Zeus: Difference between revisions

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'''Zeus''' is ~~the~~ [[rank-3 temperament]] tempering out [[121/120]] ~~and~~ [[176/175]].

'''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.

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

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

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

== Interval lattice ==

File:Lattice Zeus.png|11-limit zeus

File:Lattice Zeus13.png|13-limit zeus

</gallery>

== Chords ==

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]~~

{| class="wikitable center-1 center-2 center-3"

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

~~{| class="wikitable center-all~~"

|-

! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval]])

! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]]

! Fifth<br>(¢)

! Major<br>Third (¢)

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|}

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

== Music ==

; [[Mundoworld]]

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

[[Category:Zeus| ]]

[[Category:Rank-3 temperaments]]

[[Category:Porwell family]]

[[Category:Biyatismic clan]]

[[Category:Valinorsmic clan]]

[[Category:Keenanismic temperaments]]

@@ Line 1: / Line 1: @@
-'''Zeus''' is the [[rank-3 temperament]] tempering out [[121/120]] and [[176/175]].
+'''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.
-See [[Porwell family #Zeus]] or [[Biyatismic clan #Zeus]] for technical data.
+It also has an obvious extension to the 13-limit tempering out [[351/350]] and [[352/351]].
+See [[Biyatismic clan #Zeus]] for technical data.
+== Interval lattice ==
+<gallery>
+File:Lattice Zeus.png|11-limit zeus
+File:Lattice Zeus13.png|13-limit zeus
+</gallery>
+== Chords ==
+Zeus enables [[essentially tempered chord]]s of [[biyatismic chords|biyatismic]], [[valinorsmic chords|valinorsmic]], and [[keenanismic chords|keenanismic]].
 == Scales ==
@@ Line 15: / 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]
+{| class="wikitable center-1 center-2 center-3"
-Gencom mapping: {{mapping| 1 0 1 4 2 7 | 0 1 1 -1 1 -2 | 0 0 -2 3 -1 -1 }}
-{| class="wikitable center-all"
 |-
-! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval]])
+! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]]
 ! Fifth<br>(¢)
 ! Major<br>Third (¢)
@@ Line 111: / Line 118: @@
 |}
-[[Category:Temperaments]]
+== Music ==
+; [[Mundoworld]]
+* [https://www.youtube.com/watch?v=zo1IYJW43II ''Cloudtop Reverie''] (2021) – in Zeus[7], 99edo tuning
 [[Category:Zeus| ]] <!-- main article -->
+[[Category:Rank-3 temperaments]]
 [[Category:Porwell family]]
 [[Category:Biyatismic clan]]
 [[Category:Valinorsmic clan]]
+[[Category:Keenanismic temperaments]]