364/363: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Ratio = 364/363
| Name = minor minthma, minor gentle comma
| Monzo = 2 -1 0 1 -2 1
| Color name = 3o1uuzM, tholuluzoma
| Cents = 4.76268
| Comma = yes
| Name = gentle comma
| Color name = tholuluzo comma
| FJS name = m2<sup>7, 13</sup><sub>121</sub>
| Sound =  
}}
}}
'''364/363''', the '''gentle comma''', is a [[13-limit]] no-5 [[small comma]] measuring about 4.8{{cent}}. 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]].  
'''364/363''', the '''minor minthma''' or '''minor gentle comma''', is a [[small comma|small]] [[13-limit]] no-5 [[comma]] measuring about 4.8{{cent}}. 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.
== Commatic relations ==
In terms of commas, it is the difference between the following superparticular pairs:
* [[91/90]] and [[121/120]]
* [[243/242]] and [[729/728]]
* [[325/324]] and [[3025/3024]]
* [[351/350]] and [[9801/9800]]
* [[352/351]] and [[10648/10647]]
 
It factors into the following superparticular pairs:
* [[385/384]] and [[6656/6655]]
* [[441/440]] and [[2080/2079]]
 
Not to mention some nonsuperparticular but useful relations:
* [[676/675]] and [[1575/1573]]


== Temperaments ==
== Temperaments ==
Tempering out the gentle comma leads to a form of '''gentle temperament''' and enables [[gentle chords]].  
Tempering out this comma leads to a form of '''minor minthmic temperament''' (full 13-limit rank-5) or '''minorminth temperament''' (2.3.7.11.13 subgroup rank-4), which enables [[minor minthmic chords]].
 
== History and etymology ==
This comma was known as the ''gentle comma'' from 2011. In 2022, [[Margo Schulter]] requested it should be changed to ''minor''/''lesser gentle comma'' to distinguish it from [[352/351]], which would gain the name ''major''/''greater gentle comma''.
 
The ''minor minthma'' was also added to this comma in contrast to the ''major minthma'' of 352/351. Both commas were essential to define the [[gentle]] temperament. Gentle was named for the [[gentle region|gentle fifth]], a mild version of the [[superpyth]] fifth.  


== See also ==
== See also ==
* [[Gentle chords]]
* [[List of superparticular intervals]]
* [[List of superparticular intervals]]


[[Category:13-limit]]
[[Category:Minor minthmic]]
[[Category:Small commas]]
[[Category:Commas named for the intervals they stack]]
[[Category:Superparticular]]
[[Category:Commas named for the generator of their temperament]]
[[Category:Gentle]]

Latest revision as of 16:08, 17 July 2026

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 ¢
Names minor minthma,
minor gentle comma
Color name 3o1uuzM, tholuluzoma
FJS name [math]\displaystyle{ \text{m2}^{7,13}_{11,11} }[/math]
Special properties superparticular,
reduced
Tenney norm (log2 nd) 17.0116
Weil norm (log2 max(n, d)) 17.0156
Wilson norm (sopfr(nd)) 49
Comma size small
Open this interval in xen-calc

364/363, the minor minthma or minor gentle comma, is a small 13-limit no-5 comma measuring about 4.8 ¢. 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.

Commatic relations

In terms of commas, it is the difference between the following superparticular pairs:

It factors into the following superparticular pairs:

Not to mention some nonsuperparticular but useful relations:

Temperaments

Tempering out this comma leads to a form of minor minthmic temperament (full 13-limit rank-5) or minorminth temperament (2.3.7.11.13 subgroup rank-4), which enables minor minthmic chords.

History and etymology

This comma was known as the gentle comma from 2011. In 2022, Margo Schulter requested it should be changed to minor/lesser gentle comma to distinguish it from 352/351, which would gain the name major/greater gentle comma.

The minor minthma was also added to this comma in contrast to the major minthma of 352/351. Both commas were essential to define the gentle temperament. Gentle was named for the gentle fifth, a mild version of the superpyth fifth.

See also