3645/3584: Difference between revisions
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m add etymology section, propose alternate name that feels less awkward than current name, link, note connection to septimal meantone |
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{{Infobox interval | {{Infobox interval | ||
| Name = schismean comma{{idiosyncratic}} | | Name = tritonic diesis{{idiosyncratic}}, schismean comma{{idiosyncratic}} | ||
| Color name = Lry-2, Laruyo negative 2nd | | Color name = Lry-2, Laruyo negative 2nd | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
The '''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 '''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. | ||
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]]). | ||
== Temperaments == | == Temperaments == | ||
Tempering out this comma leads to the rank-3 [[Miscellaneous 7-limit temperaments #Schismean|schismean]] 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. | ||
Tempering out this comma leads to the rank-3 [[Miscellaneous 7-limit temperaments #Schismean|schismean]] temperament. Other rank-2 temperaments which temper out this comma include [[schism]] and [[pycnic]]. | |||
== 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]]. | |||
[[Category:Commas named by combining multiple temperament names]] | [[Category:Commas named by combining multiple temperament names]] | ||
Revision as of 19:27, 26 July 2026
| Interval information |
schismean comma[idiosyncratic term]
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.
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.