364/363

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]\displaystyle{ \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
Comma size	small
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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:

• 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

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.

See also

• List of superparticular intervals