625/616

Interval information

Ratio	625/616
Factorization	2-3 × 54 × 7-1 × 11-1
Monzo	[-3 0 4 -1 -1⟩
Size in cents	25.11101¢
Name	Quadrikite comma
Color name	1ury4-2, luruquadyo negative 2nd
FJS name	[math]\text{dd}{-2}^{5,5,5,5}_{7,11}[/math]
Special properties	reduced
Tenney height (log2 nd)	18.5545
Weil height (log2 max(n, d))	18.5754
Wilson height (sopfr(nd))	44
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.24815 bits
Comma size	small
open this interval in xen-calc

The quadrikite comma (ratio: 625/616, monzo: [-3 0 4 -1 -1⟩) is a small 11-limit (also 2.5.7.11 subgroup) comma.

It was discovered by Lumi Pakkanen and Praveen Venkataramana when prompted to create a temperament that could be called xeimtionic that produces a 6L 5s mos pattern so that the pattern could be named xeimtonic. The name quadrikite comes from the fact that a gap of four strings on the Kite guitar can be both 625/256 and 77/32 when this comma is tempered out. It was originally intended to be paired with the frostma 245/242 to produce the frostburn temperament as this was to be called xeimtionic (pronounced zeem-tee-onic) for the desired 6L 5s mos pattern. All of this was inspired by an AI generated picture of xenharmonic music theory featuring something that looks like the word XEIMTIONC, but the name was not used for TAMNAMS after all to remain temperament agnostic.

AI generated image of xenharmonic music theory.

It can be factored into (100/99)(225/224).

Temperaments

Tempering out this comma in the 2.5.7.11 subgroup leads to the rank-3 pakkanen temperament.

See also

• Small comma