Zeus - Revision history

FloraC: Text replacement - "rank-3 temperament" to "rank-3 temperament"

2026-06-08T08:36:21Z

Text replacement - "rank-3 temperament" to "rank-3 temperament"

← Older revision		Revision as of 08:36, 8 June 2026
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	\| Odd limit 2 = 13-limit 21 \| Mistuning 2 = 7.72 \| Complexity 2 = ?		\| Odd limit 2 = 13-limit 21 \| Mistuning 2 = 7.72 \| Complexity 2 = ?
	}}		}}
	'''Zeus''' is a [[rank-3 ~~temperament\|rank-3]] [[regular temperament\|~~temperament]] generated by an [[2/1\|octave]], a [[3/2\|fifth]], and a neutral second which stands in for both undecimal neutral seconds of [[11/10]] and [[12/11]] as well as the septimal neutral second of [[35/32]], [[tempering out]] [[121/120]], [[176/175]], and [[385/384]]. Notice {{nowrap\| 121/120 {{=}} (176/175)⋅(385/384)}}. That makes 11-limit harmony particularly efficient and deeply entangled with 7-limit harmony. This temperament is, in fact, one of the best ways to further temper on top of tempering out 121/120. That said, 121/120 is such a comma that, on tempering out, will neutralize the distinction between many otonal- and utonal-11 chords, so it might not fit those who wish to explore the subtlety of tones in the 11-limit.		'''Zeus''' is a [[rank-3 temperament]] generated by an [[2/1\|octave]], a [[3/2\|fifth]], and a neutral second which stands in for both undecimal neutral seconds of [[11/10]] and [[12/11]] as well as the septimal neutral second of [[35/32]], [[tempering out]] [[121/120]], [[176/175]], and [[385/384]]. Notice {{nowrap\| 121/120 {{=}} (176/175)⋅(385/384)}}. That makes 11-limit harmony particularly efficient and deeply entangled with 7-limit harmony. This temperament is, in fact, one of the best ways to further temper on top of tempering out 121/120. That said, 121/120 is such a comma that, on tempering out, will neutralize the distinction between many otonal- and utonal-11 chords, so it might not fit those who wish to explore the subtlety of tones in the 11-limit.

	It also has an obvious extension to the 13-limit tempering out [[351/350]] and [[352/351]].		It also has an obvious extension to the 13-limit tempering out [[351/350]] and [[352/351]].

FloraC: + infobox

2026-03-18T10:29:03Z

+ infobox

← Older revision		Revision as of 10:29, 18 March 2026
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			{{Infobox regtemp
			\| Title = Zeus
			\| Subgroups = 2.3.5.7.11; 2.3.5.7.11.13
			\| Comma basis = [[121/120]], [[176/175]] (11-limit); <br>[[121/120]], [[176/175]], [[351/350]] (13-limit)
			\| Edo join 1 = 31 \| Edo join 2 = 46 \| Edo join 3 = 53
			\| Mapping = 1; 1 1 -1 1 -2; 0 -2 3 -1 -1
			\| Generators = 3/2, 12/11
			\| Generators tuning = 701.9, 157.0
			\| Optimization method = CWE
			\| Odd limit 1 = 11 \| Mistuning 1 = 7.48 \| Complexity 1 = ?
			\| Odd limit 2 = 13-limit 21 \| Mistuning 2 = 7.72 \| Complexity 2 = ?
			}}
	'''Zeus''' is a [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] generated by an [[2/1\|octave]], a [[3/2\|fifth]], and a neutral second which stands in for both undecimal neutral seconds of [[11/10]] and [[12/11]] as well as the septimal neutral second of [[35/32]], [[tempering out]] [[121/120]], [[176/175]], and [[385/384]]. Notice {{nowrap\| 121/120 {{=}} (176/175)⋅(385/384)}}. That makes 11-limit harmony particularly efficient and deeply entangled with 7-limit harmony. This temperament is, in fact, one of the best ways to further temper on top of tempering out 121/120. That said, 121/120 is such a comma that, on tempering out, will neutralize the distinction between many otonal- and utonal-11 chords, so it might not fit those who wish to explore the subtlety of tones in the 11-limit.		'''Zeus''' is a [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] generated by an [[2/1\|octave]], a [[3/2\|fifth]], and a neutral second which stands in for both undecimal neutral seconds of [[11/10]] and [[12/11]] as well as the septimal neutral second of [[35/32]], [[tempering out]] [[121/120]], [[176/175]], and [[385/384]]. Notice {{nowrap\| 121/120 {{=}} (176/175)⋅(385/384)}}. That makes 11-limit harmony particularly efficient and deeply entangled with 7-limit harmony. This temperament is, in fact, one of the best ways to further temper on top of tempering out 121/120. That said, 121/120 is such a comma that, on tempering out, will neutralize the distinction between many otonal- and utonal-11 chords, so it might not fit those who wish to explore the subtlety of tones in the 11-limit.

