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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox MOS}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{MOS intro|Other Names=p-chromatic}} |
| : This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-05-12 21:29:31 UTC</tt>.<br>
| | 5L 7s represents the chromatic scales of [[Pythagorean tuning|Pythagorean]]/[[schismic]] and [[superpyth]], the former being [[Rothenberg propriety|proper]] but the latter improper until expanded by 5 more notes, producing Superpyth[17]. Such scales are characterized by having a small step ([[diatonic semitone]]) that is smaller than the [[chroma]] ([[chromatic semitone]]), the reverse of [[7L 5s]]. |
| : The original revision id was <tt>228068766</tt>.<br>
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| : 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>
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| <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">This is the MOS pattern of the Pythagorean/[[Schismatic family|schismatic/Helmholtz/Garibaldi]] chromatic scale, and also the [[Archytas clan|superpyth]] chromatic scale. In contrast to the [[7L 5s|meantone chromatic scale]], in which "diatonic" semitones are larger than "chromatic" semitones, here the reverse is true: diatonic semitones are smaller than chromatic semitones, so the [[5L 2s|diatonic scale]] subset is actually [[Rothenberg propriety|improper]].
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| The two distinct harmonic entropy minima with this MOS pattern are, on the one hand, scales very close to Pythagorean such that 64/63 is not tempered out, such as the schismatic temperaments known as "Helmholtz" and "Garibaldi", and on the other hand, the much simpler scale known as "superpyth" in which 64/63 is tempered out. | | The two distinct harmonic entropy minima are, on the one hand, scales very close to Pythagorean tuning or the schismatic temperament, and on the other hand, the simpler and less accurate temperament known as superpyth in which 64/63 is tempered out. |
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| The Pythagorean/schismatic version is proper, but the superpyth version is improper (it doesn't become proper until you add 5 more notes to form the superpyth "enharmonic" scale, superpyth[17]).
| | == Scale properties == |
| | {{TAMNAMS use}} |
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| ||||||||||~ Generator ||~ in cents ||~ Comments ||
| | === Intervals === |
| ||= 5\12 ||= ||= ||= ||= ||= 500.000 ||= ||
| | {{MOS intervals}} |
| ||= ||= ||= ||= ||= 22\53 ||= 498.113 ||= Pythagorean/Helmholtz/Garibaldi
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| is around here ||
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| ||= ||= ||= ||= 17\41 ||= ||= 497.591 ||= ||
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| ||= ||= ||= ||= ||= 29\70 ||= 497.143 ||= ||
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| ||= ||= ||= 12\29 ||= ||= ||= 496.552 ||= ||
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| ||= ||= ||= ||= ||= 31\75 ||= 496.000 ||= ||
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| ||= ||= ||= ||= 19\46 ||= ||= 495.652 ||= ||
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| ||= ||= ||= ||= ||= 26\63 ||= 495.238 ||= ||
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| ||= ||= 7\17 ||= ||= ||= ||= 494.118 ||= Boundary of propriety (generators
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| larger than this are proper) ||
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| ||= ||= ||= ||= ||= 23\56 ||= 492.857 ||= ||
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| ||= ||= ||= ||= 16\39 ||= ||= 492.308 ||= ||
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| ||= ||= ||= ||= ||= 25\61 ||= 491.803 ||= ||
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| ||= ||= ||= 9\22 ||= ||= ||= 490.909 ||= Superpyth is in this region ||
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| ||= ||= ||= ||= ||= 20\49 ||= 489.796 ||= ||
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| ||= ||= ||= ||= 11\27 ||= ||= 488.889 ||= ||
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| ||= ||= ||= ||= ||= 13\32 ||= 487.500 ||= ||
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| ||= 2\5 ||= ||= ||= ||= ||= 480.000 ||= ||</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 7s</title></head><body>This is the MOS pattern of the Pythagorean/<a class="wiki_link" href="/Schismatic%20family">schismatic/Helmholtz/Garibaldi</a> chromatic scale, and also the <a class="wiki_link" href="/Archytas%20clan">superpyth</a> chromatic scale. In contrast to the <a class="wiki_link" href="/7L%205s">meantone chromatic scale</a>, in which &quot;diatonic&quot; semitones are larger than &quot;chromatic&quot; semitones, here the reverse is true: diatonic semitones are smaller than chromatic semitones, so the <a class="wiki_link" href="/5L%202s">diatonic scale</a> subset is actually <a class="wiki_link" href="/Rothenberg%20propriety">improper</a>.<br />
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| <br />
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| The two distinct harmonic entropy minima with this MOS pattern are, on the one hand, scales very close to Pythagorean such that 64/63 is not tempered out, such as the schismatic temperaments known as &quot;Helmholtz&quot; and &quot;Garibaldi&quot;, and on the other hand, the much simpler scale known as &quot;superpyth&quot; in which 64/63 is tempered out.<br />
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| <br />
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| The Pythagorean/schismatic version is proper, but the superpyth version is improper (it doesn't become proper until you add 5 more notes to form the superpyth &quot;enharmonic&quot; scale, superpyth[17]).<br />
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| <br />
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| | === Generator chain === |
| | {{MOS genchain}} |
|
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| <table class="wiki_table">
| | === Modes === |
| <tr>
| | {{MOS mode degrees}} |
| <th colspan="5">Generator<br />
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| </th>
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| <th>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 style="text-align: center;">5\12<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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| <td style="text-align: center;"><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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| <td style="text-align: center;"><br />
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| </td>
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| <td style="text-align: center;">500.000<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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| <tr>
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| <td style="text-align: center;"><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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| <td style="text-align: center;"><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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| <td style="text-align: center;">22\53<br />
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| </td>
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| <td style="text-align: center;">498.113<br />
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| </td>
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| <td style="text-align: center;">Pythagorean/Helmholtz/Garibaldi<br />
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| is around here<br />
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| </td>
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| </tr>
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| <tr>
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| <td style="text-align: center;"><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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| <td style="text-align: center;"><br />
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| </td>
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| <td style="text-align: center;">17\41<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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| <td style="text-align: center;">497.591<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 style="text-align: center;"><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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| <td style="text-align: center;"><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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| <td style="text-align: center;">29\70<br />
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| </td>
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| <td style="text-align: center;">497.143<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 style="text-align: center;"><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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| <td style="text-align: center;">12\29<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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| <td style="text-align: center;"><br />
