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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | : ''For the tritave-equivalent 4L 5s pattern, see [[4L 5s (3/1-equivalent)]].'' |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| |
| : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-05-23 15:34:15 UTC</tt>.<br> | |
| : The original revision id was <tt>551972212</tt>.<br>
| |
| : The revision comment was: <tt></tt><br>
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| 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>
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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;white-space: pre-wrap ! important" class="old-revision-html">4L 5s refers to the structure of [[MOSScales|MOS Scales]] whose generator falls between 2\9 (two degrees of [[9edo]] = approx. 266.667¢) and 1\4 (one degree of [[4edo]] = 300¢). In the case of 9edo, L and s are the same size; in the case of 4edo, s is so small it disappears. The spectrum, then, goes something like:
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| ||||||||||~ Generator ||~ Scale ||~ Generator in cents ||~ Comments ||
| | {{Infobox MOS |
| || 2\9 || || || || ||= 1 1 1 1 1 1 1 1 1 || 266.667 ||= || | | | Name = gramitonic |
| || || || || || 9\40 ||= 4 5 4 5 4 5 4 5 4 || 270 || || | | | Periods = 1 |
| || || || || 7\31 || ||= 3 4 3 4 3 4 3 4 3 || 270.968 ||= || | | | nLargeSteps = 4 |
| || || || || || 12\53 ||= 5 7 5 7 5 7 5 7 5 || 271.698 ||= Orwell is around here || | | | nSmallSteps = 5 |
| || || || 5\22 || || ||= 2 3 2 3 2 3 2 3 2 || 272.727 ||= Optimum rank range (L/s=3/2) orwell || | | | Equalized = 2 |
| || || || || || 13\57 ||= 5 8 5 8 5 8 5 8 5 || 273.684 ||= Golden orwell (bad tuning) ||
| | | Collapsed = 1 |
| || || || || 8\35 || ||= 3 5 3 5 3 5 3 5 3 || 274.286 ||= ||
| | | Pattern = LsLsLsLss |
| || || || || || 11\48 ||= 4 7 4 7 4 7 4 7 4 || 275 || ||
| | }} |
| || || 3\13 || || || ||= 1 2 1 2 1 2 1 2 1 || 276.923 ||= Boundary of propriety: | | {{MOS intro}} |
| generators smaller than this are proper ||
| |
| || || || || || 10\43 ||= 3 7 3 7 3 7 3 7 3 || 279.07 || || | |
| || || || || 7\30 || ||= 2 5 2 5 2 5 2 5 2 || 280.000 ||= ||
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| || || || || || 11\47 ||= 3 8 3 8 3 8 3 8 3 || 280.851 || ||
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| || || || || || ||= 1 e 1 e 1 e 1 e 1 || 281.100 ||= <span style="display: block; text-align: center;">L/s = e</span> ||
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| || || || 4\17 || || ||= 1 3 1 3 1 3 1 3 1 || 282.353 ||= L/s = 3 ||
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| || || || || || ||= 1 pi 1 pi 1 pi 1 pi 1 || 282.922 ||= <span style="display: block; text-align: center;">L/s = pi</span> ||
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| || || || || || 9\38 ||= 2 7 2 <span style="font-size: 12.8000001907349px; line-height: 1.5;">7 </span><span style="font-size: 13px; line-height: 1.5;">2 7 2 7 2 </span> || 284.2105 || ||
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| || || || || 5\21 || ||= 1 4 1 4 1 4 1 4 1 || 285.714 ||= L/s = 4 ||
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| || || || || || 6\25 ||= 1 5 1 5 1 5 1 5 1 || 288 || ||
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| || 1\4 || || || || ||= 0 1 0 1 0 1 0 1 0 || 300.000 ||= ||
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| Note that between 7\31 and 5\22, g approximates frequency ratio 7:6, 2g approximates 11:8, and 3g approximates 8:5. This defines the range of Orwell Temperament, which is the only notable harmonic entropy minimum with this MOS pattern. 4L 5s scales outside of that range are not suitable for Orwell.</pre></div>
| | == Names == |
| <h4>Original HTML content:</h4>
| | The [[TAMNAMS]] name for this pattern is '''gramitonic''' (from ''grave minor third''). |
| <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>4L 5s</title></head><body>4L 5s refers to the structure of <a class="wiki_link" href="/MOSScales">MOS Scales</a> whose generator falls between 2\9 (two degrees of <a class="wiki_link" href="/9edo">9edo</a> = approx. 266.667¢) and 1\4 (one degree of <a class="wiki_link" href="/4edo">4edo</a> = 300¢). In the case of 9edo, L and s are the same size; in the case of 4edo, s is so small it disappears. The spectrum, then, goes something like:<br />
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| <br />
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|
| | == Scale properties == |
| | {{TAMNAMS use}} |
|
| |
|
| <table class="wiki_table">
| | === Intervals === |
| <tr>
| | {{MOS intervals}} |
| <th colspan="5">Generator<br />
| |
| </th>
| |
| <th>Scale<br />
| |
| </th>
| |
| <th>Generator in cents<br />
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| </th>
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| <th>Comments<br />
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| </th>
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| </tr>
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| <tr>
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| <td>2\9<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 style="text-align: center;">1 1 1 1 1 1 1 1 1<br />
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| </td>
| |
| <td>266.667<br />
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| </td>
| |
| <td style="text-align: center;"><br />
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| </td>
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| </tr>
| |
| <tr>
| |
| <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>9\40<br />
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| </td>
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| <td style="text-align: center;">4 5 4 5 4 5 4 5 4<br />
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| </td>
| |
| <td>270<br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
| |
| <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>7\31<br />
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| </td>
