3645/3584

The tritonic diesis^{[idiosyncratic term]} or schismean comma^{[idiosyncratic term]} (monzo: [-9 6 1 -1⟩, ratio: 3645/3584) is a small 7-limit comma measuring about 29.2 cents.

Interval information

Ratio	3645/3584
Factorization	2-9 × 36 × 5 × 7-1
Monzo	[-9 6 1 -1⟩
Size in cents	29.21781¢
Names	tritonic diesis[idiosyncratic term], schismean comma[idiosyncratic term]
Color name	Lry-2, Laruyo negative 2nd
FJS name	[math]\displaystyle{ \text{d}{-2}^{5}_{7} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	23.6391
Weil norm (log2 max(n, d))	23.6634
Wilson norm (sopfr(nd))	48
Comma size	small
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It is the difference between three major whole tones and a small septimal tritone, or in other words, (9/8)³/(7/5).

Temperaments

It is most notably and characteristically tempered out in septimal meantone, where 7/5 is an augmented fourth, as the flat fifth of meantone helps motivate this equivalence.

Tempering out this comma leads to the rank-3 schismean temperament. Other rank-2 temperaments which temper out this comma include schism and pycnic.

Etymology

The name schismean was given by Xenllium in 2022, most likely as a contraction of schism and meantone. The name tritonic diesis was given later in 2026 by the observation of Godtone that it fit a general algorithmic definition discussed in Diesis#Generalization, combined with the observation that the septimal tritonic diesis of (10/7)/(7/5) = 50/49 seemed to suggest the existence of a tritonic diesis with a focus on the tritone part as contrasted to the septimal part, hence the expression of it as the amount by which the "literal" tritone (9/8)³ exceeds the LCJI tritone 7/5.