2835/2816: Difference between revisions
Re-organize, giving each topic a distinct section. Make "fwiwisma" official cuz it's used to name 44/35. Recategorize accordingly. |
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 2835/2816 | | Ratio = 2835/2816 | ||
| Name = fwiwisma, 35/11 kleisma | | Name = fwiwisma, 35/11 kleisma, kalismic half pythcomma | ||
| Color name = L1uzy1, Laluzoyo comma | | Color name = L1uzy1, Laluzoyo comma | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
'''2835/2816''', the '''fwiwisma''', is a [[comma]] with a value of approximately 11.6 [[cent]]s. It represents the difference between [[45/44]] and [[64/63]] | '''2835/2816''', the '''fwiwisma''', is a [[comma]] with a value of approximately 11.6 [[cent]]s. It represents the difference between: | ||
* [[45/44]] and [[64/63]] | |||
* [[81/64]] and [[44/35]]. | |||
* [[729/512]] and [[99/70]] | |||
Due to this last difference, it notably serves as a half [[pythagorean comma]] for a strong rational representation of √2-[[hemipyth]]. | |||
It factors into simpler commas as ([[243/242]])⋅([[385/384]]) or ([[225/224]])⋅([[441/440]]). | |||
== Temperaments == | == Temperaments == | ||
[[Tempering out]] this comma results in the rank-4 '''fwiwismic''' temperament. Since this comma is the sum of 243/242 and 385/384, it is tempered out in the rank-3 temperament [[mirwomo]], and since it is the sum of 225/224 and 441/440, it is tempered out in the rank-3 temperament [[prodigy]]. As such, it is tempered out in [[miracle]], as well as [[support]]ing edos {{EDOs| 31, 41, and 72 }}. | |||
If instead tempered, in [[kalismic]], the pythagorean comma is halved, wherein each half represents 2835/2816~[[72171/71680]]. | |||
== Notation == | == Notation == | ||
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</blockquote> | </blockquote> | ||
[[Category:Fwiwismic]] | |||
[[Category:Commas named following events]] | [[Category:Commas named following events]] | ||
Latest revision as of 06:46, 19 October 2026
| Interval information |
35/11 kleisma,
kalismic half pythcomma
2835/2816, the fwiwisma, is a comma with a value of approximately 11.6 cents. It represents the difference between:
Due to this last difference, it notably serves as a half pythagorean comma for a strong rational representation of √2-hemipyth.
It factors into simpler commas as (243/242)⋅(385/384) or (225/224)⋅(441/440).
Temperaments
Tempering out this comma results in the rank-4 fwiwismic temperament. Since this comma is the sum of 243/242 and 385/384, it is tempered out in the rank-3 temperament mirwomo, and since it is the sum of 225/224 and 441/440, it is tempered out in the rank-3 temperament prodigy. As such, it is tempered out in miracle, as well as supporting edos 31, 41, and 72.
If instead tempered, in kalismic, the pythagorean comma is halved, wherein each half represents 2835/2816~72171/71680.
Notation
In the Sagittal system, this comma (possibly tempered) is represented in a secondary role by the sagittal and is called the 35/11 kleisma, or 35/11k for short, because the simplest interval it notates is 35/11 = 5×7/11 (equiv. 35/22), as for example in A–F . The primary role of is 896/891 (11/7k up). The downward version is called 11/35k or 35/11k down and is represented in a secondary role by .
Etymology
The name of this comma was coined in 2024 by Douglas Blumeyer during a conversation about what it should be. It comes from the acronym FWIW, meaning "for what it's worth."
fwiw I'd rather you not. there's already a blumeyer, blume, and yer commas which are related which I named after myself, and I don't think this is related to them. why not name it the davesma or something, by your logic? or you could name it the fwiwisma lol