Valentine comma

Interval information

Ratio	1990656/1953125
Factorization	213 × 35 × 5-9
Monzo	[13 5 -9⟩
Size in cents	32.95158¢
Name	valentine comma
Color name	satritrigu 3rd, sg93
FJS name	[math]\text{dddd3}_{5,5,5,5,5,5,5,5,5}[/math]
Special properties	reduced
Tenney height (log2 nd)	41.8222
Weil height (log2 max(n, d))	41.8496
Wilson height (sopfr(nd))	86
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.49887 bits
Comma size	medium
open this interval in xen-calc

The valentine comma (ratio: 1990656/1953125, monzo: [13 5 -9⟩ is a medium 5-limit comma. It is the amount by which a stack of four 25/24's falls short of 6/5, or a stack of five 25/24's falls short of 5/4. In terms of commas, it is the difference between the lesser diesis (128/125) and the kleisma (15625/15552), and is also equal to one-half of the difference between nine 25/24's and a perfect fifth (3/2). Tempering it out leads to the 5-limit version of valentine temperament. As it splits the perfect fifth into 9, and equates 5/4 to 5 of these steps, it is related to 9edf and therefore to Carlos Alpha.