Septiennealimmal clan - Revision history

FloraC: Text replacement - "Subgroup-val mapping: {{mapping| " to "{{Mapping|legend=2| "

2026-09-30T17:44:25Z

Text replacement - "Subgroup-val mapping: {{mapping| " to "{{Mapping|legend=2| "

← Older revision		Revision as of 17:44, 30 September 2026
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	Comma list: 41503/41472, 43923/43904		Comma list: 41503/41472, 43923/43904

	~~Subgroup-val mapping:~~ {{~~mapping~~\| 9 0 11 24 \| 0 2 2 1 }}		{{Mapping\|legend=2\| 9 0 11 24 \| 0 2 2 1 }}
	: mapping generators: ~121/112, ~343/198		: mapping generators: ~121/112, ~343/198

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	Comma list: 1216/1215, 1540/1539, 2080/2079, 2376/2375, 2401/2400		Comma list: 1216/1215, 1540/1539, 2080/2079, 2376/2375, 2401/2400

	~~Subgroup-val mapping:~~ {{~~mapping~~\| 9 1 1 12 -75 -106 -48 \| 0 2 3 2 16 21 13 }}		{{Mapping\|legend=2\| 9 1 1 12 -75 -106 -48 \| 0 2 3 2 16 21 13 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 169/168, 31213/31104		Comma list: 169/168, 31213/31104

	~~Subgroup-val mapping:~~ {{~~mapping~~\| 9 0 11 19 \| 0 1 1 1 }}		{{Mapping\|legend=2\| 9 0 11 19 \| 0 1 1 1 }}

	Optimal tunings:		Optimal tunings:

FloraC: Text replacement - "{{Mapping|legend=2| " to "{{Mapping|legend=3| "

2026-09-30T17:39:10Z

Text replacement - "{{Mapping|legend=2| " to "{{Mapping|legend=3| "

← Older revision		Revision as of 17:39, 30 September 2026
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	[[Comma list]]: 40353607/40310784		[[Comma list]]: 40353607/40310784

	{{Mapping\|legend=2\| 9 0 11 \| 0 1 1 }}		{{Mapping\|legend=3\| 9 0 11 \| 0 1 1 }}
	: mapping generators: ~2592/2401, ~3		: mapping generators: ~2592/2401, ~3

FloraC: Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

2026-09-24T12:33:13Z

Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

Show changes

FloraC: /* Enneabiotic */ + an obvious add-19 extension

2026-08-31T07:27:22Z

Enneabiotic: + an obvious add-19 extension

← Older revision		Revision as of 07:27, 31 August 2026
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	Badness (Sintel): 0.912		Badness (Sintel): 0.912

			===== 2.3.5.7.11.13.19 subgroup =====
			Subgroup: 2.3.5.7.11.13.19

			Comma list: 1216/1215, 1540/1539, 2080/2079, 2376/2375, 2401/2400

			Subgroup-val mapping: {{mapping\| 9 1 1 12 -75 -106 -48 \| 0 2 3 2 16 21 13 }}

			Optimal tunings:
			* WE: ~27/25 = 133.3209{{c}}, ~5/3 = 884.3968{{c}} (~36/35 = 48.8494{{c}})
			* CWE: ~27/25 = 133.3333{{c}}, ~5/3 = 884.4722{{c}} (~36/35 = 48.8612{{c}})

			{{Optimal ET sequence\|legend=0\| 99ef, 171ef, 270, 639h, 909h, 1179h }}

			Badness (Sintel): 0.684

	==== Enneabio ====		==== Enneabio ====

FloraC: Recategorize

2026-08-15T07:42:16Z

Recategorize

← Older revision		Revision as of 07:42, 15 August 2026
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	[[Category:Septiennealimmal clan\| ]] <!-- main article -->		[[Category:Septiennealimmal clan\| ]] <!-- main article -->
	[[Category:Temperament clans]]		[[Category:Temperament clans]]
			[[Category:Catalogs of rank-2 temperaments]]

FloraC: /* Ennealimmal */ update

2026-06-29T04:18:42Z

Ennealimmal: update

← Older revision		Revision as of 04:18, 29 June 2026
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	== Ennealimmal ==		== Ennealimmal ==
	{{Main\| Ennealimmal }}		{{Main\| Ennealimmal }}
	: ''For the 5-limit version, see [[~~Ennealimma~~ #Ennealimmal]].''		: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Ennealimmal]].''

