Zeus: Difference between revisions
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'''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. | |||
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 == | |||
* [[Zeus1]] | |||
* [[Zeus2]] | |||
* [[Zeus3]] | |||
* [[Zeus4]] | |||
* [[Zeus5]] | |||
* [[Zeus6]] | |||
* [[Zeus7]] | |||
* [[Zeus7tri]] | |||
* [[Zeus8tri]] | |||
* [[Genus1155zeus]] | |||
== Tunings == | |||
=== Tuning spectrum === | |||
This spectrum assumes pure 2 and 7/5. | |||
{| class="wikitable center- | {| class="wikitable center-1 center-2 center-3" | ||
|- | |- | ||
! [[ | ! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]] | ||
! | ! Fifth<br>(¢) | ||
! | ! Major<br>Third (¢) | ||
! | ! Comments | ||
|- | |- | ||
| 12/11 | | 12/11 | ||
| Line 97: | Line 118: | ||
|} | |} | ||
[[ | == Music == | ||
; [[Mundoworld]] | |||
* [https://www.youtube.com/watch?v=zo1IYJW43II ''Cloudtop Reverie''] (2021) – in Zeus[7], 99edo tuning | |||
[[Category:Zeus| ]] <!-- main article --> | [[Category:Zeus| ]] <!-- main article --> | ||
[[Category:Rank-3 temperaments]] | |||
[[Category:Porwell family]] | [[Category:Porwell family]] | ||
[[Category:Biyatismic clan]] | [[Category:Biyatismic clan]] | ||
[[Category:Valinorsmic clan]] | [[Category:Valinorsmic clan]] | ||
[[Category:Keenanismic temperaments]] | |||