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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}} |
| : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-05-22 13:44:42 UTC</tt>.<br>
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| : The original revision id was <tt>551908100</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>
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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">2L 5s refers to a Moment of Symmetry scale with two large steps and five small steps. Common names for such a tuning are mavila and anti-diatonic. The generator is a sharp fourth (or flat fifth), falling between 3\7 (3 degrees of [[7edo]]) and 1\2 (1 degree of [[2edo]] — the half-octave tritone that appears in every even-numbered edo).
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| The word "mavila" is used in different ways by different folks. Not every user of the word would consider every 2L 5s scale an instance of "mavila." In particular, between 13\29 and 14\31, and centered on 9\20, is the albitonic scale for the 2.7.11.13 subgroup temperament [[Chromatic pairs#Score|score]], which is not intended to be treated as having any kind of fifth, flat or otherwise.
| | Antidiatonic is similar to [[5L 2s|diatonic]] except interval classes are flipped. For example, there are natural, harmonic, and melodic major scales instead of minor scales, and its locrian scale, called "antilocrian", has an augmented fifth instead of a diminished fifth. The flatter the fifth, the less this scale resembles diatonic. |
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|
| In terms of harmonic entropy, the most significant minimum is at [[Meantone family|Liese]]/Triton, in which the generator is about 7/5 and three of them make a 3/1.
| | The most well-known forms of this scale are produced by [[mavila]], with fifths sharp enough to resemble diatonic. Other temperaments that produce this scale include [[score]], [[casablanca]], and [[triton]], whose fifths are so flat that they cannot be interpreted as a diatonic 5th, flattened or otherwise. |
| ||||||||||||||~ generator in degrees of an [[edo]] ||~ generator in cents ||~ tetrachord ||~ L in cents ||~ s in cents ||~ L to s ratio ||~ comments ||
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| ||= 3\7 ||= ||= ||= ||= || || ||= 514.3 ||= 1 1 1 ||= 171.4 ||= 171.4 ||= 1.00 ||= ||
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| ||= ||= ||= ||= ||= 13\30 || || ||= 520.0 ||= 4 4 5 ||= 200.0 ||= 160.0 ||= 1.25 ||= Mavila extends from here... ||
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| ||= ||= ||= ||= 10\23 ||= || || ||= 521.7 ||= 3 3 4 ||= 208.7 ||= 156.5 ||= 1.33 ||= ||
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| ||= ||= ||= ||= ||= 17\39 || || ||= 523.1 ||= 5 5 7 ||= 215.4 ||= 153.8 ||= 1.40 ||= ||
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| ||= ||= ||= 7\16 ||= ||= || || ||= 525.0 ||= 2 2 3 ||= 225.0 ||= 150.0 ||= 1.50 ||= Mavila in Armodue
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| Optimum rank range (L/s=3/2) ||
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| ||= ||= ||= ||= ||= 18\41 || || ||= 526.8 ||= 5 5 8 ||= 234.1 ||= 146.3 ||= 1.60 ||= ||
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| || || || || || || || ||= 1200*5/(13-phi) ||= 1 1 phi ||= 235.7 ||= 145.7 ||= phi ||= Golden mavila ||
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| || || || || || || 29\66 || ||= 527.3 ||= 8 8 13 ||= 236.4 ||= 145.5 ||= 1.62 ||= ||
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| ||= ||= ||= ||= 11\25 ||= || || ||= 528.0 ||= 3 3 5 ||= 240.0 ||= 144.0 ||= 1.67 ||= ||
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| ||= ||= ||= ||= ||= 15\34 || || ||= 529.4 ||= 4 4 7 ||= 247.1 ||= 141.2 ||= 1.75 ||= ...to somewhere around here ||
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| ||= ||= 4\9 ||= ||= ||= || || ||= 533.3 ||= 1 1 2 ||= 266.7 ||= 133.3 ||= 2.00 ||= Boundary of propriety (generators
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| smaller than this are proper) ||
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| ||= ||= ||= ||= ||= 13\29 || || ||= 537.9 ||= 3 3 7 ||= 289.7 ||= 124.1 ||= 2.33 ||= ||
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| ||= ||= ||= ||= 9\20 ||= || || ||= 540.0 ||= 2 2 5 ||= 300.0 ||= 120.0 ||= 2.50 ||= ||
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| ||= ||= ||= ||= ||= 14\31 || || ||= 541.9 ||= 3 3 8 ||= 309.7 ||= 116.1 ||= 2.66 ||= ||
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| || || || || || || || ||= 542<span style="line-height: 1.5;">.5</span> ||= 1 1 e ||= 321.55 ||= 115.0 ||= e ||= L/s = e ||
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| ||= ||= ||= 5\11 ||= ||= || || ||= 545.5 ||= 1 1 3 ||= 327.3 ||= 109.1 ||= 3.00 ||= L/s = 3 ||
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| || || || || || || || ||= 546.8 ||= 1 1 pi ||= 334.1 ||= 106.35 ||= pi ||= <span style="display: block; text-align: center;">L/s = pi</span> ||
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| ||= ||= ||= ||= ||= 11\24 || || ||= 550.0 ||= 2 2 7 ||= 350.0 ||= 100.0 ||= 3.50 ||= ||
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| ||= ||= ||= ||= 6\13 ||= || || ||= 553.8 ||= 1 1 4 ||= 369.2 ||= 92.3 ||= 4.00 ||= Thuja is optimal around here
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| L/s = 4 ||