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| <td><br />
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| </td>
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| <td style="text-align: center;">3 4 3 4 3 4 3 4 3<br />
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| </td>
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| <td>270.968<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>
| |
| <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>12\53<br />
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| </td>
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| <td style="text-align: center;">5 7 5 7 5 7 5 7 5<br />
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| </td>
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| <td>271.698<br />
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| </td>
| |
| <td style="text-align: center;">Orwell is around here<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>5\22<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 style="text-align: center;">2 3 2 3 2 3 2 3 2<br />
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| </td>
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| <td>272.727<br />
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| </td>
| |
| <td style="text-align: center;">Optimum rank range (L/s=3/2) orwell<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>13\57<br />
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| </td>
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| <td style="text-align: center;">5 8 5 8 5 8 5 8 5<br />
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| </td>
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| <td>273.684<br />
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| </td>
| |
| <td style="text-align: center;">Golden orwell (bad tuning)<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>8\35<br />
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| </td>
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| <td><br />
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| </td>
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| <td style="text-align: center;">3 5 3 5 3 5 3 5 3<br />
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| </td>
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| <td>274.286<br />
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| </td>
| |
| <td style="text-align: center;"><br />
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| </td>
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| </tr>
| |
| <tr>
| |
| <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>11\48<br />
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| </td>
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| <td style="text-align: center;">4 7 4 7 4 7 4 7 4<br />
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| </td>
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| <td>275<br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
| |
| <tr>
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| <td><br />
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| </td>
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| <td>3\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 style="text-align: center;">1 2 1 2 1 2 1 2 1<br />
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| </td>
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| <td>276.923<br />
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| </td>
| |
| <td style="text-align: center;">Boundary of propriety:<br />
| |
| generators smaller than this are proper<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <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>10\43<br />
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| </td>
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| <td style="text-align: center;">3 7 3 7 3 7 3 7 3<br />
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| </td>
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| <td>279.07<br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
| |
| <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>7\30<br />
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| </td>
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| <td><br />
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| </td>
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| <td style="text-align: center;">2 5 2 5 2 5 2 5 2<br />
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| </td>
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| <td>280.000<br />
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| </td>
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| <td style="text-align: center;"><br />
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| </td>
| |
| </tr>
| |
| <tr>
| |
| <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>11\47<br />
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| </td>
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| <td style="text-align: center;">3 8 3 8 3 8 3 8 3<br />
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| </td>
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| <td>280.851<br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
| |
| <tr>
| |
| <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 style="text-align: center;">1 e 1 e 1 e 1 e 1<br />
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| </td>
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| <td>281.100<br />
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| </td>
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| <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = e</span><br />
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| </td>
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| </tr>
| |
| <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>4\17<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 style="text-align: center;">1 3 1 3 1 3 1 3 1<br />
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| </td>
