Zeus: Difference between revisions

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'''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.

'''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.

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.

== Interval lattice ==

File:Lattice Zeus.png|11-limit zeus

File:Lattice Zeus13.png|13-limit zeus

</gallery>

== Chords ==

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

|-

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

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

! Fifth<br>(¢)

! Major<br>Third (¢)

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-'''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.
+'''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.
+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.
+== Interval lattice ==
+<gallery>
+File:Lattice Zeus.png|11-limit zeus
+File:Lattice Zeus13.png|13-limit zeus
+</gallery>
 == Chords ==
@@ Line 28: / Line 36: @@
 {| class="wikitable center-1 center-2 center-3"
 |-
-! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval]])
+! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]]
 ! Fifth<br>(¢)
 ! Major<br>Third (¢)