FloraC: /* Tunings */ + basic norm-based tunings

2025-12-01T13:50:06Z

Tunings: + basic norm-based tunings

@@ Line 27: / Line 27: @@
 == Tunings ==
 === Tuning spectrum ===
 This spectrum assumes pure 2 and 7/5.

FloraC at 13:45, 1 December 2025

2025-12-01T13:45:12Z

← Older revision		Revision as of 13:45, 1 December 2025
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	</gallery>		</gallery>

	== Chords ==		== Chords and harmony ==
	Zeus enables [[essentially tempered chord]]s of [[biyatismic chords\|biyatismic]], [[valinorsmic chords\|valinorsmic]], [[keenanismic chords\|keenanismic]], and [[zeus chords\|zeus]]. In the 13-limit, it enables chords of [[ratwolfsmic chords\|ratwolfsmic]], [[major minthmic chords\|major minthmic]], and [[catadictmic chords\|catadictmic]].		Zeus enables [[essentially tempered chord]]s of [[biyatismic chords\|biyatismic]], [[valinorsmic chords\|valinorsmic]], [[keenanismic chords\|keenanismic]], and [[zeus chords\|zeus]]. In the 13-limit, it enables chords of [[ratwolfsmic chords\|ratwolfsmic]], [[major minthmic chords\|major minthmic]], and [[catadictmic chords\|catadictmic]].

FloraC: Note some 13-limit chords

2025-12-01T10:49:31Z

Note some 13-limit chords

← Older revision		Revision as of 10:49, 1 December 2025
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	== Chords ==		== Chords ==
	Zeus enables [[essentially tempered chord]]s of [[biyatismic chords\|biyatismic]], [[valinorsmic chords\|valinorsmic]], ~~and~~ [[keenanismic chords\|keenanismic]].		Zeus enables [[essentially tempered chord]]s of [[biyatismic chords\|biyatismic]], [[valinorsmic chords\|valinorsmic]], [[keenanismic chords\|keenanismic]], and [[zeus chords\|zeus]]. In the 13-limit, it enables chords of [[ratwolfsmic chords\|ratwolfsmic]], [[major minthmic chords\|major minthmic]], and [[catadictmic chords\|catadictmic]].

	== Scales ==		== Scales ==

FloraC: - parent category

2025-04-29T09:54:54Z

- parent category

← Older revision		Revision as of 09:54, 29 April 2025
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	* [https://www.youtube.com/watch?v=zo1IYJW43II ''Cloudtop Reverie''] (2021) – in Zeus[7], 99edo tuning		* [https://www.youtube.com/watch?v=zo1IYJW43II ''Cloudtop Reverie''] (2021) – in Zeus[7], 99edo tuning

	~~[[Category:Temperaments]]~~
	[[Category:Zeus\| ]] <!-- main article -->		[[Category:Zeus\| ]] <!-- main article -->
	[[Category:Rank-3 temperaments]]		[[Category:Rank-3 temperaments]]

Lériendil at 00:07, 20 April 2025

2025-04-20T00:07:29Z

← Older revision		Revision as of 00:07, 20 April 2025
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	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Zeus\| ]] <!-- main article -->		[[Category:Zeus\| ]] <!-- main article -->
			[[Category:Rank-3 temperaments]]
	[[Category:Porwell family]]		[[Category:Porwell family]]
	[[Category:Biyatismic clan]]		[[Category:Biyatismic clan]]
	[[Category:Valinorsmic clan]]		[[Category:Valinorsmic clan]]
	[[Category:Keenanismic temperaments]]		[[Category:Keenanismic temperaments]]

FloraC: Improve the intro

2025-04-04T08:10:38Z

Improve the intro

← Older revision		Revision as of 08:10, 4 April 2025
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	'''Zeus''' is ~~the~~ [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] [[tempering out]] [[121/120]], [[176/175]], and [[385/384]]. Notice {{nowrap\| 121/120 {{=}} (176/175)⋅(385/384)}}~~. It thus equates the septimal neutral second of [[35/32]] with both [[11/10]] and [[12/11]]~~. That makes 11-limit harmony particularly efficient and deeply entangled with 7-limit harmony. ~~The~~ temperament is, in fact, one of the best ways to further temper on top of tempering out 121/120. That said, 121/120 is such a comma that, on tempering out, will neutralize the distinction between many otonal- and utonal-11 chords, so it might not fit those who wish to explore the subtlety of tones in the 11-limit.		'''Zeus''' is a [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] generated by an [[2/1\|octave]], a [[3/2\|fifth]], and a neutral second which stands in for both undecimal neutral seconds of [[11/10]] and [[12/11]] as well as the septimal neutral second of [[35/32]], [[tempering out]] [[121/120]], [[176/175]], and [[385/384]]. Notice {{nowrap\| 121/120 {{=}} (176/175)⋅(385/384)}}. That makes 11-limit harmony particularly efficient and deeply entangled with 7-limit harmony. This temperament is, in fact, one of the best ways to further temper on top of tempering out 121/120. That said, 121/120 is such a comma that, on tempering out, will neutralize the distinction between many otonal- and utonal-11 chords, so it might not fit those who wish to explore the subtlety of tones in the 11-limit.

