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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Interwiki |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | en = 5L 3s |
| : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-02-11 14:14:24 UTC</tt>.<br>
| | | de = |
| : The original revision id was <tt>540641396</tt>.<br>
| | | es = |
| : The revision comment was: <tt></tt><br>
| | | ja = |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | | ko = 5L3s (Korean) |
| <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">5L 3s refers to the structure of moment of symmetry scales with generators ranging from 2\5 (two degrees of [[5edo]] = 480¢) to 3\8 (three degrees of [[8edo]] = 450¢). In the case of 8edo, L and s are the same size; in the case of 5edo, s becomes so small it disappears (and all that remains are the five equal L's). The spectrum looks like this:
| | {{Infobox MOS |
| ||~ ||~ ||~ ||~ ||~ ||~ ||~ ||~ ||~ <span style="display: block; text-align: center;">tetrachord</span> ||~ <span style="display: block; text-align: center;">g in cents</span> ||~ <span style="display: block; text-align: center;">2g</span> ||~ <span style="display: block; text-align: center;">3g</span> ||~ <span style="display: block; text-align: center;">4g</span> ||~ <span style="display: block; text-align: center;">Comments</span> ||
| | | Neutral = 2L 6s |
| || 2\5 || || || || || || || || <span style="text-align: center;">1 0 1</span> || 480.000 || 960.000 || 240.00 || <span style="line-height: 15.6000003814697px;">720.000</span> ||= || | | }} |
| || 21\53 || || || || || || || || <span style="text-align: center;">10 1 10</span> || 475.472 || 950.943 || 226.415 || 701.887 ||= <span style="text-align: center;">Vulture/Buzzard is around here</span> || | | : ''For the tritave-equivalent MOS structure with the same step pattern, see [[5L 3s (3/1-equivalent)]].'' |
| || 19\48 || || || || || || || || <span style="text-align: center;">9 1 9</span> || 475 || 950 || 225 || 700 ||= || | | {{MOS intro}} |
| || 17\43 || || || || || || || || <span style="text-align: center;">8 1 8</span> || 474.419 || 948.837 || 223.256 || 697.674 ||= || | | 5L 3s can be seen as a [[Warped diatonic|warped diatonic scale]], because it has one extra small step compared to diatonic ([[5L 2s]]). |
| || 15\38 || || || || || || || || <span style="text-align: center;">7 1 7</span> || 473.684 || 947.368 || 221.053 || 694.737 ||= ||
| |
| || 13\33 || || || || || || || || <span style="text-align: center;">6 1 6</span> || 472.727 || 945.455 || 218.181 || 690.909 ||= ||
| |
| || 11\28 || || || || || || || || <span style="text-align: center;">5 1 5</span> || 471.429 || 942.857 || 214.286 || 685.714 ||= || | |
| || 9\23 || || || || || || || || <span style="text-align: center;">4 1 4</span> || 469.565 || 939.130 || 208.696 || 678.261 ||= <span style="text-align: center;">L/s = 4</span> ||
| |
| || || || || || || || || || 3.03 1 3.03 || 466.769 || 933.538 || 200.307 || 667.076 ||= <span style="display: block; text-align: center;">L/s = 3*2^(1/75)</span> ||
| |
| || 7\18 || || || || || || || || <span style="text-align: center;">3 1 3</span> || 466.667 || 933.333 || 200.000 || 666.667 ||= <span style="text-align: center;">L/s = 3</span> ||
| |
| || || || || || || || || || 2.97 1 2.97 || 466.564 || 933.127 || 199.691 || 666.255 ||= <span style="display: block; text-align: center;">L/s = 3/2^(1/75)</span> ||
| |
| || || 12\31 || || || || || || || <span style="text-align: center;">5 2 5</span> || 464.516 || 929.032 || 193.549 || 658.065 ||= ||
| |
| || 5\13 || || || || || || || || <span style="text-align: center;">2 1 2</span> || 461.538 || 923.077 || 184.615 || 646.154 ||= ||
| |
| || || 13\34 || || || || || || || <span style="text-align: center;">5 3 5</span> || 458.824 || 917.647 || 176.471 || 635.294 ||= ||
| |
| || || || || 34\89 || || || || || <span style="text-align: center;">13 8 13</span> || 458.427 || 916.854 || 175.281 || 633.708 ||= ||
| |
| || || || || || || 89\233 || || || <span style="text-align: center;">34 21 34</span> || <span style="line-height: 15.6000003814697px;">458.369</span> || <span style="text-align: center;">916.738</span> || 175.107 || <span style="line-height: 15.6000003814697px;">633.473</span> ||= ||
| |
| || || || || || || || || 233\610 || <span style="text-align: center;">89 55 89</span> || 458.361 || 916.721 || 175.082 || 633.443 ||= <span style="text-align: center;">Golden father</span> ||
| |
| || || || || || || || 144\377 || || <span style="text-align: center;">55 34 55</span> || 458.355 || 916.711 || 175.066 || 633.422 ||= ||
| |
| || || || || || 55\144 || || || || <span style="text-align: center;">21 13 21</span> || 458.333 || 916.666 || 175 || 633.333 ||= ||
| |
| || || || 21\55 || || || || || || <span style="text-align: center;">8 5 8</span> || 458.182 || 916.364 || 174.545 || 632.727 ||= ||
| |