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| ||= ||= ||= ||= ||= 7\15 || || ||= 560.0 ||= 1 1 5 ||= 400.0 ||= 80.0 ||= 5.00 ||= ie. (11/8)^5 = 5/1 ||
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| ||= ||= ||= ||= ||= ||= 8\17 ||= ||= 564.7 ||= 1 1 6 ||= 423.5 ||= 70.6 ||= 6.00 ||= ||
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| ||= ||= ||= ||= ||= ||= ||= 9\19 ||= 568.4 ||= 1 1 7 ||= 442.1 ||= 63.2 ||= 7.00 ||= Liese/Triton is around here ||
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| ||= 1\2 ||= ||= ||= ||= || || ||= 600.0 ||= 0 0 1 ||= 600.0 ||= 0 ||= — ||= ||</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>2L 5s</title></head><body>2L 5s refers to a Moment of Symmetry scale with two large steps and five small steps. Common names for such a tuning are mavila and anti-diatonic. The generator is a sharp fourth (or flat fifth), falling between 3\7 (3 degrees of <a class="wiki_link" href="/7edo">7edo</a>) and 1\2 (1 degree of <a class="wiki_link" href="/2edo">2edo</a> — the half-octave tritone that appears in every even-numbered edo).<br />
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| <br />
| |
| The word &quot;mavila&quot; is used in different ways by different folks. Not every user of the word would consider every 2L 5s scale an instance of &quot;mavila.&quot; In particular, between 13\29 and 14\31, and centered on 9\20, is the albitonic scale for the 2.7.11.13 subgroup temperament <a class="wiki_link" href="/Chromatic%20pairs#Score">score</a>, which is not intended to be treated as having any kind of fifth, flat or otherwise.<br />
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| <br />
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| In terms of harmonic entropy, the most significant minimum is at <a class="wiki_link" href="/Meantone%20family">Liese</a>/Triton, in which the generator is about 7/5 and three of them make a 3/1.<br />
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| | == Name == |
| | [[TAMNAMS]] suggests the temperament-agnostic name '''antidiatonic''' for this scale, adopted from the common use of the term to refer to diatonic ([[5L 2s]]) but with the large and small steps switched. |
|
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|
| <table class="wiki_table">
| | The scale is also often called peletonic or '''peltonic''', based on its prefix. |
| <tr>
| |
| <th colspan="7">generator in degrees of an <a class="wiki_link" href="/edo">edo</a><br />
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| </th>
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| <th>generator in cents<br />
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| </th>
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| <th>tetrachord<br />
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| </th>
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| <th>L in cents<br />
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| </th>
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| <th>s in cents<br />
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| </th>
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| <th>L to s ratio<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;">3\7<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><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;">514.3<br />
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| </td>
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| <td style="text-align: center;">1 1 1<br />
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| </td>
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| <td style="text-align: center;">171.4<br />
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| </td>
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| <td style="text-align: center;">171.4<br />
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| </td>
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| <td style="text-align: center;">1.00<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\30<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;">520.0<br />
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| </td>
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| <td style="text-align: center;">4 4 5<br />
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| </td>
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| <td style="text-align: center;">200.0<br />
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| </td>
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| <td style="text-align: center;">160.0<br />
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| </td>
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| <td style="text-align: center;">1.25<br />
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| </td>
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| <td style="text-align: center;">Mavila extends from 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;">10\23<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><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;">521.7<br />
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| </td>
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| <td style="text-align: center;">3 3 4<br />
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| </td>
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| <td style="text-align: center;">208.7<br />
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| </td>
