Zeus: Difference between revisions

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-See [[Porwell family #Zeus]] for technical data.
+'''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.
-== Spectrum of zeus tunings by eigenmonzos ==
+It also has an obvious extension to the 13-limit tempering out [[351/350]] and [[352/351]].
-This spectrum assumes pure 2 and 7/5.
+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]].
-Gencom: [2 3 11/10; 121/120 176/175 351/350]
+== Scales ==
+* [[Zeus1]]
+* [[Zeus2]]
+* [[Zeus3]]
+* [[Zeus4]]
+* [[Zeus5]]
+* [[Zeus6]]
+* [[Zeus7]]
+* [[Zeus7tri]]
+* [[Zeus8tri]]
+* [[Genus1155zeus]]
-Gencom Mapping: [&lt;1 0 1 4 2 7|, &lt;0 1 1 -1 1 -2|, &lt;0 0 -2 3 -1 -1|]
+== Tunings ==
+=== Tuning spectrum ===
+This spectrum assumes pure 2 and 7/5.
-{| class="wikitable center-1 right-2 right-3"
+{| class="wikitable center-1 center-2 center-3"
 |-
-! Eigenmonzo
+! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]]
-! 3/2
+! Fifth<br>(¢)
-! 5/4
+! Major<br>Third (¢)
 ! Comments
 |-
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 |
 |}
+== 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 temperaments]]
+[[Category:Biyatismic clan]]
-[[Category:Valinorsmic temperaments]]
+[[Category:Valinorsmic clan]]
-{{IoT}}
+[[Category:Keenanismic temperaments]]
-{{todo| intro }}