179edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:30:08Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:30, 13 March 2026
Line 81:		Line 81:
	\| [[Mabila]] (5-limit)		\| [[Mabila]] (5-limit)
	\|}		\|}
	<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==

FloraC: /* Regular temperament properties */ + subfourth

2025-10-28T11:25:31Z

Regular temperament properties: + subfourth

← Older revision		Revision as of 11:25, 28 October 2025
Line 19:		Line 19:
	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br />8ve stretch (¢)		! rowspan="2" \| Optimal<br>8ve stretch (¢)
	! colspan="2" \| Tuning error		! colspan="2" \| Tuning error
	\|-		\|-
Line 26:		Line 26:
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\| 284 -179 }}		\| {{Monzo\| 284 -179 }}
	\| {{~~mapping~~\| 179 284 }}		\| {{Mapping\| 179 284 }}
	\| −0.6169		\| −0.6169
	\| 0.6166		\| 0.6166
Line 33:		Line 33:
	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\| 20 -17 3 }}, {{monzo\| 28 -3 -10 }}		\| {{Monzo\| 20 -17 3 }}, {{monzo\| 28 -3 -10 }}
	\| {{~~mapping~~\| 179 284 416 }}		\| {{Mapping\| 179 284 416 }}
	\| −0.7718		\| −0.7718
	\| 0.5490		\| 0.5490
Line 41:		Line 41:
	\| 2.3.5.7		\| 2.3.5.7
	\| 3136/3125, 4375/4374, 65536/64827		\| 3136/3125, 4375/4374, 65536/64827
	\| {{~~mapping~~\| 179 284 416 503 }}		\| {{Mapping\| 179 284 416 503 }}
	\| −0.8673		\| −0.8673
	\| 0.5034		\| 0.5034
Line 51:		Line 51:
	\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	\|-		\|-
	! Periods<br />per 8ve		! Periods<br>per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br />ratio*		! Associated<br>ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 68:		Line 68:
	\| 6/5		\| 6/5
	\| [[Parakleismic]]		\| [[Parakleismic]]
			\|-
			\| 1
			\| 71\179
			\| 475.98
			\| 21/16
			\| [[Subfourth]] (179ef)
	\|-		\|-
	\| 1		\| 1
Line 75:		Line 81:
	\| [[Mabila]] (5-limit)		\| [[Mabila]] (5-limit)
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==

Lériendil: cohemimabila

2025-04-19T02:43:42Z

cohemimabila

← Older revision		Revision as of 02:43, 19 April 2025
Line 5:		Line 5:
	179edo does not approximate well any odd [[harmonic]] up to 23, best being [[21/16]] with 22% error. Nonetheless, it is [[consistent]] in the [[7-odd-limit]] and there are a number of temperaments to be considered.		179edo does not approximate well any odd [[harmonic]] up to 23, best being [[21/16]] with 22% error. Nonetheless, it is [[consistent]] in the [[7-odd-limit]] and there are a number of temperaments to be considered.

	The equal temperament [[tempering out\|tempers out]] the [[parakleisma]], {{monzo\| 8 14 -13 }} in the 5-limit, and [[support]]s [[parakleismic]] and its [[extension]]s, providing the [[optimal patent val]] for 11- and 13-limit [[Ragismic microtemperaments #parkleismic\|parkleismic]] temperament. In the 7-limit it tempers out [[3136/3125]], [[4375/4374]] and [[10976/10935]], in the 11-limit [[176/175]] and 1375/1372 and in the 13-limit [[169/168]], [[325/324]], [[351/350]] and [[352/351]], providing the optimal patent val for 11- and 13-limit [[ulmo]] temperament.		The equal temperament [[tempering out\|tempers out]] the [[parakleisma]], {{monzo\| 8 14 -13 }} in the 5-limit, and [[support]]s [[parakleismic]] and its [[extension]]s, providing the [[optimal patent val]] for 11- and 13-limit [[Ragismic microtemperaments #parkleismic\|parkleismic]] temperament. In the 7-limit it tempers out [[3136/3125]], [[4375/4374]] and [[10976/10935]], in the 11-limit [[176/175]] and 1375/1372 and in the 13-limit [[169/168]], [[325/324]], [[351/350]] and [[352/351]], providing the optimal patent val for 11- and 13-limit [[ulmo]] temperament. It is additionally the optimal patent val for 7-limit [[cohemimabila]].

