325/324

The marveltwin comma, 325/324, is a small 13-limit (also 2.3.5.13 subgroup) superparticular comma measuring about 5.3 cents. Its significance is in that it marks the difference between 16/13 and a stack of two 10/9's, and 13/9 and a stack of two 6/5's. It can also be expressed as the difference between 1053/1024 and a stack of two 81/80's.

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 norm (log2 nd)	16.6841
Weil norm (log2 max(n, d))	16.6886
Wilson norm (sopfr(nd))	39
Comma size	small
S-expressions	S25⋅S26, S10/S12
Open this interval in xen-calc

In terms of other superparticular ratios, it is the difference between:

• 25/24 and 27/26
• 100/99 and 144/143

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)
• (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