| || 8\21 || || || || || || || || <span style="text-align: center;">3 2 3</span> || 457.143 || 914.286 || 171.429 || 628.571 ||= <span style="text-align: center;">Optimum rank range (L/s=3/2) father</span> ||
| |
| || 11\29 || || || || || || || || <span style="text-align: center;">4 3 4</span> || 455.172 || 910.345 || 165.517 || 620.690 ||= ||
| |
| || 3\8 || || || || || || || || <span style="text-align: center;">1 1 1</span> || 450.000 || 900.000 || 150.000 || 600.000 ||= ||
| |
| The only notable harmonic entropy minimum is Vulture/[[Hemifamity temperaments|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes.</pre></div>
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| <h4>Original HTML content:</h4>
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| <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>5L 3s</title></head><body>5L 3s refers to the structure of moment of symmetry scales with generators ranging from 2\5 (two degrees of <a class="wiki_link" href="/5edo">5edo</a> = 480¢) to 3\8 (three degrees of <a class="wiki_link" href="/8edo">8edo</a> = 450¢). In the case of 8edo, L and s are the same size; in the case of 5edo, s becomes so small it disappears (and all that remains are the five equal L's). The spectrum looks like this:<br />
| |
|
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|
| | == Name == |
| | {{TAMNAMS name}} 'Oneiro' is sometimes used as a shortened form. |
|
| |
|
| <table class="wiki_table">
| | 'Father' is sometimes also used to denote 5L 3s, but it's a misnomer, as [[father]] is technically an abstract [[regular temperament]] (although a very inaccurate one), not a generator range. There are father tunings which generate 3L 5s. A more correct but still not quite correct name would be 'father[8]' or 'father octatonic'. "Father" is also vague regarding the number of notes, because optimal generators for it also generate [[3L 2s]]. |
| <tr>
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| <th><br />
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| </th>
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| <th><br />
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| </th>
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| <th><br />
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| </th>
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| <th><br />
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| </th>
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| <th><br />
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| </th>
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| <th><br />
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| </th>
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| <th><br />
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| </th>
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| <th><br />
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| </th>
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| <th><span style="display: block; text-align: center;">tetrachord</span><br />
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| </th>
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| <th><span style="display: block; text-align: center;">g in cents</span><br />
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| </th>
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| <th><span style="display: block; text-align: center;">2g</span><br />
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| </th>
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| <th><span style="display: block; text-align: center;">3g</span><br />
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| </th>
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| <th><span style="display: block; text-align: center;">4g</span><br />
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| </th>
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| <th><span style="display: block; text-align: center;">Comments</span><br />
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| </th>
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| </tr>
| |
| <tr>
| |
| <td>2\5<br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
| |
| <td><span style="text-align: center;">1 0 1</span><br />
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| </td>
| |
| <td>480.000<br />
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| </td>
| |
| <td>960.000<br />
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| </td>
| |
| <td>240.00<br />
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| </td>
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| <td><span style="line-height: 15.6000003814697px;">720.000</span><br />
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| </td>
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| <td style="text-align: center;"><br />
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| </td>
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| </tr>