	=== Odd harmonics ===		=== Odd harmonics ===

ArrowHead294 at 14:07, 20 February 2025

2025-02-20T14:07:21Z

← Older revision		Revision as of 14:07, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|179~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 17:50, 15 January 2025

2025-01-15T17:50:55Z

← Older revision		Revision as of 17:50, 15 January 2025
Line 28:		Line 28:
	\| {{monzo\| 284 -179 }}		\| {{monzo\| 284 -179 }}
	\| {{mapping\| 179 284 }}		\| {{mapping\| 179 284 }}
	\| -0.6169		\| −0.6169
	\| 0.6166		\| 0.6166
	\| 9.20		\| 9.20
Line 35:		Line 35:
	\| {{monzo\| 20 -17 3 }}, {{monzo\| 28 -3 -10 }}		\| {{monzo\| 20 -17 3 }}, {{monzo\| 28 -3 -10 }}
	\| {{mapping\| 179 284 416 }}		\| {{mapping\| 179 284 416 }}
	\| -0.7718		\| −0.7718
	\| 0.5490		\| 0.5490
	\| 8.19		\| 8.19
Line 42:		Line 42:
	\| 3136/3125, 4375/4374, 65536/64827		\| 3136/3125, 4375/4374, 65536/64827
	\| {{mapping\| 179 284 416 503 }}		\| {{mapping\| 179 284 416 503 }}
	\| -0.8673		\| −0.8673
	\| 0.5034		\| 0.5034
	\| 7.51		\| 7.51
Line 75:		Line 75:
	\| [[Mabila]] (5-limit)		\| [[Mabila]] (5-limit)
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "in a hopeless situation" from ''hope in dark times'' (2024) ~~–~~ [https://open.spotify.com/track/787NGqkI5FHjQcfEOu4y4w Spotify] \| [https://francium223.bandcamp.com/track/in-a-hopeless-situation Bandcamp] \| [https://www.youtube.com/watch?v=kGdWmP81jwc YouTube]		* "in a hopeless situation" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/787NGqkI5FHjQcfEOu4y4w Spotify] \| [https://francium223.bandcamp.com/track/in-a-hopeless-situation Bandcamp] \| [https://www.youtube.com/watch?v=kGdWmP81jwc YouTube]

	[[Category:Listen]]		[[Category:Listen]]

ArrowHead294: Partial undo

2024-11-16T12:58:50Z

Partial undo

← Older revision		Revision as of 12:58, 16 November 2024
Line 14:		Line 14:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
Line 36:		Line 45:
	\| 0.5034		\| 0.5034
	\| 7.51		\| 7.51
	~~{{comma basis end}~~}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
Line 58:		Line 74:
	\| 512/375		\| 512/375
	\| [[Mabila]] (5-limit)		\| [[Mabila]] (5-limit)
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	== Music ==		== Music ==

ArrowHead294 at 03:02, 16 November 2024

2024-11-16T03:02:11Z

← Older revision		Revision as of 03:02, 16 November 2024
Line 14:		Line 14:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! rowspan="2" \| [[Subgroup]]~~
	~~! rowspan="2" \| [[Comma list\|Comma List]]~~
	~~! rowspan="2" \| [[Mapping]]~~
	~~! rowspan="2" \| Optimal<br>8ve Stretch (¢)~~
	~~! colspan="2" \| Tuning Error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3		\| 2.3
Line 44:		Line 36:
	\| 0.5034		\| 0.5034
	\| 7.51		\| 7.51
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
Line 72:		Line 58:
	\| 512/375		\| 512/375
	\| [[Mabila]] (5-limit)		\| [[Mabila]] (5-limit)
	\|}		{{rank-2 end}}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "in a hopeless situation" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/787NGqkI5FHjQcfEOu4y4w Spotify] \| [https://francium223.bandcamp.com/track/in-a-hopeless-situation Bandcamp] \| [https://www.youtube.com/watch?v=kGdWmP81jwc YouTube]		* "in a hopeless situation" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/787NGqkI5FHjQcfEOu4y4w Spotify] \| [https://francium223.bandcamp.com/track/in-a-hopeless-situation Bandcamp] \| [https://www.youtube.com/watch?v=kGdWmP81jwc YouTube]

	[[Category:Listen]]		[[Category:Listen]]

FloraC: Correct a comma basis

2024-04-25T09:36:48Z

Correct a comma basis

← Older revision		Revision as of 09:36, 25 April 2024
Line 39:		Line 39:
	\|-		\|-
	\| 2.3.5.7		\| 2.3.5.7
	\| 3136/3125, 4375/4374, ~~10976~~/~~10935~~		\| 3136/3125, 4375/4374, 65536/64827
	\| {{mapping\| 179 284 416 503 }}		\| {{mapping\| 179 284 416 503 }}
	\| -0.8673		\| -0.8673
Line 71:		Line 71:
	\| 529.61		\| 529.61
	\| 512/375		\| 512/375
	\| [[Mabila]]		\| [[Mabila]] (5-limit)
	\|}		\|}
	<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

FloraC: Cleanup

2024-04-25T09:33:41Z

Cleanup

← Older revision		Revision as of 09:33, 25 April 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|179}}		{{EDO intro\|179}}

	== Theory ==		== Theory ==
	179edo ~~doesn't~~ approximate well any odd harmonic up to 23, best being [[21/16]] with 22% error. Nonetheless, it is consistent in the 7-limit and there are a number of temperaments to be considered.		179edo does not approximate well any odd [[harmonic]] up to 23, best being [[21/16]] with 22% error. Nonetheless, it is [[consistent]] in the [[7-odd-limit]] and there are a number of temperaments to be considered.

