Zeus: Difference between revisions

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-See [[Porwell family #Zeus]] for technical data.
+{{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.
-== Tuning spectrum ==
+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 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]].
+== Scales ==
+* [[Zeus1]]
+* [[Zeus2]]
+* [[Zeus3]]
+* [[Zeus4]]
+* [[Zeus5]]
+* [[Zeus6]]
+* [[Zeus7]]
+* [[Zeus7tri]]
+* [[Zeus8tri]]
+* [[Genus1155zeus]]
+== Tunings ==
+=== Norm-based tunings ===
+{| class="wikitable mw-collapsible mw-collapsed"
+|+ style="font-size: 105%; white-space: nowrap;" | 11-limit norm-based tunings
+|-
+! rowspan="2" |
+! colspan="3" | Euclidean
+|-
+! Constrained
+! Constrained & skewed
+! Destretched
+|-
+! Tenney
+| CTE: ~3/2 = 702.5294{{c}}, ~12/11 = 157.2407{{c}}
+| CWE: ~3/2 = 702.2478{{c}}, ~12/11 = 157.1265{{c}}
+| POTE: ~3/2 = 702.1530{{c}}, ~12/11 = 157.0881{{c}}
+|}
-Gencom: [2 3 11/10; 121/120 176/175 351/350]
+{| class="wikitable mw-collapsible mw-collapsed"
+|+ style="font-size: 105%; white-space: nowrap;" | 13-limit norm-based tunings
+|-
+! rowspan="2" |
+! colspan="3" | Euclidean
+|-
+! Constrained
+! Constrained & skewed
+! Destretched
+|-
+! Tenney
+| CTE: ~3/2 = 701.9638{{c}}, ~12/11 = 156.9485{{c}}
+| CWE: ~3/2 = 701.8818{{c}}, ~12/11 = 156.9568{{c}}
+| POTE: ~3/2 = 701.8679{{c}}, ~12/11 = 156.9582{{c}}
+|}
-Gencom Mapping: [{{map|1 0 1 4 2 7}}, {{map|0 1 1 -1 1 -2}}, {{map|0 0 -2 3 -1 -1}}]
+=== Tuning spectrum ===
+This spectrum assumes pure 2 and 7/5.
-{| class="wikitable center-all"
+{| class="wikitable center-1 center-2 center-3"
 |-
-! [[eigenmonzo|eigenmonzo<br>(unchanged-interval]])
+! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]]
-! fifth<br>(¢)
+! Fifth<br>(¢)
-! major<br>third (¢)
+! Major<br>Third (¢)
-! comments
+! Comments
 |-
 | 12/11
@@ Line 97: / Line 163: @@
 |}
-[[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]]
-{{Todo| intro }}