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| <tr>
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| <td>21\53<br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><span style="text-align: center;">10 1 10</span><br />
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| </td>
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| <td>475.472<br />
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| </td>
| |
| <td>950.943<br />
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| </td>
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| <td>226.415<br />
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| </td>
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| <td>701.887<br />
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| </td>
| |
| <td style="text-align: center;"><span style="text-align: center;">Vulture/Buzzard is around here</span><br />
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| </td>
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| </tr>
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| <tr>
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| <td>19\48<br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><span style="text-align: center;">9 1 9</span><br />
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| </td>
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| <td>475<br />
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| </td>
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| <td>950<br />
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| </td>
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| <td>225<br />
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| </td>
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| <td>700<br />
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| </td>
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| <td style="text-align: center;"><br />
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| </td>
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| </tr>
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| <tr>
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| <td>17\43<br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><span style="text-align: center;">8 1 8</span><br />
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| </td>
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| <td>474.419<br />
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| </td>
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| <td>948.837<br />
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| </td>
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| <td>223.256<br />
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| </td>
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| <td>697.674<br />
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| </td>
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| <td style="text-align: center;"><br />
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| </td>
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| </tr>
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| <tr>
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| <td>15\38<br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><span style="text-align: center;">7 1 7</span><br />
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| </td>
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| <td>473.684<br />
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| </td>
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| <td>947.368<br />
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| </td>
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| <td>221.053<br />
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| </td>
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| <td>694.737<br />
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| </td>
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| <td style="text-align: center;"><br />
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| </td>
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| </tr>
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| <tr>
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| <td>13\33<br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><span style="text-align: center;">6 1 6</span><br />
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| </td>
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| <td>472.727<br />
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| </td>
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| <td>945.455<br />
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| </td>
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| <td>218.181<br />
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| </td>
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| <td>690.909<br />
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| </td>