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| </td>
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| <td style="text-align: center;">496.552<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 style="text-align: center;"><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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| <td style="text-align: center;"><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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| <td style="text-align: center;">31\75<br />
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| </td>
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| <td style="text-align: center;">496.000<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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| <tr>
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| <td style="text-align: center;"><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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| <td style="text-align: center;"><br />
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| </td>
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| <td style="text-align: center;">19\46<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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| <td style="text-align: center;">495.652<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 style="text-align: center;"><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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| <td style="text-align: center;"><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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| <td style="text-align: center;">26\63<br />
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| </td>
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| <td style="text-align: center;">495.238<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 style="text-align: center;"><br />
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| </td>
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| <td style="text-align: center;">7\17<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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| <td style="text-align: center;"><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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| <td style="text-align: center;">494.118<br />
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| </td>
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| <td style="text-align: center;">Boundary of propriety (generators<br />
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| larger than this are proper)<br />
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| </td>
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| </tr>
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| <tr>
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| <td style="text-align: center;"><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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| <td style="text-align: center;"><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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| <td style="text-align: center;">23\56<br />
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| </td>
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| <td style="text-align: center;">492.857<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 style="text-align: center;"><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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| <td style="text-align: center;"><br />
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| </td>
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| <td style="text-align: center;">16\39<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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| <td style="text-align: center;">492.308<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 style="text-align: center;"><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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| <td style="text-align: center;"><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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| <td style="text-align: center;">25\61<br />
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| </td>
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| <td style="text-align: center;">491.803<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 style="text-align: center;"><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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| <td style="text-align: center;">9\22<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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| <td style="text-align: center;"><br />
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| </td>
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| <td style="text-align: center;">490.909<br />
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| </td>
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| <td style="text-align: center;">Superpyth is in this region<br />
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| </td>
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| </tr>
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| <tr>
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| <td style="text-align: center;"><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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| <td style="text-align: center;"><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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| <td style="text-align: center;">20\49<br />
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| </td>
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| <td style="text-align: center;">489.796<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 style="text-align: center;"><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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| <td style="text-align: center;"><br />
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| </td>
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| <td style="text-align: center;">11\27<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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| <td style="text-align: center;">488.889<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 style="text-align: center;"><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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| <td style="text-align: center;"><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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| <td style="text-align: center;">13\32<br />
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| </td>
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| <td style="text-align: center;">487.500<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 style="text-align: center;">2\5<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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| <td style="text-align: center;"><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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| <td style="text-align: center;"><br />
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| </td>
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| <td style="text-align: center;">480.000<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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|
| </body></html></pre></div> | | === Proposed names === |
| | The modes are named by [[Eliora]] after Chinese zodiac animals. 5L 7s is the opposite mos to [[7L 5s]], named after a Western concept, Gregorian months, therefore this mos scale has Eastern nomenclature. Furthermore, 12edo (equalized tuning of this MOS) was independently discovered in China. |
| | |
| | {{MOS modes |
| | | Mode Names= |
| | Rat $ |
| | Ox $ |
| | Tiger $ |
| | Rabbit $ |
| | Dragon $ |
| | Snake $ |
| | Horse $ |
| | Goat $ |
| | Monkey $ |
| | Rooster $ |
| | Dog $ |
| | Pig $ |
| | }} |
| | |
| | == Scales == |
| | * [[Pythagorean12]] – Pythagorean tuning |
| | * [[Garibaldi12]] – 94edo tuning |
| | * [[Cotoneum12]] – 217edo tuning |
| | * [[Edson12]] – 29edo tuning |
| | * [[Pepperoni12]] – 271edo tuning |
| | * [[Supra12]] – 56edo tuning |
| | * [[Archy12]] – 472edo tuning |
| | * [[12-22a]] – 22edo tuning |
| | |
| | == Scale tree == |
| | {{MOS tuning spectrum |
| | | 6/5 = [[Photia]], ↑ [[grackle]] |
| | | 5/4 = [[Helmholtz (temperament)|Helmholtz]], [[Pythagorean tuning]] (701.955{{c}}) |
| | | 9/7 = [[Garibaldi]] / [[cassandra]] |
| | | 4/3 = Garibaldi / [[andromeda]] |
| | | 11/8 = [[Kwai]] |
| | | 10/7 = [[Undecental]], argent tuning (702.944{{c}}) |
| | | 3/2 = [[Edson]] |
| | | 13/8 = [[Polypyth]], golden neogothic (704.096{{c}}) |
| | | 5/3 = [[Leapday]] |
| | | 12/7 = [[Leapweek]] |
| | | 7/3 = [[Supra]] |
| | | 13/5 = Golden supra (708.054{{c}}) |
| | | 8/3 = [[Quasisuper]] / [[quasisupra]] |
| | | 3/1 = [[Suprapyth]] |
| | | 7/2 = [[Superpyth]] |
| | | 6/1 = ↓ [[Oceanfront]] / [[ultrapyth]] |
| | }} |
| | |
| | [[Category:12-tone scales]] |
| | [[Category:P-chromatic| ]]<!-- main article --> |
| | [[Category:Chromatic scales]] |