325/324

Interval information

Ratio	325/324
Factorization	2-2 × 3-4 × 52 × 13
Monzo	[-2 -4 2 0 0 1⟩
Size in cents	5.335086¢
Name	marveltwin comma
Color name	3oyy1, thoyoyo 1sn, Thoyoyo comma
FJS name	[math]\displaystyle{ \text{P1}^{5,5,13} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	16.6841
Weil height (log2 max(n, d))	16.6886
Wilson height (sopfr(nd))	39
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.46029 bits
Comma size	small
S-expressions	S25 × S26, S10 / S12
Open this interval in xen-calc

The marveltwin comma, 325/324, is a 13-limit (also 2.3.5.13 subgroup) comma measuring about 5.3 ¢. Its significance is in that it marks the difference between 16/13 and a stack of two 10/9's, or between 13/9 and a stack of two 6/5's. It can also be expressed as (25/24)/(27/26) and (100/99)/(144/143), among other expressions.

Being a triangle superparticular, it factors neatly into (625/624)(676/675). Other factorizations are (385/384)(2080/2079), (364/363)(3025/3024), (352/351)(4225/4224), and (351/350)(4375/4374). In the 17-limit it additionally factors into (595/594)(715/714).

Temperaments

Tempering out this comma leads to the rank-5 marveltwin temperament, which identifies 16/13 by two 10/9's stacked and enables marveltwin chords. The most significant further temperament is to temper out 625/624 and/or 676/675, equating 26/25 with 25/24~27/26. This in the 2.3.5.13 subgroup is the rank-2 cata temperament.

See also

• Marveltwin
• List of superparticular intervals