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| <td style="text-align: center;"><br />
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| </td>
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| </tr>
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| <tr>
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| <td>11\28<br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><span style="text-align: center;">5 1 5</span><br />
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| </td>
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| <td>471.429<br />
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| </td>
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| <td>942.857<br />
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| </td>
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| <td>214.286<br />
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| </td>
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| <td>685.714<br />
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| </td>
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| <td style="text-align: center;"><br />
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| </td>
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| </tr>
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| <tr>
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| <td>9\23<br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><span style="text-align: center;">4 1 4</span><br />
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| </td>
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| <td>469.565<br />
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| </td>
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| <td>939.130<br />
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| </td>
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| <td>208.696<br />
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| </td>
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| <td>678.261<br />
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| </td>
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| <td style="text-align: center;"><span style="text-align: center;">L/s = 4</span><br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>3.03 1 3.03<br />
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| </td>
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| <td>466.769<br />
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| </td>
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| <td>933.538<br />
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| </td>
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| <td>200.307<br />
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| </td>
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| <td>667.076<br />
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| </td>
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| <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 3*2^(1/75)</span><br />
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| </td>
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| </tr>
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| <tr>
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| <td>7\18<br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><span style="text-align: center;">3 1 3</span><br />
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| </td>
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| <td>466.667<br />
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| </td>
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| <td>933.333<br />
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| </td>
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| <td>200.000<br />
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| </td>
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| <td>666.667<br />
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| </td>
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| <td style="text-align: center;"><span style="text-align: center;">L/s = 3</span><br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>2.97 1 2.97<br />
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| </td>
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| <td>466.564<br />
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| </td>
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| <td>933.127<br />
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| </td>
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| <td>199.691<br />
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| </td>
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| <td>666.255<br />
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| </td>
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| <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 3/2^(1/75)</span><br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td>12\31<br />
