Zeus: Difference between revisions

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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]].

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

See [[Biyatismic clan #Zeus]] for technical data.

== Interval lattice ==

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== 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 ==

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* [[Genus1155zeus]]

== Tuning spectrum ==

== Tunings ==

=== Tuning spectrum ===

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"

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== Music ==

; [[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]]

@@ Line 1: / Line 1: @@
-'''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]].
-See [[Porwell family #Zeus]] or [[Biyatismic clan #Zeus]] for technical data.
+See [[Biyatismic clan #Zeus]] for technical data.
 == Interval lattice ==
@@ Line 12: / Line 12: @@
 == 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 ==
@@ Line 26: / Line 26: @@
 * [[Genus1155zeus]]
-== Tuning spectrum ==
+== Tunings ==
+=== Tuning spectrum ===
 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"
@@ Line 124: / Line 120: @@
 == Music ==
 ; [[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]]