/2]].  
In terms of commas, it can be characterized by ([[91/90]])/([[121/120]]), ([[243/242]])/([[729/728]]), ([[325/324]])/([[3025/3024]]), ([[351/350]])/([[9801/9800]]), or ([[352/351]])/([[10648/10647]]). It factors into ([[385/384]])([[6656/6655]]), ([[441/440]])([[2080/2079]]), or ([[676/675]])([[1575/1573]]) among many other options.


== Temperaments ==
== Temperaments ==

Revision as of 10:16, 7 October 2021

Interval information
Ratio 364/363
Factorization 22 × 3-1 × 7 × 11-2 × 13
Monzo [2 -1 0 1 -2 1
Size in cents 4.762683 ¢
Name gentle comma
Color name tholuluzo comma
FJS name [math]\displaystyle{ \text{m2}^{7,13}_{121} }[/math]
Special properties superparticular,
reduced
Tenney norm (log2 nd) 17.0116
Weil norm (log2 max(n, d)) 17.0156
Wilson norm (sopfr(nd)) 49
Open this interval in xen-calc

The gentle comma, 364/363, is a 13-limit no-5 comma measuring about 4.8 cents. It is the amount by which an undecimal major third 14/11 and a tridecimal minor third 13/11 exceed a just perfect fifth 3/2.

In terms of commas, it can be characterized by (91/90)/(121/120), (243/242)/(729/728), (325/324)/(3025/3024), (351/350)/(9801/9800), or (352/351)/(10648/10647). It factors into (385/384)(6656/6655), (441/440)(2080/2079), or (676/675)(1575/1573) among many other options.

Temperaments

Tempering out the gentle comma leads to a form of gentle temperament and enables gentle chords.

See also