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| </td>
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| <td><br />
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| </td>
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| <td><span style="text-align: center;">5 2 5</span><br />
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| </td>
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| <td>464.516<br />
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| </td>
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| <td>929.032<br />
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| </td>
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| <td>193.549<br />
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| </td>
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| <td>658.065<br />
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| </td>
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| <td style="text-align: center;"><br />
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| </td>
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| </tr>
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| <tr>
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| <td>5\13<br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><span style="text-align: center;">2 1 2</span><br />
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| </td>
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| <td>461.538<br />
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| </td>
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| <td>923.077<br />
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| </td>
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| <td>184.615<br />
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| </td>
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| <td>646.154<br />
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| </td>
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| <td style="text-align: center;"><br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td>13\34<br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><span style="text-align: center;">5 3 5</span><br />
| |
| </td>
| |
| <td>458.824<br />
| |
| </td>
| |
| <td>917.647<br />
| |
| </td>
| |
| <td>176.471<br />
| |
| </td>
| |
| <td>635.294<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>34\89<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><span style="text-align: center;">13 8 13</span><br />
| |
| </td>
| |
| <td>458.427<br />
| |
| </td>
| |
| <td>916.854<br />
| |
| </td>
| |
| <td>175.281<br />
| |
| </td>
| |
| <td>633.708<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>89\233<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><span style="text-align: center;">34 21 34</span><br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">458.369</span><br />
| |
| </td>
| |
| <td><span style="text-align: center;">916.738</span><br />
| |
| </td>
| |
| <td>175.107<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">633.473</span><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>233\610<br />
| |
| </td>
| |
| <td><span style="text-align: center;">89 55 89</span><br />
| |
| </td>
| |
| <td>458.361<br />
| |
| </td>
| |
| <td>916.721<br />
| |
| </td>
| |
| <td>175.082<br />
| |
| </td>
| |
| <td>633.443<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="text-align: center;">Golden father</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>144\377<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><span style="text-align: center;">55 34 55</span><br />
| |
| </td>
| |
| <td>458.355<br />
| |
| </td>
| |
| <td>916.711<br />
| |
| </td>
| |
| <td>175.066<br />
| |
| </td>
| |
| <td>633.422<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>55\144<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><span style="text-align: center;">21 13 21</span><br />
| |
| </td>
| |
| <td>458.333<br />
| |
| </td>
| |
| <td>916.666<br />
| |
| </td>
| |
| <td>175<br />
| |
| </td>
| |
| <td>633.333<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>21\55<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><span style="text-align: center;">8 5 8</span><br />
| |
| </td>
| |
| <td>458.182<br />
| |
| </td>
| |
| <td>916.364<br />
| |
| </td>
| |
| <td>174.545<br />
| |
| </td>
| |
| <td>632.727<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8\21<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><span style="text-align: center;">3 2 3</span><br />
| |
| </td>
| |
| <td>457.143<br />
| |
| </td>
| |
| <td>914.286<br />
| |
| </td>
| |
| <td>171.429<br />
| |
| </td>
| |
| <td>628.571<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="text-align: center;">Optimum rank range (L/s=3/2) father</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11\29<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><span style="text-align: center;">4 3 4</span><br />