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| <td style="text-align: center;">156.5<br />
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| </td>
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| <td style="text-align: center;">1.33<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;">17\39<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;">523.1<br />
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| </td>
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| <td style="text-align: center;">5 5 7<br />
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| </td>
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| <td style="text-align: center;">215.4<br />
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| </td>
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| <td style="text-align: center;">153.8<br />
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| </td>
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| <td style="text-align: center;">1.40<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;">7\16<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><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;">525.0<br />
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| </td>
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| <td style="text-align: center;">2 2 3<br />
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| </td>
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| <td style="text-align: center;">225.0<br />
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| </td>
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| <td style="text-align: center;">150.0<br />
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| </td>
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| <td style="text-align: center;">1.50<br />
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| </td>
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| <td style="text-align: center;">Mavila in Armodue<br />
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| Optimum rank range (L/s=3/2)<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;">18\41<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;">526.8<br />
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| </td>
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| <td style="text-align: center;">5 5 8<br />
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| </td>
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| <td style="text-align: center;">234.1<br />
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| </td>
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| <td style="text-align: center;">146.3<br />
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| </td>
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| <td style="text-align: center;">1.60<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><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 style="text-align: center;">1200*5/(13-phi)<br />
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| </td>
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| <td style="text-align: center;">1 1 phi<br />
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| </td>
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| <td style="text-align: center;">235.7<br />
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| </td>
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| <td style="text-align: center;">145.7<br />
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| </td>
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| <td style="text-align: center;">phi<br />
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| </td>
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| <td style="text-align: center;">Golden mavila<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>29\66<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;">527.3<br />
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| </td>
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| <td style="text-align: center;">8 8 13<br />
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| </td>
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| <td style="text-align: center;">236.4<br />
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| </td>
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| <td style="text-align: center;">145.5<br />
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| </td>
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| <td style="text-align: center;">1.62<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\25<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><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;">528.0<br />
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| </td>
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| <td style="text-align: center;">3 3 5<br />
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| </td>
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| <td style="text-align: center;">240.0<br />
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| </td>
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| <td style="text-align: center;">144.0<br />
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| </td>
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| <td style="text-align: center;">1.67<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;">15\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 style="text-align: center;">529.4<br />