	~~179edo~~ tempers out the parakleisma, ~~1224440064/1220703125~~ in the 5-limit, and [[support]]s parakleismic and its ~~extensions~~, providing the optimal patent val for 11- and 13-limit [[~~Ragismic_microtemperaments~~\|parkleismic ~~temperament~~]]. In the 7-limit it tempers out 3136/3125, 4375/4374 and 10976/10935, in the 11-limit 176/175 and 1375/1372 and in the 13-limit 169/168, 325/324, 351/350 and 352/351, providing the optimal patent val for 11- and 13-limit [[~~Valinorismic_temperaments#Ulmo\|~~ulmo ~~temperament~~]].		The equal temperament [[tempering out\|tempers out]] the [[parakleisma]], {{monzo\| 8 14 -13 }} in the 5-limit, and [[support]]s [[parakleismic]] and its [[extension]]s, providing the [[optimal patent val]] for 11- and 13-limit [[Ragismic microtemperaments #parkleismic\|parkleismic]] temperament. In the 7-limit it tempers out [[3136/3125]], [[4375/4374]] and [[10976/10935]], in the 11-limit [[176/175]] and 1375/1372 and in the 13-limit [[169/168]], [[325/324]], [[351/350]] and [[352/351]], providing the optimal patent val for 11- and 13-limit [[ulmo]] temperament.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 12:		Line 13:
	179edo is the 41st [[prime edo]].		179edo is the 41st [[prime edo]].

	==Regular temperament properties==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \|[[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \|Optimal<br>8ve Stretch (¢)		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
	! colspan="2" \|Tuning Error		! colspan="2" \| Tuning Error
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\|2.3		\| 2.3
	\|{{monzo\|284 -179}}		\| {{monzo\| 284 -179 }}
	\|{{~~val~~\|179 284}}		\| {{mapping\| 179 284 }}
	\| -0.6169		\| -0.6169
	\| 0.6166		\| 0.6166
	\| 9.20		\| 9.20
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|20 -17 3}}, {{monzo\|28 -3 -10}}		\| {{monzo\| 20 -17 3 }}, {{monzo\| 28 -3 -10 }}
	\|{{~~val~~\|179 284 416}}		\| {{mapping\| 179 284 416 }}
	\| -0.7718		\| -0.7718
	\| 0.5490		\| 0.5490
	\| 8.19		\| 8.19
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|3136/3125, 4375/4374, 10976/10935		\| 3136/3125, 4375/4374, 10976/10935
	\|{{~~val~~\|179 284 416 503}}		\| {{mapping\| 179 284 416 503 }}
	\| -0.8673		\| -0.8673
	\| 0.5034		\| 0.5034
Line 49:		Line 50:
	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(reduced)~~		! Generator*
	! Cents~~<br>(reduced)~~		! Cents*
	! Associated<br>~~ratio~~		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|35\179		\| 35\179
	\|234.64		\| 234.64
	\|8/7		\| 8/7
	\|[[Rodan]]		\| [[Rodan]] (179d)
	\|-		\|-
	\|1		\| 1
	\|47\179		\| 47\179
	\|315.08		\| 315.08
	\|6/5		\| 6/5
	\|[[Parakleismic]]		\| [[Parakleismic]]
	\|-		\|-
	\|1		\| 1
	\|79\~~167~~		\| 79\179
	\|529.61		\| 529.61
	\|512/375		\| 512/375
	\|[[Mabila]]		\| [[Mabila]]
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	== Music ==		== Music ==
Line 77:		Line 79:
	* "in a hopeless situation" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/787NGqkI5FHjQcfEOu4y4w Spotify] \| [https://francium223.bandcamp.com/track/in-a-hopeless-situation Bandcamp] \| [https://www.youtube.com/watch?v=kGdWmP81jwc YouTube]		* "in a hopeless situation" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/787NGqkI5FHjQcfEOu4y4w Spotify] \| [https://francium223.bandcamp.com/track/in-a-hopeless-situation Bandcamp] \| [https://www.youtube.com/watch?v=kGdWmP81jwc YouTube]

	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~
	~~[[Category:Prime EDO]]~~
	[[Category:Listen]]		[[Category:Listen]]

Francium: +categories

2024-02-13T17:50:07Z

+categories

← Older revision		Revision as of 17:50, 13 February 2024
Line 79:		Line 79:
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->
	[[Category:Prime EDO]]		[[Category:Prime EDO]]
			[[Category:Listen]]