2835/2816: Difference between revisions

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{{Infobox Interval

| Ratio = 2835/2816

| Name = fwiwisma, 35/11 kleisma

| Name = fwiwisma, 35/11 kleisma, kalismic half pythcomma

| Color name = L1uzy1, Laluzoyo comma

| 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]]

* [[81/64]] and [[44/35]].

* [[729/512]] and [[99/70]]

~~The [[Sagittal]] '''35/11 kleisma''' or '''fwiwisma''' is~~ a [[comma]] ~~with a [[ratio]] of '''2835/2816''' and~~ a ~~value~~ of approximately 11.64 [[cent]]s. In the Sagittal system, this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{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{{nbhsp}}{{sagittal | )|( }}. The primary role of {{ sagittal | )|( }} is~~ [[~~896/891#Sagittal notation|896/891~~]] ~~(11/7k up). The downward version is called '''11/35k''' or '''35/11k down''' and is represented (in a secondary role) by {{sagittal| )!( }}~~.

Due to this last difference, it notably serves as a half [[pythagorean comma]] for a strong rational representation of √2-[[hemipyth]].

==Etymology==

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 [[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 ==

In the [[Sagittal]] system, this comma (possibly tempered) is represented in a secondary role by the sagittal {{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{{nbhsp}}{{sagittal| )|( }}. The primary role of {{sagittal| )|( }} is [[896/891 #Sagittal notation|896/891]] (11/7k up). The downward version is called '''11/35k''' or '''35/11k down''' and is represented in a secondary role by {{sagittal| )!( }}.

== 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."

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</blockquote>

[[Category:Commas named ~~systematically~~]]

[[Category:Fwiwismic]]

[[Category:Commas named following events]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
 | Ratio = 2835/2816
-| Name = fwiwisma, 35/11 kleisma
+| Name = fwiwisma, 35/11 kleisma, kalismic half pythcomma
 | Color name = L1uzy1, Laluzoyo comma
 | 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]]
+* [[81/64]] and [[44/35]].
+* [[729/512]] and [[99/70]]
-The [[Sagittal]] '''35/11 kleisma''' or '''fwiwisma''' is a [[comma]] with a [[ratio]] of '''2835/2816''' and a value of approximately 11.64 [[cent]]s. In the Sagittal system, this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{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{{nbhsp}}{{sagittal | )|( }}. The primary role of {{ sagittal | )|( }} is [[896/891#Sagittal notation|896/891]] (11/7k up). The downward version is called '''11/35k''' or '''35/11k down''' and is represented (in a secondary role) by {{sagittal| )!( }}.
+Due to this last difference, it notably serves as a half [[pythagorean comma]] for a strong rational representation of √2-[[hemipyth]].
-==Etymology==
+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 [[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 ==
+In the [[Sagittal]] system, this comma (possibly tempered) is represented in a secondary role by the sagittal {{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{{nbhsp}}{{sagittal| )|( }}. The primary role of {{sagittal| )|( }} is [[896/891 #Sagittal notation|896/891]] (11/7k up). The downward version is called '''11/35k''' or '''35/11k down''' and is represented in a secondary role by {{sagittal| )!( }}.
+== 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."
@@ Line 15: / Line 29: @@
 </blockquote>
-[[Category:Commas named systematically]]
+[[Category:Fwiwismic]]
+[[Category:Commas named following events]]

2835/2816: Difference between revisions

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