Mystery comma

Interval information

Ratio	70368744177664/68630377364883
Factorization	246 × 3-29
Monzo	[46 -29⟩
Size in cents	43.30497¢
Names	29-comma, mystery comma, Pythagorean quadridietic semilimma
Color name	Wa-29, s4w4
FJS name	[math]\displaystyle{ \text{dddd4} }[/math]
Special properties	reduced, reduced subharmonic
Tenney height (log2 nd)	91.9639
Weil height (log2 max(n, d))	92
Wilson height (sopfr(nd))	179
Comma size	medium
Open this interval in xen-calc

[46 -29⟩, the 29-comma or mystery comma of 43.305 cents, is the difference between 46 octaves and 29 fifths, in other words 2⁴⁶/3²⁹. Because this comma is a Pythagorean interval and is almost exactly half of the traditional Pythagorean limma in addition to being a quadruple-diminished fourth, one can also call this interval the Pythagorean quadridietic semilimma.

Temperaments

Tempering out this comma splits the octave into 29 equal parts and maps the harmonic 3 to 17\29, leading to the 5-limit version of mystery temperament. For EDOs up to 400, the 29-comma is tempered out if and only if 29 divides it, for example 29edo, 58edo or 87edo.

See also

• Medium comma