8th-octave temperaments - Revision history

FloraC: Complete links

2026-07-05T07:04:34Z

Complete links

← Older revision		Revision as of 07:04, 5 July 2026
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	Temperaments discussed elsewhere include:		Temperaments discussed elsewhere include:
	* ''[[Octant]]'' → [[Schismatic family#Octant\|Schismatic family]]		* ''[[Octant]]'' → [[Schismatic family #Octant\|Schismatic family]]
			* ''[[Octonion]]'' → [[Diminished family #Octonion\|Diminished family]]
			* ''[[Twilight]]'' → [[Undim family #Twilight\|Undim family]]
	* [[Octoid]] → [[Ragismic microtemperaments #Octoid\|Ragismic microtemperaments]]		* [[Octoid]] → [[Ragismic microtemperaments #Octoid\|Ragismic microtemperaments]]
	* ''[[Octatonic (temperament)\|Octatonic]]'' → [[No-fives subgroup temperaments #Octatonic\|No-fives subgroup temperaments]]		* ''[[Octatonic (temperament)\|Octatonic]]'' → [[No-fives subgroup temperaments #Octatonic\|No-fives subgroup temperaments]]

	{{Navbox fractional-octave}}		{{Navbox fractional-octave}}

FloraC: - duplicate data (moved to no-5)

2026-07-05T06:58:48Z

- duplicate data (moved to no-5)

@@ Line 6: / Line 6: @@
 * ''[[Octant]]'' → [[Schismatic family#Octant|Schismatic family]]
 * [[Octoid]] → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]]
+* ''[[Octatonic (temperament)|Octatonic]]'' → [[No-fives subgroup temperaments #Octatonic|No-fives subgroup temperaments]]
 {{Navbox fractional-octave}}

FloraC: Review, + badness and optimal tunings

2026-07-05T06:56:09Z

Review, + badness and optimal tunings

← Older revision		Revision as of 06:56, 5 July 2026
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	== Octatonic ==		== Octatonic ==
	[[12/11]] is very close to 1 step of 8edo, and hence this temperament tempers out the octatonic comma, the difference between a stack of 8 12/11's and the octave~~. The octatonic temperament makes a [[consistent circle]]~~.		[[12/11]] is very close to 1 step of 8edo, and hence this temperament tempers out the [[undecimal octatonic comma]], the difference between a stack of eight 12/11's and the octave.

	[[Subgroup]]: 2.3.11		[[Subgroup]]: 2.3.11

	[[Comma list]]: ~~{{monzo\|15 8 0 0 -8}}~~		[[Comma list]]: 214990848/214358881

	{{Mapping\|legend=1\|8 0 15\|0 1 1}}		{{Mapping\|legend=2\| 8 0 15 \| 0 1 1 }}
			: mapping generators: ~12/11, ~3

	: ~~Mapping generators~~: ~12/11, ~3		[[Optimal tuning]]s:
			* [[WE]]: ~12/11 = 149.9917{{c}}, ~3/2 = 701.9324{{c}}
			: [[error map]]: {{val\| -0.066 -0.089 +0.424 }}
			* [[CWE]]: ~12/11 = 150.0000{{c}}, ~3/2 = 701.9147{{c}}
			: error map: {{val\| 0.000 -0.040 +0.597 }}

	~~[[Support]]ing [[ET]]s:~~ {{~~EDOs~~\|16, 24, 32, 48, 56, 72, 80, ~~120~~, ~~128~~, ~~152~~}}~~, ..~~.		{{Optimal ET sequence\|legend=1\| 8, 16, 24, 104, 128, 152, 176, 200, 1024e, 1224e, 1424e, 1624e }}

			[[Badness]] (Sintel): 0.515

	{{Navbox fractional-octave}}		{{Navbox fractional-octave}}

FloraC: - 5-limit octoid

2026-07-03T16:52:56Z

- 5-limit octoid

@@ Line 4: / Line 4: @@
 Temperaments discussed elsewhere include:
-* ''Octant'' → [[Schismatic family#Octant|Schismatic family]]
+* ''[[Octant]]'' → [[Schismatic family#Octant|Schismatic family]]
 == Octatonic ==
@@ Line 18: / Line 19: @@
 [[Support]]ing [[ET]]s: {{EDOs|16, 24, 32, 48, 56, 72, 80, 120, 128, 152}}, ...
 {{Navbox fractional-octave}}

FloraC: Delete octium

2026-07-03T16:40:53Z

Delete octium

← Older revision		Revision as of 16:40, 3 July 2026
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	[[Support]]ing [[ET]]s: {{EDOs\|16, 24, 32, 48, 56, 72, 80, 120, 128, 152}}, ...		[[Support]]ing [[ET]]s: {{EDOs\|16, 24, 32, 48, 56, 72, 80, 120, 128, 152}}, ...