	Ennealimmal tempers out the two smallest 7-limit [[superparticular]] commas, [[2401/2400]] and [[4375/4374]], leading to a temperament of unusual [[efficiency]]. It also tempers out the [[landscape comma]], which is (2401/2400)/(4375/4374), and the [[wizma]], which is (2401/2400)⋅(4375/4374). 7-limit ennealimmal's [[S-expression]]-based comma list is {[[4375/4374\|S25/S27]], [[2401/2400\|S49]]}.		Ennealimmal tempers out the two smallest 7-limit [[superparticular]] commas, [[2401/2400]] and [[4375/4374]], leading to a temperament of unusual [[efficiency]]. It also tempers out the [[landscape comma]], which is (2401/2400)/(4375/4374), and the [[wizma]], which is (2401/2400)⋅(4375/4374). 7-limit ennealimmal's [[S-expression]]-based comma list is {[[4375/4374\|S25/S27]], [[2401/2400\|S49]]}.

FloraC: Change several names, as planned

2026-05-19T08:42:14Z

Change several names, as planned

← Older revision		Revision as of 08:42, 19 May 2026
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	[[Badness]] (Sintel): 0.0914		[[Badness]] (Sintel): 0.0914

	=== ~~11-limit~~ ===		=== Enneabiotic ===
	~~The undecimal ennealimmal temperament can be described as~~ {{nowrap\| 99e & 171e }}~~, which~~ tempers out [[5632/5625]] (vishdel comma) and [[19712/19683]] (symbiotic comma).		Enneabiotic ({{nowrap\| 99e & 171e }}) tempers out [[5632/5625]] (vishdel comma) and [[19712/19683]] (symbiotic comma). It is catalogued as ''undecimal ennealimmal'' in [[Graham Breed]]'s [https://x31eq.com/temper/ Temperament Finder].

	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11
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	==== 13-limit ====		==== 13-limit ====
			Subgroup: 2.3.5.7.11.13

			Comma list: 2080/2079, 2401/2400, 4375/4374, 5632/5625

			Mapping: {{mapping\| 9 1 1 12 -75 -106 \| 0 2 3 2 16 21 }}

			Optimal tunings:
			* WE: ~27/25 = 133.3215{{c}}, ~5/3 = 884.4027{{c}} (~36/35 = 48.8479{{c}})
			* CWE: ~27/25 = 133.3333{{c}}, ~5/3 = 884.4745{{c}} (~36/35 = 48.8589{{c}})

			{{Optimal ET sequence\|legend=0\| 99ef, 171ef, 270, 639, 909, 1179, 2088bce }}

			Badness (Sintel): 0.912

			==== Enneabio ====
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

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	Badness (Sintel): 1.25		Badness (Sintel): 1.25

	===~~= Ennealimmalis =~~===		=== Ennealympic ===
	~~Subgroup: 2.3.5.7.11.13~~		Ennealympic ({{nowrap\| 99 & 171 }}, formerly ''ennealimmia'') is an alternative extension which tempers out [[131072/130977]] (olympia).

	~~Comma list: 2080/2079, 2401/2400, 4375/4374, 5632/5625~~

	~~Mapping:~~ {{~~mapping~~\| ~~9 1 1 12 -75 -106 \| 0 2 3 2 16 21 }}~~

	~~Optimal tunings:~~
	* WE: ~27/25 = 133.3215{{c}}, ~~~5/3 = 884.4027{{c}} (~36/35 = 48.8479{{c}}~~)
	* CWE: ~27/25 = 133.3333{{c}}, ~5/3 = 884.4745{{c}} (~36/35 = 48.8589{{c}})

	~~{{Optimal ET sequence\|legend=0\| 99ef, 171ef, 270, 639, 909, 1179, 2088bce }}~~

	~~Badness (Sintel): 0.912~~

	~~=== Ennealimmia ===~~
	~~The ennealimmia temperament~~ is an alternative extension ~~and can be described as {{nowrap\| 99 & 171 }},~~ which tempers out [[131072/130977]] (olympia).

	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11
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	=== Ennealimnic ===		=== Ennealimnic ===
	{{Distinguish\| Ennealimmic }}		{{Distinguish\| Ennealimmic }}
			{{See also\| Chords of ennealimnic }}

	Ennealimnic ({{nowrap\| 72 & 171 }}) equates 11/9 with 27/22, 49/40, and 60/49 as a neutral third interval.		Ennealimnic ({{nowrap\| 72 & 171 }}) equates 11/9 with 27/22, 49/40, and 60/49 as a neutral third interval.
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	Badness (Sintel): 0.673		Badness (Sintel): 0.673

	~~See also: [[Chords of ennealimnic]]~~

	==== 13-limit ====		==== 13-limit ====
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	* CWE: ~27/26 = 66.6667{{c}}, ~26/15 = 951.0386{{c}}		* CWE: ~27/26 = 66.6667{{c}}, ~26/15 = 951.0386{{c}}