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| </td>
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| <td style="text-align: center;">4 4 7<br />
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| </td>
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| <td style="text-align: center;">247.1<br />
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| </td>
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| <td style="text-align: center;">141.2<br />
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| </td>
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| <td style="text-align: center;">1.75<br />
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| </td>
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| <td style="text-align: center;">...to somewhere 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;">4\9<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><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;">533.3<br />
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| </td>
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| <td style="text-align: center;">1 1 2<br />
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| </td>
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| <td style="text-align: center;">266.7<br />
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| </td>
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| <td style="text-align: center;">133.3<br />
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| </td>
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| <td style="text-align: center;">2.00<br />
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| </td>
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| <td style="text-align: center;">Boundary of propriety (generators<br />
| |
| smaller 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;">13\29<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;">537.9<br />
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| </td>
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| <td style="text-align: center;">3 3 7<br />
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| </td>
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| <td style="text-align: center;">289.7<br />
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| </td>
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| <td style="text-align: center;">124.1<br />
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| </td>
| |
| <td style="text-align: center;">2.33<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;">9\20<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><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;">540.0<br />
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| </td>
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| <td style="text-align: center;">2 2 5<br />
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| </td>
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| <td style="text-align: center;">300.0<br />
| |
| </td>
| |
| <td style="text-align: center;">120.0<br />
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| </td>
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| <td style="text-align: center;">2.50<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">14\31<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">541.9<br />
| |
| </td>
| |
| <td style="text-align: center;">3 3 8<br />
| |
| </td>
| |
| <td style="text-align: center;">309.7<br />
| |
| </td>
| |
| <td style="text-align: center;">116.1<br />
| |
| </td>
| |
| <td style="text-align: center;">2.66<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 style="text-align: center;">542<span style="line-height: 1.5;">.5</span><br />
| |
| </td>
| |
| <td style="text-align: center;">1 1 e<br />
| |
| </td>
| |
| <td style="text-align: center;">321.55<br />
| |
| </td>
| |
| <td style="text-align: center;">115.0<br />
| |
| </td>
| |
| <td style="text-align: center;">e<br />
| |
| </td>
| |
| <td style="text-align: center;">L/s = e<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">5\11<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">545.5<br />
| |
| </td>
| |
| <td style="text-align: center;">1 1 3<br />
| |
| </td>
| |
| <td style="text-align: center;">327.3<br />
| |
| </td>
| |
| <td style="text-align: center;">109.1<br />
| |
| </td>
| |
| <td style="text-align: center;">3.00<br />
| |
| </td>
| |
| <td style="text-align: center;">L/s = 3<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 style="text-align: center;">546.8<br />
| |
| </td>
| |
| <td style="text-align: center;">1 1 pi<br />
| |
| </td>
| |
| <td style="text-align: center;">334.1<br />
| |
| </td>
| |
| <td style="text-align: center;">106.35<br />
| |
| </td>
| |
| <td style="text-align: center;">pi<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = pi</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">11\24<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">550.0<br />
| |
| </td>
| |
| <td style="text-align: center;">2 2 7<br />
| |
| </td>
| |
| <td style="text-align: center;">350.0<br />
| |
| </td>
| |
| <td style="text-align: center;">100.0<br />
| |
| </td>
| |
| <td style="text-align: center;">3.50<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">6\13<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">553.8<br />
| |
| </td>
| |
| <td style="text-align: center;">1 1 4<br />
| |
| </td>
| |
