|
|
| (14 intermediate revisions by 6 users not shown) |
| Line 1: |
Line 1: |
| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | '''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. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-12-06 21:46:49 UTC</tt>.<br>
| |
| : The original revision id was <tt>475389304</tt>.<br>
| |
| : The revision comment was: <tt></tt><br>
| |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| |
| <h4>Original Wikitext content:</h4>
| |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">See[[Porwell family#Zeus|Zeus]]
| |
|
| |
|
| Gencom: [2 3 11/10; 121/120 176/175 351/350]
| | It also has an obvious extension to the 13-limit tempering out [[351/350]] and [[352/351]]. |
| Gencom Mapping: [<1 0 1 4 2 7|, <0 1 1 -1 1 -2|, <0 0 -2 3 -1 -1|]
| |
| =Spectrum of Zeus Tunings by Eigenmonzos, Assuming Pure 2 and 7/5=
| |
| ||~ Eigenmonzo ||~ 3/2 ||~ 5/4 ||
| |
| || 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 ||
| |
| || 10/9 || 702.551 || 387.505 ||
| |
| || 6/5 || 703.296 || 387.654 ||
| |
| || 13/11 || 703.597 || 387.714 ||
| |
| || 11/8 || 713.034 || 389.602 ||
| |
| || 11/10 || 721.254 || 391.246 ||
| |
| </pre></div>
| |
| <h4>Original HTML content:</h4>
| |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Zeus</title></head><body>See<a class="wiki_link" href="/Porwell%20family#Zeus">Zeus</a><br />
| |
| <br />
| |
| Gencom: [2 3 11/10; 121/120 176/175 351/350]<br />
| |
| Gencom Mapping: [&lt;1 0 1 4 2 7|, &lt;0 1 1 -1 1 -2|, &lt;0 0 -2 3 -1 -1|]<br />
| |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Spectrum of Zeus Tunings by Eigenmonzos, Assuming Pure 2 and 7/5"></a><!-- ws:end:WikiTextHeadingRule:0 -->Spectrum of Zeus Tunings by Eigenmonzos, Assuming Pure 2 and 7/5</h1>
| |
|
| |
|
| | See [[Biyatismic clan #Zeus]] for technical data. |
|
| |
|
| <table class="wiki_table">
| | == Interval lattice == |
| <tr>
| | <gallery> |
| <th>Eigenmonzo<br />
| | File:Lattice Zeus.png|11-limit zeus |
| </th>
| | File:Lattice Zeus13.png|13-limit zeus |
| <th>3/2<br />
| | </gallery> |
| </th>
| |
| <th>5/4<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>12/11<br />
| |
| </td>
| |
| <td>685.337<br />
| |
| </td>
| |
| <td>384.062<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/11<br />
| |
| </td>
| |
| <td>689.089<br />
| |
| </td>
| |
| <td>384.813<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5/4<br />
| |
| </td>
| |
| <td>696.593<br />
| |
| </td>
| |
| <td>386.314<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/9<br />
| |
| </td>
| |
| <td>697.207<br />
| |
| </td>
| |
| <td>386.436<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14/13<br />
| |
| </td>
| |
| <td>700.880<br />
| |
| </td>
| |
| <td>387.171<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16/15<br />
| |
| </td>
| |
| <td>701.061<br />
| |
| </td>
| |
| <td>387.207<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/13<br />
| |
| </td>
| |
| <td>701.179<br />
| |
| </td>
| |
| <td>387.231<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16/13<br />
| |
| </td>
| |
| <td>701.237<br />
| |
| </td>
| |
| <td>387.243<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/12<br />
| |
| </td>
| |
| <td>701.449<br />
| |
| </td>
| |
| <td>387.285<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18/13<br />
| |
| </td>
| |
| <td>701.564<br />
| |
| </td>
| |
| <td>387.308<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4/3<br />
| |
| </td>
| |
| <td>701.955<br />
| |
| </td>
| |
| <td>387.386<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10/9<br />
| |
| </td>
| |
| <td>702.551<br />
| |
| </td>
| |
| <td>387.505<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6/5<br />
| |
| </td>
| |
| <td>703.296<br />
| |
| </td>
| |
| <td>387.654<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/11<br />
| |
| </td>
| |
| <td>703.597<br />
| |
| </td>
| |
| <td>387.714<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/8<br />
| |
| </td>
| |
| <td>713.034<br />
| |
| </td>
| |
| <td>389.602<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/10<br />
| |
| </td>
| |
| <td>721.254<br />
| |
| </td>
| |
| <td>391.246<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| </body></html></pre></div>
| | == 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 center-2 center-3" |
| | |- |
| | ! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]] |
| | ! Fifth<br>(¢) |
| | ! Major<br>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 == |
| | ; [[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]] |
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
- Mundoworld
11-limit zeus
13-limit zeus
