3645/3584

Interval information

Ratio	3645/3584
Factorization	2-9 × 36 × 5 × 7-1
Monzo	[-9 6 1 -1⟩
Size in cents	29.21781¢
Names	aberdiesis[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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The aberdiesis^{[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. It is the difference between three major whole tones and a small septimal tritone, or in other words, (9/8)³/(7/5).

It factors into simpler commas as (81/80)⋅(225/224) or (126/125)⋅(225/224)². In the 11-limit it further factors into (99/98)⋅(2835/2816), (385/384)⋅(2187/2156), and (540/539)⋅(2079/2048).

Temperaments

Tempering out this comma leads to the rank-3 aberdietic temperament. 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. 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 aberdiesis was given later in 2026 by the observation of Fumica to observe a pun with the closely-related comma (10/7)/(9/8)³ = S8/S9 = 5120/5103, the aberschisma, in light of Godtone's observation that it behaves in almost all ways like a diesis according to a specific intuitively-motivated definition discussed in Diesis #Generalization.