| <td style="text-align: center;">369.2<br />
| |
| </td>
| |
| <td style="text-align: center;">92.3<br />
| |
| </td>
| |
| <td style="text-align: center;">4.00<br />
| |
| </td>
| |
| <td style="text-align: center;">Thuja is optimal around here<br />
| |
| L/s = 4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">7\15<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">560.0<br />
| |
| </td>
| |
| <td style="text-align: center;">1 1 5<br />
| |
| </td>
| |
| <td style="text-align: center;">400.0<br />
| |
| </td>
| |
| <td style="text-align: center;">80.0<br />
| |
| </td>
| |
| <td style="text-align: center;">5.00<br />
| |
| </td>
| |
| <td style="text-align: center;">ie. (11/8)^5 = 5/1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">8\17<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">564.7<br />
| |
| </td>
| |
| <td style="text-align: center;">1 1 6<br />
| |
| </td>
| |
| <td style="text-align: center;">423.5<br />
| |
| </td>
| |
| <td style="text-align: center;">70.6<br />
| |
| </td>
| |
| <td style="text-align: center;">6.00<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">9\19<br />
| |
| </td>
| |
| <td style="text-align: center;">568.4<br />
| |
| </td>
| |
| <td style="text-align: center;">1 1 7<br />
| |
| </td>
| |
| <td style="text-align: center;">442.1<br />
| |
| </td>
| |
| <td style="text-align: center;">63.2<br />
| |
| </td>
| |
| <td style="text-align: center;">7.00<br />
| |
| </td>
| |
| <td style="text-align: center;">Liese/Triton is around here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">1\2<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">600.0<br />
| |
| </td>
| |
| <td style="text-align: center;">0 0 1<br />
| |
| </td>
| |
| <td style="text-align: center;">600.0<br />
| |
| </td>
| |
| <td style="text-align: center;">0<br />
| |
| </td>
| |
| <td style="text-align: center;">—<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| </body></html></pre></div> | | == Intervals == |
| | {{TAMNAMS use}} |
| | {{MOS intervals}} |
| | |
| | == Notation == |
| | The most common way of notating this scale, particularly when working with mavila, is to use the same note names and accidentals as that of diatonic (CDEFGAB, #, and b), but read as antidiatonic instead. |
| | |
| | {{Mavila|Tuning=2L 5s}} |
| | |
| | Under harmonic antidiatonic notation, the basic gamut (for D anti-dorian) is the following: {{MOS gamut|Notation=DEFGABC; b; #|Step Ratio=2/1}}. |
| | |
| | Under melodic antidiatonic notation, the basic gamut is the following: {{MOS gamut|Notation=DEFGABC; #; b|Step Ratio=2/1}}. |
| | |
| | == Theory == |
| | === Low harmonic entropy scales === |
| | There is one notable harmonic entropy minimum: [[Liese]]/triton, in which the generator is [[10/7]] (632.5{{cent}}) and three of them make a [[3/1]] (1897.6{{cent}}). |
| | |
| | === Temperament interpretations === |
| | 2L 5s has several rank-2 temperament interpretations, such as: |
| | * [[Mavila]], with generators around 679.8{{c}}. |
| | * [[Casablanca]], with generators around 657.8{{c}}. |
| | * [[Liese]], with generators around 632.4{{c}}. |
| | |
| | == Tuning ranges == |
| | === Simple tunings === |
| | The simplest tunings are those with step ratios 2:1, 3:1, and 3:2, producing [[9edo]], [[11edo]], and [[16edo]]. |
| | {{MOS tunings}} |
| | |
| | === Soft-of-basic tunings === |
| | {{See also| Mavila }} |
| | Much of the range for soft-of-basic antidiatonic tunings (1:1 to 2:1) corresponds to mavila temperament. Edos include 9edo (not shown), [[16edo]], and [[23edo]]. |
| | {{MOS tunings|Step Ratios=Soft-of-basic}} |
| | |
| | === Hypohard tunings === |
| | The range of hard-of-basic tunings correspond to temperaments that have significantly flattened antidiatonic 5ths, such as score and casablanca. [[20edo]] and [[31edo]] represent these two temperaments quite well. |
| | {{MOS tunings|Step Ratios=Hypohard}} |
| | |
| | === Ultrahard tunings === |
| | Ultrahard tunings, particularly with the harder end of the spectrum, correspond to [[liese]] temperament, represent by edos such as 17edo, 19edo, and larger edos such as 55edo. |
| | {{MOS tunings|Step Ratios=4/1; 5/1; 6/1; 7/1}} |
| | |
| | == Modes == |
| | {{MOS mode degrees}} |
| | |
| | === Proposed names === |
| | Modes of antidiatonic are usually named as "anti-" combined with the corresponding mode of the diatonic scale, where anti-locrian is the brightest mode and anti-lydian is the darkest mode. [[User:CompactStar|CompactStar]] also gave original names based on regions of France to mirror how modes of the diatonic scale are named on regions of Greece and Turkey. |
| | {{MOS modes |
| | | Mode Names= |
| | Anti-locrian $ |
| | Anti-phrygian $ |
| | Anti-aeolian $ |
| | Anti-dorian $ |
| | Anti-mixolydian $ |
| | Anti-ionian $ |
| | Anti-lydian |
| | | Table Headers=CompactStar's names |
| | | Table Entries= |
| | Corsican $ |
| | Breton $ |
| | Burgundian $ |
| | Picardian $ |
| | Norman $ |
| | Provencal $ |
| | Alsatian |
| | }} |
| | |
| | == Scale tree == |
| | {{MOS tuning spectrum |
| | | 6/5 = [[Gravity]] ↑ |
| | | 3/2 = [[Mavila]] |
| | | 13/8 = Golden mavila (527.1497{{c}}) |
| | | 9/5 = [[Mabila]]/[[amavil]] |
| | | 2/1 = [[Pelog]] |
| | | 5/2 = Score |
| | | 13/5 = Unnamed golden tuning (541.3837{{c}}) |
| | | 8/3 = [[Casablanca]] |
| | | 11/3 = [[Freivald]]/[[emka]] |
| | | 7/15 = [[Thuja]] |
| | | 6/1 = [[Liese]] ↓, [[triton]] ↓ |
| | }} |
| | |
| | [[Category:Antidiatonic| ]] <!-- main article --> |