	It also has an obvious extension to the 13-limit tempering out [[351/350]] and [[352/351]].		It also has an obvious extension to the 13-limit tempering out [[351/350]] and [[352/351]].

FloraC: Cleanup

2025-04-04T08:03:42Z

Cleanup

← Older revision		Revision as of 08:03, 4 April 2025
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	'''Zeus''' is the [[~~Rank~~-3 temperament\|rank-3]] [[temperament]] [[tempering out]] [[121/120]], [[176/175]], and [[385/384]]. Notice 121/120 = (176/175)(385/384)~~, it~~ thus equates the septimal neutral second of [[35/32]] with both [[11/10]] and [[12/11]]. That makes 11-limit harmony particularly efficient and deeply entangled with 7-limit harmony. The temperament is, in fact, one of the best ways to further temper on top of tempering out 121/120. That said, 121/120 is such a comma that, on tempering out, will neutralize the distinction between many otonal- and utonal-11 chords, so it might not fit those who wish to explore the subtlety of tones in the 11-limit.		'''Zeus''' is the [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] [[tempering out]] [[121/120]], [[176/175]], and [[385/384]]. Notice {{nowrap\| 121/120 {{=}} (176/175)⋅(385/384)}}. It thus equates the septimal neutral second of [[35/32]] with both [[11/10]] and [[12/11]]. That makes 11-limit harmony particularly efficient and deeply entangled with 7-limit harmony. The temperament is, in fact, one of the best ways to further temper on top of tempering out 121/120. That said, 121/120 is such a comma that, on tempering out, will neutralize the distinction between many otonal- and utonal-11 chords, so it might not fit those who wish to explore the subtlety of tones in the 11-limit.

	It also has an obvious extension to the 13-limit tempering out [[351/350]] and [[352/351]].		It also has an obvious extension to the 13-limit tempering out [[351/350]] and [[352/351]].

	See ~~[[Porwell family #Zeus]] or~~ [[Biyatismic clan #Zeus]] for technical data.		See [[Biyatismic clan #Zeus]] for technical data.

	== Interval lattice ==		== Interval lattice ==
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	== Chords ==		== Chords ==
	Zeus enables [[essentially tempered chord]]s of [[~~Biyatismic~~ chords\|biyatismic]], [[~~Valinorsmic~~ chords\|valinorsmic]], and [[~~Keenanismic~~ chords\|keenanismic]].		Zeus enables [[essentially tempered chord]]s of [[biyatismic chords\|biyatismic]], [[valinorsmic chords\|valinorsmic]], and [[keenanismic chords\|keenanismic]].

	== Scales ==		== Scales ==
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	* [[Genus1155zeus]]		* [[Genus1155zeus]]

	== Tuning spectrum ==		== Tunings ==
			=== Tuning spectrum ===
	This spectrum assumes pure 2 and 7/5.		This spectrum assumes pure 2 and 7/5.

	~~Gencom: [2 3 11/10; 121/120 176/175 351/350]~~

	~~Gencom mapping: {{mapping\| 1 0 1 4 2 7 \| 0 1 1 -1 1 -2 \| 0 0 -2 3 -1 -1 }}~~

	{\| class="wikitable center-1 center-2 center-3"		{\| class="wikitable center-1 center-2 center-3"
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	== Music ==		== Music ==
	; [[Mundoworld]]		; [[Mundoworld]]
	* [https://www.youtube.com/watch?v=zo1IYJW43II ''Cloudtop Reverie''] (2021) – ~~zeus~~[7] in 99edo tuning		* [https://www.youtube.com/watch?v=zo1IYJW43II ''Cloudtop Reverie''] (2021) – in Zeus[7], 99edo tuning

	[[Category:Temperaments]]		[[Category:Temperaments]]

FloraC: +music

2023-10-24T08:49:56Z

+music

← Older revision		Revision as of 08:49, 24 October 2023
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	\|		\|
	\|}		\|}

			== Music ==
			; [[Mundoworld]]
			* [https://www.youtube.com/watch?v=zo1IYJW43II ''Cloudtop Reverie''] (2021) – zeus[7] in 99edo tuning

	[[Category:Temperaments]]		[[Category:Temperaments]]