11859211/11859210 - Revision history

FloraC: Simpler pump. No extra factors introduced.

2026-04-12T13:27:08Z

Simpler pump. No extra factors introduced.

← Older revision		Revision as of 13:27, 12 April 2026
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	'''11859211/11859210''', the '''tredekisma''', is the smallest [[superparticular ratio]] in the [[19-limit]] and [[23-limit]].		'''11859211/11859210''', the '''tredekisma''', is the smallest [[superparticular ratio]] in the [[19-limit]] and [[23-limit]].

	It can be seen as the difference between a stack of a [[25/16]] ~~plus~~ a [[~~minisma]] plus a [[131072~~/~~130321\|undevicesimal diminished comma~~]], and a [[~~1024~~/~~729\|diminished fifth~~]] ~~plus two [[128~~/~~121\|Axirabian limmas]]:~~		It can be seen as the difference between a stack of four [[38/33]]'s and a stack consisting of [[10/7]] and [[16/13]]: (38/33)<sup>4</sup>/((10/7)⋅(16/13)).

	~~((25/16)⋅(4096/4095)⋅(131072/130321))/((1024/729)(128/121)<sup>2</sup>)~~		A possible S-expression of it is (S76⋅S441)/(S77⋅S324).

	~~Its~~ S-expression is (~~(S76)(S441)~~)/(~~(S77)(S324)~~)

	== Temperaments ==		== Temperaments ==

FloraC: Whoever named this should be responsible for what it is

2026-04-12T12:59:54Z

Whoever named this should be responsible for what it is

← Older revision		Revision as of 12:59, 12 April 2026
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	[[Optimal tuning]]s: TBA		[[Optimal tuning]]s: TBA

	{{Optimal ET sequence\|\|legend=1 TBA }}		{{Optimal ET sequence\|\|legend=1\|TBA }}

	[[Badness]] (Sintel): TBA		[[Badness]] (Sintel): TBA
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	== Etymology ==		== Etymology ==
	The name ''tredekisma'' comes from ''tredek'', which is one step of [[270edo]], ~~which~~ is an excellent 2.3.5.7.11.13.19 subgroup system that tempers it out.		This comma was named by [[Eufalesio]] in 2026. The name ''tredekisma'' comes from ''tredek'', which is the name of one step of [[270edo]] by [[Joseph Monzo]], and 270edo is an excellent 2.3.5.7.11.13.19-subgroup system that tempers it out.

	[[Category:Commas named for their regular temperament properties]]		[[Category:Commas named for their regular temperament properties]]

FloraC: Cleanup

2026-04-12T12:56:04Z

Cleanup

Show changes

Eufalesio: Added more edos

2026-03-29T11:18:41Z

Added more edos

← Older revision		Revision as of 11:18, 29 March 2026
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	== Temperaments ==		== Temperaments ==
	Only being 0.00014 cents, it is an insanely, unfathomably narrow comma; hundreds of times narrower than well known atomic commas like the [[Chalmersia]] and ~~the~~ [[Kirnberger's atom]]. As such, tempering out or fudging this either way ~~are~~ aurally identical to JI to human ears. It is ~~notably~~ tempered out in ~~[[270edo]] thanks to its very well approximated 2.3.5.7.11.13.19, hence its name; also tempered out in other~~ edos like {{EDOs\|94, 118, 152, 364}}, among others.		Only being 0.00014 cents, it is an insanely, unfathomably narrow comma; hundreds of times narrower than well known atomic commas like the [[Chalmersia]] and [[Kirnberger's atom]]. As such, tempering out or fudging this alone either way is aurally identical to JI to human ears. It is tempered out in notable edos like {{nowrap\|{{EDOs\| 24, 84, 94, 118, 152, 176, 364, 388, 624, 742, 3125, 8269, 8539}}}}... among others. It is also tempered out in any union between these edos, such as [[vishnu]] and [[gariwizmic]].

	=== Tredekic ===		=== Tredekic ===

Overthink: + Etymology

2026-03-28T22:56:35Z

+ Etymology

← Older revision		Revision as of 22:56, 28 March 2026
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	[[Badness]] (Sintel): TBA		[[Badness]] (Sintel): TBA

			== Etymology ==
			The name ''tredekisma'' comes from ''tredek'', which is one step of [[270edo]], which is an excellent 2.3.5.7.11.13.19 subgroup system that tempers it out.

			[[Category:Commas named for their regular temperament properties]]

Eufalesio at 08:20, 28 March 2026

2026-03-28T08:20:35Z

← Older revision		Revision as of 08:20, 28 March 2026
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	(25/16)(4096/4095)(131072/130321)÷(1024/729)(128/121)^2		(25/16)(4096/4095)(131072/130321)÷(1024/729)(128/121)^2

	Its S-expression is (S76)(S441)÷(S77)(~~324~~)		Its S-expression is (S76)(S441)÷(S77)(S324)

	== Temperaments ==		== Temperaments ==

Eufalesio: S-expression and fixes!