	~~== Octium ==~~
	Octium temperament is named after an "extended provisional" name for oxygen, the 8th element. The term [[oxygen]] itself is already the name of an exotemperament. It reaches [[24/23]] in one generator and [[19/16]] in two.

	~~Subgroup: 2.3.19.23.29.31~~

	~~Comma list: 94221/94208, 419957/419904, 219501/219488, 7997934975003/7996960669696~~

	~~{{Mapping\|legend=2\| 8 2 35 25 47 2 \| 0 21 -2 22 -16 74 }}~~

	~~: Mapping generators: ~10051/9216, ~24/23~~

	~~[[Optimal tuning]] ([[CTE]]): ~24/23 = 76.284~~

	~~[[Support]]ing [[ET]]s: {{EDOs\|472, 1400, 1872, 3272, 5144}}~~

	== Octoid ==		== Octoid ==

Xenllium at 23:32, 20 February 2026

2026-02-20T23:32:12Z

← Older revision		Revision as of 23:32, 20 February 2026
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	An 8th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 8.		An 8th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 8.

	~~Discussed~~ elsewhere ~~are~~:		Temperaments discussed elsewhere include:
	* ''Octant'', → [[Schismatic family#Octant\|Schismatic family]]		* ''Octant'' → [[Schismatic family#Octant\|Schismatic family]]
	* ''Octoid'', → [[Ragismic microtemperaments#Octoid\|Ragismic microtemperaments]]

	== Octatonic ==		== Octatonic ==
	[[12/11]] is very close to 1 step of 8edo, and hence this temperament tempers out the octatonic comma, the difference between a stack of 8 12/11's and the octave. The octatonic temperament makes a [[consistent circle]].		[[12/11]] is very close to 1 step of 8edo, and hence this temperament tempers out the octatonic comma, the difference between a stack of 8 12/11's and the octave. The octatonic temperament makes a [[consistent circle]].

	Subgroup: 2.3.11		[[Subgroup]]: 2.3.11

	Comma list: {{monzo\|15 8 0 0 -8}}		[[Comma list]]: {{monzo\|15 8 0 0 -8}}

	{{Mapping\|legend=1\|8 0 15\|0 1 1}}		{{Mapping\|legend=1\|8 0 15\|0 1 1}}

	: Mapping generators: ~12/11 ~~= 1\8~~, ~3		: Mapping generators: ~12/11, ~3

	[[Support]]ing [[ET]]s: {{EDOs\|16, 24, 32, 48, 56, 80~~, 72~~, 120, 128, 152}}, ...		[[Support]]ing [[ET]]s: {{EDOs\|16, 24, 32, 48, 56, 72, 80, 120, 128, 152}}, ...

	== Octium ==		== Octium ==
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	{{Mapping\|legend=2\| 8 2 35 25 47 2 \| 0 21 -2 22 -16 74 }}		{{Mapping\|legend=2\| 8 2 35 25 47 2 \| 0 21 -2 22 -16 74 }}

	: Mapping generators: ~10051/9216 ~~= 1\8~~, ~24/23 ~~= 76.284~~		: Mapping generators: ~10051/9216, ~24/23

	[[Optimal tuning]] ([[CTE]]): ~24/23 = 76.284		[[Optimal tuning]] ([[CTE]]): ~24/23 = 76.284
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	[[Support]]ing [[ET]]s: {{EDOs\|472, 1400, 1872, 3272, 5144}}		[[Support]]ing [[ET]]s: {{EDOs\|472, 1400, 1872, 3272, 5144}}

	== Octoid ~~(5-limit)~~ ==		== Octoid ==
	''For the 7-limit temperament, see [[Ragismic microtemperaments#Octoid]].''		: ''For the 7-limit temperament, see [[Ragismic microtemperaments #Octoid]].''

	Subgroup: 2.3.5		[[Subgroup]]: 2.3.5

	Comma list: 59604644775390625/59296646043258912		[[Comma list]]: 59604644775390625/59296646043258912

	{{Mapping\|legend=2\| 8 1 3 \| 0 3 4 }}		{{Mapping\|legend=1\| 8 1 3 \| 0 3 4 }}

	~~[[Optimal tuning]] ([[CWE]])~~: ~2125764/1953125 ~~= 1\8~~, ~4374/3125 ~~= 584.025~~		: Mapping generators: ~2125764/1953125, ~4374/3125

	[[~~Support~~]]~~ing~~ [[ET]]s: {{~~EDOs~~\|8, ~~152~~, ~~224~~, 72, ~~376~~, 80, ~~600, 528, 296, 64c, 232, 88bc, 824~~, ~~680~~}}		[[Optimal tuning]]s:
			* [[WE]]: ~2125764/1953125 = 150.001{{c}}, ~4374/3125 = 584.027{{c}}
			* [[CWE]]: ~2125764/1953125 = 150.000{{c}}, ~4374/3125 = 584.025{{c}}

