3645/3584: Difference between revisions
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{{Infobox interval | {{Infobox interval | ||
| Name = | | 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 ''' | 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 | It factors into simpler commas as ([[81/80]])⋅([[225/224]]) or ([[126/125]])⋅(225/224)<sup>2</sup>. In the [[11-limit]] it further factors into ([[99/98]])⋅([[2835/2816]]), ([[385/384]])⋅([[2187/2156]]), and ([[540/539]])⋅([[2079/2048]]). | ||
== Temperaments == | == 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 [[miscellaneous 7-limit temperaments #Aberdietic|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 == | == Etymology == | ||
The name ''schismean'' was given by [[ | 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)<sup>3</sup> = [[64/63|S8]]/[[81/80|S9]] = [[5120/5103]], the aberschisma, in light of {{u|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]] | ||
Latest revision as of 11:00, 30 July 2026
| Interval information |
schismean comma[idiosyncratic term]
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.