3645/3584: Difference between revisions

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Godtone (talk | contribs)
m add etymology section, propose alternate name that feels less awkward than current name, link, note connection to septimal meantone
Godtone (talk | contribs)
m this seems like an acceptable fix
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{{Infobox interval
{{Infobox interval
| Name = tritonic diesis{{idiosyncratic}}, schismean comma{{idiosyncratic}}
| Name = aberdiesis{{idiosyncratic}}, schismean comma{{idiosyncratic}}
| Color name = Lry-2, Laruyo negative 2nd
| Color name = Lry-2, Laruyo negative 2nd
| Comma = yes
| Comma = yes
}}
}}


The '''tritonic diesis'''{{idiosyncratic}} or '''schismean comma'''{{idiosyncratic}} ([[monzo]]: {{monzo|-9 6 1 -1}}, [[ratio]]: 3645/3584) is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 29.2 [[cent]]s.
The '''aberdiesis'''{{idiosyncratic}} or '''schismean comma'''{{idiosyncratic}} ([[monzo]]: {{monzo|-9 6 1 -1}}, [[ratio]]: 3645/3584) is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 29.2 [[cent]]s.


It is the difference between three major whole tones and a small septimal tritone, or in other words, ([[9/8]])<sup>3</sup>/([[7/5]]).
It is the difference between three major whole tones and a small septimal tritone, or in other words, ([[9/8]])<sup>3</sup>/([[7/5]]).
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== Etymology ==
== Etymology ==
The name ''schismean'' was given by [[User:Xenllium|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 [[User:Godtone|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 [[729/512|(9/8)<sup>3</sup>]] exceeds the LCJI tritone [[7/5]].
The name ''schismean'' was given by [[User:Xenllium|Xenllium]] in 2022, most likely as a contraction of [[schism]] and [[meantone]]. The name ''aberdiesis'' was given later in 2026 by the observation of [[User:FloraC|Fumica]] to observe a pun with the closely-related comma (10/7)/(9/8)<sup>3</sup> = [[64/63|S8]]/[[81/80|S9]] = [[5120/5103]], the aberschisma, in light of [[User:Godtone|Godtone]]'s observation that it behaves in almost all ways like a diesis according to a specific intuitively-motivated definition discussed in [[Diesis#Generalization]].


[[Category:Commas named by combining multiple temperament names]]
[[Category:Commas named by combining multiple temperament names]]

Revision as of 21:55, 28 July 2026

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
Open this interval in xen-calc

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).

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 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.