364/363

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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 3o1uuz2, tholuluzo 2nd,
Tholuluzo comma
FJS name [math]\text{m2}^{7,13}_{11,11}[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 17.0116
Weil height (log2 max(n, d)) 17.0156
Wilson height (sopfr(nd)) 49
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~1.40762 bits
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 reason why the temperament was named “gentle” in the first place does not appear to be written down anywhere.

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.

See also