			{{Optimal ET sequence\|legend=1\| 8, 56bcc, 64c, 72, 152, 224, 376, 976 }}

			[[Badness]] (Sintel): 6.687

	{{Navbox fractional-octave}}		{{Navbox fractional-octave}}

Xenllium at 13:30, 13 April 2025

2025-04-13T13:30:55Z

← Older revision		Revision as of 13:30, 13 April 2025
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			{{Technical data page}}
	{{Infobox fractional-octave\|8}}		{{Infobox fractional-octave\|8}}
			An 8th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 8.

	Discussed elsewhere are:		Discussed elsewhere are:
	* ''Octant'', → [[Schismatic family#Octant\|Schismatic family]]		* ''Octant'', → [[Schismatic family#Octant\|Schismatic family]]
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	{{Mapping\|legend=1\|8 0 15\|0 1 1}}		{{Mapping\|legend=1\|8 0 15\|0 1 1}}

	: ~~mapping~~ generators: ~12/11 = 1\8, ~3		: Mapping generators: ~12/11 = 1\8, ~3

	[[Support]]ing [[ET]]s: {{EDOs\|16, 24, 32, 48, 56, 80, 72, 120, 128, 152}}, ...		[[Support]]ing [[ET]]s: {{EDOs\|16, 24, 32, 48, 56, 80, 72, 120, 128, 152}}, ...
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	{{Mapping\|legend=2\| 8 2 35 25 47 2 \| 0 21 -2 22 -16 74 }}		{{Mapping\|legend=2\| 8 2 35 25 47 2 \| 0 21 -2 22 -16 74 }}

	: ~~mapping~~ generators: ~10051/9216 = 1\8, ~24/23 = 76.284		: Mapping generators: ~10051/9216 = 1\8, ~24/23 = 76.284

	[[Optimal tuning]] ([[CTE]]): ~24/23 = 76.284		[[Optimal tuning]] ([[CTE]]): ~24/23 = 76.284

ArrowHead294 at 03:59, 14 February 2025

2025-02-14T03:59:30Z

← Older revision		Revision as of 03:59, 14 February 2025
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	{{~~Fractional~~-octave ~~navigation~~\|8}}		{{Infobox fractional-octave\|8}}
	Discussed elsewhere are:		Discussed elsewhere are:
	* ''Octant'', → [[Schismatic family#Octant\|Schismatic family]]		* ''Octant'', → [[Schismatic family#Octant\|Schismatic family]]
	* ''Octoid'', → [[Ragismic microtemperaments#Octoid\|Ragismic microtemperaments]]		* ''Octoid'', → [[Ragismic microtemperaments#Octoid\|Ragismic microtemperaments]]

	== Octatonic ==		== Octatonic ==
	[[12/11]] is very close to 1 step of 8edo, and hence this temperament tempers out the octatonic comma, the difference between a stack of 8 12/11's and the octave. The octatonic temperament makes a [[consistent circle]].		[[12/11]] is very close to 1 step of 8edo, and hence this temperament tempers out the octatonic comma, the difference between a stack of 8 12/11's and the octave. The octatonic temperament makes a [[consistent circle]].

BudjarnLambeth: navbox

2024-12-05T07:16:27Z

navbox

← Older revision		Revision as of 07:16, 5 December 2024
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	[[Support]]ing [[ET]]s: {{EDOs\|8, 152, 224, 72, 376, 80, 600, 528, 296, 64c, 232, 88bc, 824, 680}}		[[Support]]ing [[ET]]s: {{EDOs\|8, 152, 224, 72, 376, 80, 600, 528, 296, 64c, 232, 88bc, 824, 680}}

			{{Navbox fractional-octave}}

Eliora: note the specialty

2024-09-08T19:17:47Z

note the specialty

← Older revision		Revision as of 19:17, 8 September 2024
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	* ''Octoid'', → [[Ragismic microtemperaments#Octoid\|Ragismic microtemperaments]]		* ''Octoid'', → [[Ragismic microtemperaments#Octoid\|Ragismic microtemperaments]]
	== Octatonic ==		== Octatonic ==
	[[12/11]] is very close to 1 step of 8edo, and hence this temperament tempers out the octatonic comma, the difference between a stack of 8 12/11's and the octave.		[[12/11]] is very close to 1 step of 8edo, and hence this temperament tempers out the octatonic comma, the difference between a stack of 8 12/11's and the octave. The octatonic temperament makes a [[consistent circle]].

	Subgroup: 2.3.11		Subgroup: 2.3.11