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| <td>282.353<br />
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| </td>
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| <td style="text-align: center;">L/s = 3<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 style="text-align: center;">1 pi 1 pi 1 pi 1 pi 1<br />
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| </td>
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| <td>282.922<br />
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| </td>
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| <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = pi</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>9\38<br />
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| </td>
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| <td style="text-align: center;">2 7 2 <span style="font-size: 12.8000001907349px; line-height: 1.5;">7 </span><span style="font-size: 13px; line-height: 1.5;">2 7 2 7 2 </span><br />
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| </td>
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| <td>284.2105<br />
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| </td>
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| <td><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>5\21<br />
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| </td>
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| <td><br />
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| </td>
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| <td style="text-align: center;">1 4 1 4 1 4 1 4 1<br />
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| </td>
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| <td>285.714<br />
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| </td>
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| <td style="text-align: center;">L/s = 4<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>6\25<br />
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| </td>
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| <td style="text-align: center;">1 5 1 5 1 5 1 5 1<br />
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| </td>
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| <td>288<br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td>1\4<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 style="text-align: center;">0 1 0 1 0 1 0 1 0<br />
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| </td>
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| <td>300.000<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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| </table>
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|
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|
| <br />
| | === Generator chain === |
| Note that between 7\31 and 5\22, g approximates frequency ratio 7:6, 2g approximates 11:8, and 3g approximates 8:5. This defines the range of Orwell Temperament, which is the only notable harmonic entropy minimum with this MOS pattern. 4L 5s scales outside of that range are not suitable for Orwell.</body></html></pre></div>
| | {{MOS genchain}} |
| | |
| | === Modes === |
| | {{MOS mode degrees}} |
| | |
| | ==== Proposed names ==== |
| | [http://twitter.com/Lilly__Flores/status/1640779893108805632 Lilly Flores] proposed using the Greek name relating to water as mode names. The names are in reference to the scale's former name ''orwelloid'' because the word Orwell comes from 'a spring situated near a promontory'. |
| | {{MOS modes |
| | | Mode Names= |
| | Roi $ |
| | Steno $ |
| | Limni $ |
| | Telma $ |
| | Krini $ |
| | Elos $ |
| | Mychos $ |
| | Akti $ |
| | Dini $ |
| | }} |
| | |
| | == Theory == |
| | The only low harmonic entropy minimum corresponds to [[orwell]] temperament, where 1 generator approximates [[7/6]], 2 generators approximate [[11/8]], and 3 generators approximate [[8/5]]. |
| | |
| | == Tuning ranges == |
| | === Parasoft === |
| | Parasoft tunings of 4L 5s have a step ratio between 4/3 and 3/2, implying a generator sharper than {{nowrap|7\31 {{=}} 270.97{{c}}}} and flatter than {{nowrap|5\22 {{=}} 272.73{{c}}}}. |
| | |
| | Parasoft 4L 5s edos include [[22edo]], [[31edo]], [[53edo]], and [[84edo]]. |
| | * [[22edo]] can be used to make large and small steps more distinct (the step ratio is 3/2). |
| | * [[31edo]] can be used for its nearly pure [[5/4]] and having a better approximation of [[13/8]] than 22edo. |
| | * [[53edo]] can be used for its nearly pure [[3/2]] and [[5/4]] and having much more accurate approximations of 13-limit intervals than 22edo or 31edo. |
| | |
| | The sizes of the generator, large step and small step of 4L 5s are as follows in various parasoft 4L 5s tunings. |
| | |
| | {| class="wikitable right-2 right-3 right-4 right-5 right-6 right-7" |
| | |- |
| | ! |
| | ! [[22edo]] |
| | ! [[31edo]] |
| | ! [[53edo]] |
| | ! [[84edo]] |
| | ! JI intervals represented |
| | |- |
| | | generator (g) |
| | | 5\22, 272.73 |
| | | 7\31, 270.97 |
| | | 12\53, 271.70 |
| | | 19\84, 271.43 |
| | | [[7/6]] |
| | |- |
| | | L (5g − octave) |
| | | 3\22, 163.64 |
| | | 4\31, 154.84 |
| | | 7\53, 158.49 |
| | | 11\84, 157.14 |
| | | [[12/11]], [[11/10]] |
| | |- |
| | | s (octave − 4g) |
| | | 2\22, 109.09 |
| | | 3\31, 116.13 |
| | | 5\53, 113.21 |
| | | 8\84, 114.29 |
| | | [[16/15]], [[15/14]] |
| | |} |
| | |
| | This set of JI interpretations ({{nowrap|g → 7/6|2g → 11/8|3g → 8/5|7g → 3/2}}) is called 11-limit [[Orwell]] temperament in regular temperament theory. |
| | |
| | == Scales == |
| | * [[Guanyintet9]] – [[311edo|70\311]] tuning |
| | * [[Orwell9]] – [[84edo|19\84]] tuning |
| | * [[Lovecraft9]] – [[116edo|27\116]] tuning |
| | |
| | == Scale tree == |
| | {{MOS tuning spectrum |
| | | 6/5 = Lower range of [[Orwell]] |
| | | 5/3 = Upper range of Orwell |
| | | 13/8 = Unnamed golden tuning |
| | | 12/5 = [[Lovecraft]] |
| | | 13/5 = Golden lovecraft |
| | | 6/1 = [[Gariberttet]]/[[Quasitemp]]/[[Kleiboh]] ↓ |
| | }} |
| | |
| | [[Category:Gramitonic]] <!-- main article --> |