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-1 | {| class="wikitable center-1 center-2 center-3" | ||
|- | |- | ||
! Eigenmonzo | ! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]] | ||
! | ! Fifth<br>(¢) | ||
! | ! Major<br>Third (¢) | ||
! Comments | ! Comments | ||
|- | |- | ||
| Line 96: | Line 117: | ||
| | | | ||
|} | |} | ||
== 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 | [[Category:Biyatismic clan]] | ||
[[Category:Valinorsmic temperaments]] | [[Category:Valinorsmic clan]] | ||
[[Category:Keenanismic temperaments]] | |||
Latest revision as of 09:54, 29 April 2025
Zeus is a rank-3 temperament generated by an octave, a 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 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
-
11-limit zeus -
13-limit zeus
Chords
Zeus enables essentially tempered chords of biyatismic, valinorsmic, and keenanismic.
Scales
Tunings
Tuning spectrum
This spectrum assumes pure 2 and 7/5.
| Eigenmonzo (Unchanged-interval) |
Fifth (¢) |
Major Third (¢) |
Comments |
|---|---|---|---|
| 12/11 | 685.337 | 384.062 | |
| 15/11 | 689.089 | 384.813 | |
| 5/4 | 696.593 | 386.314 | |
| 11/9 | 697.207 | 386.436 | |
| 14/13 | 700.880 | 387.171 | |
| 16/15 | 701.061 | 387.207 | |
| 15/13 | 701.179 | 387.231 | |
| 16/13 | 701.237 | 387.243 | |
| 13/12 | 701.449 | 387.285 | |
| 18/13 | 701.564 | 387.308 | |
| 4/3 | 701.955 | 387.386 | 7-, 9- and 15-odd-limit minimax |
| 10/9 | 702.551 | 387.505 | 11- and 13-odd-limit minimax |
| 6/5 | 703.296 | 387.654 | |
| 13/11 | 703.597 | 387.714 | |
| 11/8 | 713.034 | 389.602 | |
| 11/10 | 721.254 | 391.246 |
Music
- Cloudtop Reverie (2021) – in Zeus[7], 99edo tuning