2026-03-28T08:16:21Z

S-expression and fixes!

← Older revision		Revision as of 08:16, 28 March 2026
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	{{Infobox Interval\|Name=tredekisma\|Color name=quadno-athoquadlu-azogu 4th, 19o^43o1u^4zg4, Quadno-athoquadlu-azogu comma,\|Sound=\|Comma=yes}}11859211/11859210, the ''tredekisma'', is the smallest [[superparticular ratio]] in the [[19-limit]] and [[23-limit]].		{{Infobox Interval\|Name=tredekisma\|Color name=quadno-athoquadlu-azogu 4th, <br>19o^43o1u^4zg4, <br>Quadno-athoquadlu-azogu comma\|Sound=\|Comma=yes}}11859211/11859210, the ''tredekisma'', is the smallest [[superparticular ratio]] in the [[19-limit]] and [[23-limit]].

	It can be seen as the ~~differencebetween~~ a stack of a [[25/16]] plus a [[minisma]] plus a [[131072/130321\|Saquadnu comma]], and a [[1024/729\|diminished fifth]] plus two [[128/121\|Axirabian limmas]]:		It can be seen as the difference between a stack of a [[25/16]] plus a [[minisma]] plus a [[131072/130321\|Saquadnu comma]], and a [[1024/729\|diminished fifth]] plus two [[128/121\|Axirabian limmas]]:

	(25/16)(4096/4095)(131072/130321)÷(1024/729)(128/121)^2		(25/16)(4096/4095)(131072/130321)÷(1024/729)(128/121)^2

			Its S-expression is (S76)(S441)÷(S77)(324)

	== Temperaments ==		== Temperaments ==

Eufalesio: Birth

2026-03-28T08:04:34Z

Birth

New page

{{Infobox Interval|Name=tredekisma|Color name=quadno-athoquadlu-azogu 4th, 19o^43o1u^4zg4, Quadno-athoquadlu-azogu comma,|Sound=|Comma=yes}}11859211/11859210, the ''tredekisma'', is the smallest [[superparticular ratio]] in the [[19-limit]] and [[23-limit]].

It can be seen as the differencebetween a stack of a [[25/16]] plus a [[minisma]] plus a [[131072/130321|Saquadnu comma]], and a [[1024/729|diminished fifth]] plus two [[128/121|Axirabian limmas]]:

(25/16)(4096/4095)(131072/130321)÷(1024/729)(128/121)^2

== Temperaments ==
Only being 0.00014 cents, it is an insanely, unfathomably narrow comma; hundreds of times narrower than well known atomic commas like the [[Chalmersia]] and the [[Kirnberger's atom]]. As such, tempering out or fudging this either way are aurally identical to JI to human ears. It is notably tempered out in [[270edo]] thanks to its very well approximated 2.3.5.7.11.13.19, hence its name; also tempered out in other edos like {{EDOs|94, 118, 152, 364}}, among others.

=== Tredekic ===
[[Subgroup]]: 2.3.5.7.11.13.19
{| class="right-all"
|[⟨
|1
|0
|0
|0
|0
|1
|0
|],
|-
|⟨
|0
|1
|0
|0
|0
|0
|1
|],
|-
|⟨
|0
|0
|1
|0
|0
|1
|0
|],
|-
|⟨
|0
|0
|0
|1
|0
|3
| -1
|],
|-
|⟨
|0
|0
|0
|0
|1
|0
|1
|],
|-
|⟨
|0
|0
|0
|0
|0
| -4
|1
|]]
|}
mapping generators: ~2, ~3, ~5, ~7, ~11, ~133/33

[[Optimal tuning|Optimal tunings]]: TBA

{{Optimal ET sequence|TBA|legend=1}}

[[Badness]] (Sintel): TBA

=== Tredekismic ===
[[Subgroup]]: 2.3.5.7.11.13.17.19
{| class="right-all"
|[⟨
|1
|0
|0
|0
|0
|1
|0
|0
|],
|-
|⟨
|0
|1
|0
|0
|0
|0
|0
|1
|],
|-
|⟨
|0
|0
|1
|0
|0
|1
|0
|0
|],
|-
|⟨
|0
|0
|0
|1
|0
|3
|0
| -1
|],
|-
|⟨
|0
|0
|0
|0
|1
|0
|0
|1
|],
|-
|⟨
|0
|0
|0
|0
|0
| -4
|0
|1
|],
|-
|⟨
|0
|0
|0
|0
|0
|0
|1
|0
|]]
|}
mapping generators: ~2, ~3, ~5, ~7, ~11, ~17, ~133/33

[[Optimal tuning|Optimal tunings]]: TBA

{{Optimal ET sequence|TBA|legend=1}}

[[Badness]] (Sintel): TBA