| |
| </td>
| |
| <td>455.172<br />
| |
| </td>
| |
| <td>910.345<br />
| |
| </td>
| |
| <td>165.517<br />
| |
| </td>
| |
| <td>620.690<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3\8<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><span style="text-align: center;">1 1 1</span><br />
| |
| </td>
| |
| <td>450.000<br />
| |
| </td>
| |
| <td>900.000<br />
| |
| </td>
| |
| <td>150.000<br />
| |
| </td>
| |
| <td>600.000<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| The only notable harmonic entropy minimum is Vulture/<a class="wiki_link" href="/Hemifamity%20temperaments">Buzzard</a>, in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes.</body></html></pre></div> | | == Scale properties == |
| | |
| | === Intervals === |
| | {{MOS intervals}} |
| | |
| | === Generator chain === |
| | {{MOS genchain}} |
| | |
| | === Modes === |
| | {{MOS mode degrees}} |
| | |
| | ==== Proposed mode names ==== |
| | The following names have been proposed for the modes of 5L 3s, and are named after cities in the Dreamlands. |
| | {{MOS modes |
| | | Mode Names= |
| | Dylathian $ |
| | Ilarnekian $ |
| | Celephaïsian $ |
| | Ultharian $ |
| | Mnarian $ |
| | Kadathian $ |
| | Hlanithian $ |
| | Sarnathian $ |
| | | Collapsed=1 |
| | }} |
| | |
| | == Tunings== |
| | === Simple tunings === |
| | The simplest tuning for 5L 3s correspond to 13edo, 18edo, and 21edo, with step ratios 2:1, 3:1, and 3:2, respectively. |
| | |
| | {{MOS tunings|JI Ratios=Int Limit: 30; Prime Limit: 19; Tenney Height: 7.7}} |
| | |
| | === Hypohard tunings === |
| | [[Hypohard]] oneirotonic tunings have step ratios between 2:1 and 3:1 and can be considered "meantone oneirotonic", sharing the following features with [[meantone]] diatonic tunings: |
| | * The large step is a "meantone", around the range of [[10/9]] to [[9/8]]. |
| | * The major 2-mosstep is a [[meantone]]- to [[flattone]]-sized major third, thus is a stand-in for the classical diatonic major third. |
| | |
| | With step ratios between 5:2 and 2:1, the minor 2-mosstep is close to [[7/6]]. |
| | |
| | EDOs that are in the hypohard range include [[13edo]], [[18edo]], and [[31edo]], and are associated with [[5L 3s/Temperaments#A-Team|A-Team]] temperament. |
| | * 13edo has characteristically small 1-mossteps of about 185{{c}}. It is uniformly compressed 12edo, so it has distorted versions of non-diatonic 12edo scales. It essentially has the best [[11/8]] out of all hypohard tunings. |
| | * 18edo can be used for a large step ratio of 3, (thus 18edo oneirotonic is distorted 17edo diatonic, or for its nearly pure 9/8 and 7/6. It also makes rising fifths (733.3{{c}}, a perfect 5-mosstep) and falling fifths (666.7{{c}}, a major 4-mosstep) almost equally off from a just perfect fifth. 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry. |
| | * 31edo can be used to make the major 2-mosstep a near-just 5/4. |
| | * [[44edo]] (generator {{nowrap|17\44 {{=}} 463.64{{c}}}}), [[57edo]] (generator {{nowrap|22\57 {{=}} 463.16{{c}}}}), and [[70edo]] (generator 27\70 {{=}} 462.857{{c}}}}) offer a compromise between 31edo's major third and 13edo's 11/8 and 13/8. In particular, 70edo has an essentially pure 13/8. |
| | |
| | {{MOS tunings|Step Ratios=Hypohard|JI Ratios=Subgroup: 2.5.9.21; Int Limit:40; Complements Only: 1|Tolerance=15}} |
| | |
| | === Hyposoft tunings === |
| | [[Hyposoft]] oneirotonic tunings have step ratios between 3:2 and 2:1, which remains relatively unexplored. In these tunings, |
| | * The large step of oneirotonic tends to be intermediate in size between [[10/9]] and [[11/10]]; the small step size is a semitone close to [[17/16]], about 92{{c}} to 114{{c}}. |
| | * The major 2-mosstep (made of two large steps) in these tunings tends to be more of a neutral third, ranging from 6\21 (342{{c}}) to 4\13 (369{{c}}). |
| | |
| | * [[21edo]]'s P1-L1ms-L2ms-L4ms approximates 9:10:11:13 better than the corresponding 13edo chord does. 21edo will serve those who like the combination of neogothic minor thirds (285.71{{c}}) and Baroque diatonic semitones (114.29{{c}}, close to quarter-comma meantone's 117.11{{c}}). |
| | * [[34edo]]'s 9:10:11:13 is even better. |
| | |
| | This set of JI identifications is associated with [[5L 3s/Temperaments#Petrtri|petrtri]] temperament. (P1-M1ms-P3ms could be said to approximate 5:11:13 in all soft-of-basic tunings, which is what "basic" [[petrtri]] temperament is.) |
| | |
| | {{MOS tunings |
| | | Step Ratios = Hyposoft |
| | | JI Ratios = |
| | 1/1; |
| | 16/15; |
| | 10/9; 11/10; |
| | 13/11; 20/17; |
| | 11/9; |
| | 5/4; |
| | 13/10; |
| | 18/13; 32/23; |
| | 13/9; 23/16; |
| | 20/13; |
| | 8/5; |
| | 18/11; |
| | 22/13; 17/10; |
| | 9/5; |
| | 15/8; |
| | 2/1 |
| | }} |
| | |
| | === Parasoft and ultrasoft tunings === |
