325/324

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 two 10/9's
• 13/8 and 81/50 (8/5 * 81/80)
• 13/9 and two 6/5's
• 1053/1024 and two 81/80's
• 25/24 and 27/26
• 100/99 and 144/143

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
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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)
• (595/594)(715/714) In the 17-limit.

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