Zeus: Difference between revisions

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

'''Zeus''' is the [[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.

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

== Chords ==

Zeus enables [[essentially tempered chord]]s of [[Biyatismic chords|biyatismic]], [[Valinorsmic chords|valinorsmic]], and [[Keenanismic chords|keenanismic]].

== Scales ==

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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~~"

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

|-

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

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[[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 the [[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.
 See [[Porwell family #Zeus]] or [[Biyatismic clan #Zeus]] for technical data.
+== Chords ==
+Zeus enables [[essentially tempered chord]]s of [[Biyatismic chords|biyatismic]], [[Valinorsmic chords|valinorsmic]], and [[Keenanismic chords|keenanismic]].
 == Scales ==
@@ Line 23: / Line 26: @@
 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"
+{| class="wikitable center-1 center-2 center-3"
 |-
 ! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval]])
@@ Line 116: / Line 119: @@
 [[Category:Biyatismic clan]]
 [[Category:Valinorsmic clan]]
+[[Category:Keenanismic temperaments]]