| | The range of oneirotonic tunings of step ratio between 6:5 and 3:2 is closely related to [[porcupine]] temperament; these tunings equate three oneirotonic large steps to a diatonic perfect fourth, i.e. they equate the oneirotonic large step to a [[porcupine]] generator. The chord 10:11:13 is very well approximated in 29edo. |
| | |
| | {{MOS tunings |
| | | Step Ratios = 6/5; 3/2; 4/3 |
| | | JI Ratios = |
| | 1/1; |
| | 14/13; |
| | 11/10; |
| | 9/8; |
| | 15/13; |
| | 13/11; |
| | 14/11; |
| | 13/10; |
| | 4/3; |
| | 15/11; |
| | 7/5; |
| | 10/7; |
| | 22/15; |
| | 3/2; |
| | 20/13; |
| | 11/7; |
| | 22/13; |
| | 26/15; |
| | 16/9; |
| | 20/11; |
| | 13/7; |
| | 2/1 |
| | }} |
| | |
| | === Parahard tunings === |
| | 23edo oneiro combines the sound of neogothic tunings like [[46edo]] and the sounds of "superpyth" and "semaphore" scales. This is because 23edo oneirotonic has a large step of 208.7¢, same as [[46edo]]'s neogothic major second, and is both a warped [[22edo]] [[superpyth]] [[diatonic]] and a warped [[24edo]] [[semaphore]] [[semiquartal]] (and both nearby scales are [[superhard]] MOSes). |
| | |
| | {{MOS tunings |
| | | JI Ratios = |
| | 1/1; |
| | 21/17; |
| | 17/16; |
| | 14/11; |
| | 6/5; |
| | 21/16; |
| | 21/17; |
| | 34/21; |
| | 32/21; |
| | 5/3; |
| | 11/7; |
| | 32/17; |
| | 34/21; |
| | 2/1 |
| | | Step Ratios = 4/1 |
| | }} |
| | |
| | === Ultrahard tunings === |
| | {{Main|5L 3s/Temperaments#Buzzard}} |
| | |
| | [[Buzzard]] is a rank-2 temperament in the [[Step ratio|pseudocollapsed]] range. It represents the only [[harmonic entropy]] minimum of the oneirotonic spectrum. |
| | |
| | In the broad sense, Buzzard can be viewed as any tuning that divides the 3rd harmonic into 4 equal parts. [[23edo]], [[28edo]] and [[33edo]] can nominally be viewed as supporting it, but are still very flat and in an ambiguous zone between 18edo and true Buzzard in terms of harmonies. [[38edo]] & [[43edo]] are good compromises between melodic utility and harmonic accuracy, as the small step is still large enough to be obvious to the untrained ear, but [[48edo]] is where it really comes into its own in terms of harmonies, providing not only an excellent [[3/2]], but also [[7/4]] and [[The_Archipelago|archipelago]] harmonies, as by dividing the 5th in 4 it obviously also divides it in two as well. |
| | |
| | Beyond that, it's a question of which intervals you want to favor. [[53edo]] has an essentially perfect [[3/2]], [[58edo]] gives the lowest overall error for the Barbados triads 10:13:15 and 26:30:39, while [[63edo]] does the same for the basic 4:6:7 triad. You could in theory go up to [[83edo]] if you want to favor the [[7/4]] above everything else, but beyond that, general accuracy drops off rapidly and you might as well be playing equal pentatonic. |
| | |
| | {{MOS tunings |
| | | JI Ratios = |
| | 1/1; |
| | 8/7; |
| | 13/10; |
| | 21/16; |
| | 3/2; |
| | 12/7, 22/13; |
| | 26/15; |
| | 49/25, 160/81; |
| | 2/1 |
| | | Step Ratios = 7/1; 10/1; 12/1 |
| | | Tolerance = 30 |
| | }} |
| | |
| | == Approaches == |
| | * [[5L 3s/Temperaments]] |
| | |
| | == Samples == |
| | [[File:The Angels' Library edo.mp3]] [[:File:The Angels' Library edo.mp3|The Angels' Library]] by [[Inthar]] in the Sarnathian (23233233) mode of 21edo oneirotonic ([[:File:The Angels' Library Score.pdf|score]]) |
| | |
| | [[File:13edo Prelude in J Oneirominor.mp3]] |
| | |
| | [[WT13C]] [[:File:13edo Prelude in J Oneirominor.mp3|Prelude II (J Oneirominor)]] ([[:File:13edo Prelude in J Oneirominor Score.pdf|score]]) – Simple two-part Baroque piece. It stays in oneirotonic even though it modulates to other keys a little. |
| | |
| | [[File:13edo_1MC.mp3]] |
| | |
| | (13edo, first 30 seconds is in J Celephaïsian) |
| | |
| | [[File:A Moment of Respite.mp3]] |
| | |
| | (13edo, L Ilarnekian) |
| | |
| | [[File:Lunar Approach.mp3]] |
| | |
| | (by [[Igliashon Jones]], 13edo, J Celephaïsian) |
| | |
| | === 13edo Oneirotonic Modal Studies === |
| | * [[File:Inthar-13edo Oneirotonic Studies 1 Dylathian.mp3]]: Tonal Study in Dylathian |
| | * [[File:Inthar-13edo Oneirotonic Studies 2 Ultharian.mp3]]: Tonal Study in Ultharian |
| | * [[File:Inthar-13edo Oneirotonic Studies 3 Hlanithian.mp3]]: Tonal Study in Hlanithian |
| | * [[File:Inthar-13edo Oneirotonic Studies 4 Illarnekian.mp3]]: Tonal Study in Ilarnekian |
| | * [[File:Inthar-13edo Oneirotonic Studies 5 Mnarian.mp3]]: Tonal Study in Mnarian |
| | * [[File:Inthar-13edo Oneirotonic Studies 6 Sarnathian.mp3]]: Tonal Study in Sarnathian |
| | * [[File:Inthar-13edo Oneirotonic Studies 7 Celephaisian.mp3]]: Tonal Study in Celephaïsian |
| | * [[File:Inthar-13edo Oneirotonic Studies 8 Kadathian.mp3]]: Tonal Study in Kadathian |
| | |
| | == Scale tree == |
| | {{MOS tuning spectrum |
| | | 13/8 = Golden oneirotonic (458.3592{{c}}) |
| | | 13/5 = Golden A-Team (465.0841{{c}}) |
| | }} |
| | |
| | [[Category:Oneirotonic| ]] <!-- sort order in category: this page shows above A --> |
| | [[Category:Pages with internal sound examples]] |