	{{Optimal ET sequence\|legend=1\| 72, 198g, 270 }}		{{Optimal ET sequence\|legend=0\| 72, 198g, 270 }}

	Badness (Sintel): 0.812		Badness (Sintel): 0.812
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	Badness (Sintel): 0.927		Badness (Sintel): 0.927

	=== ~~Semiennealimmal~~ ===		=== Ennealimmapine ===
	~~Semiennealimmal~~ tempers out [[4000/3993]], and uses a ~140/121 semifourth generator. ~~Notably, however~~, ~~two generator steps do not reach~~ ~4/3, ~~despite that~~ the ~~name may suggest so. In fact~~, ~~it splits~~ the ~~generator~~ of ~~ennealimmal into three~~.		Ennealimmapine (formerly ''semiennealimmal'') tempers out [[4000/3993]], and uses a ~140/121 semifourth generator, six of which and 1/3 octave give the 3rd harmonic. Perhaps a better generator is the [[secor]], ~77/72, six of which give the perfect fifth, or the [[ptolemisma]], six of which and 1/3 octave give the perfect fourth.

	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

FloraC: Move septiennealic to the bottom as it skips two primes

2026-04-30T12:31:09Z

Move septiennealic to the bottom as it skips two primes

@@ Line 29: / Line 29: @@
 [[Badness]] (Sintel): 0.191
 === Ennea ===
 Subgroup: 2.3.7.11
@@ Line 804: / Line 783: @@
 Badness (Sintel): 1.49
 [[Category:Septiennealimmal clan| ]] <!-- main article -->
 [[Category:Temperament clans]]

FloraC: - undecipherable nonsense

2026-03-20T11:21:16Z

- undecipherable nonsense

← Older revision		Revision as of 11:21, 20 March 2026
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	=== Hemiennealimmal ===		=== Hemiennealimmal ===
	Hemiennealimmal ({{nowrap\| 72 & 198 }}) has a period of 1/18 octave and tempers out the four smallest superparticular commas of the 11-limit JI, 2401/2400, [[3025/3024]], 4375/4374, and [[9801/9800]]. ~~Tempering out 9801/9800 leads to an octave split into two equal parts. Notably, every one of these commas is part of one or more known infinite comma families; see directly below.~~		Hemiennealimmal ({{nowrap\| 72 & 198 }}) has a period of 1/18 octave and tempers out the four smallest superparticular commas of the 11-limit JI, 2401/2400, [[3025/3024]], 4375/4374, and [[9801/9800]]. Its [[S-expression]]-based comma list is {([[3025/3024\|S22/S24 = S55 = S25/S27 × S99]]), [[4375/4374\|S25/S27]], [[2401/2400\|S49]], [[9801/9800\|S33/S35 = S99]]}. Tempering out 9801/9800 leads to an octave split into two equal parts.

	Its [[S-expression]]-based comma list is {([[3025/3024\|S22/S24 = S55 = S25/S27 × S99]]), [[4375/4374\|S25/S27]], [[2401/2400\|S49]], [[9801/9800\|S33/S35 = S99]]}.

	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

FloraC: Note source of names

2026-03-20T11:18:25Z

Note source of names

← Older revision		Revision as of 11:18, 20 March 2026
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	== Undecentic ==		== Undecentic ==
	~~Undecentic~~ ({{nowrap\| 99 & 198 }}) has a period of 1/99 octave.		{{Distinguish\| Undecental }}

			Named by [[Xenllium]] in 2021, undecentic ({{nowrap\| 99 & 198 }}) has a period of 1/99 octave.

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11
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	== Schisennealimmal ==		== Schisennealimmal ==
	Schisennealimmal ({{nowrap\| 171 & 342 }}) has a period of 1/171 octave. [[171edo]] and its multiples are members of both [[schismic]] and ennealimmal~~, and from this it derives its name~~.		Schisennealimmal ({{nowrap\| 171 & 342 }}) has a period of 1/171 octave. It was named by [[Xenllium]] in 2021 for the fact that [[171edo]] and its multiples are members of both [[schismic]] and ennealimmal.

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11
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	== Lunennealimmal ==		== Lunennealimmal ==
	Lunennealimmal ({{nowrap\| 441 & 882 }}) has has a period of 1/441 octave. [[441edo]] and its multiples are members of both [[luna]] and ennealimmal~~, and from this it derives its name~~.		Lunennealimmal ({{nowrap\| 441 & 882 }}) has has a period of 1/441 octave. It was named by [[Xenllium]] in 2021 for the fact that [[441edo]] and its multiples are members of both [[luna]] and ennealimmal.

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11