Wikispaces>Andrew_Heathwaite |
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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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2010-10-26 16:54:25 UTC</tt>.<br>
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| : The original revision id was <tt>173860929</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."
| | 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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| Generalized form in seven modes:
| | 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. |
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| s s L s s s L
| | == Name == |
| s L s s s L s
| | [[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. |
| L s s s L s s
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| s s s L s s L
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| s s L s s L s
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| s L s s L s s
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| L s s L s s s
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| ||||||||||~ generator in degrees of an [[edo]] ||~ generator in cents ||~ scale ||~ L in cents ||~ s in cents ||~ L to s ratio ||
| | The scale is also often called peletonic or '''peltonic''', based on its prefix. |
| ||= 3\7 ||= ||= ||= ||= ||= 514.3 ||= 1 1 1 1 1 1 1 ||= 171.4 ||= 171.4 ||= 1.00 ||
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| ||= ||= ||= ||= ||= 13\30 ||= 520.0 ||= 4 4 5 4 4 4 5 ||= 200.0 ||= 160.0 ||= 1.25 ||
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| ||= ||= ||= ||= 10\23 ||= ||= 521.7 ||= 3 3 4 3 3 3 4 ||= 208.7 ||= 156.5 ||= 1.33 ||
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| ||= ||= ||= ||= ||= 17\39 ||= 523.1 ||= 5 5 7 5 5 5 7 ||= 215.4 ||= 153.8 ||= 1.40 ||
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| ||= ||= ||= 7\16 ||= ||= ||= 525.0 ||= 2 2 3 2 2 2 3 ||= 225.0 ||= 150.0 ||= 1.50 ||
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| ||= ||= ||= ||= ||= 18\41 ||= 526.8 ||= 5 5 8 5 5 5 8 ||= 234.1 ||= 146.3 ||= 1.60 ||
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| ||= ||= ||= ||= 11\25 ||= ||= 528.0 ||= 3 3 5 3 3 3 5 ||= 240.0 ||= 144.0 ||= 1.67 ||
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| ||= ||= ||= ||= ||= 15\34 ||= 529.4 ||= 4 4 7 4 4 4 7 ||= 247.1 ||= 141.2 ||= 1.75 ||
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| ||= ||= 4\9 ||= ||= ||= ||= 533.3 ||= 1 1 2 1 1 1 2 ||= 266.7 ||= 133.3 ||= 2.00 ||
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| ||= ||= ||= ||= ||= 13\29 ||= 537.9 ||= 3 3 7 3 3 3 7 ||= 289.7 ||= 124.1 ||= 2.33 ||
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| ||= ||= ||= ||= 9\20 ||= ||= 540.0 ||= 2 2 5 2 2 2 5 ||= 300.0 ||= 120.0 ||= 2.50 ||
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| ||= ||= ||= ||= ||= 14\31 ||= 541.9 ||= 3 3 8 3 3 3 8 ||= 309.7 ||= 116.1 ||= 2.66 ||
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| ||= ||= ||= 5\11 ||= ||= ||= 545.5 ||= 1 1 3 1 1 1 3 ||= 327.3 ||= 109.1 ||= 3.00 ||
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| ||= ||= ||= ||= ||= 11\24 ||= 550.0 ||= 2 2 7 2 2 2 7 ||= 350.0 ||= 100.0 ||= 3.50 ||
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| ||= ||= ||= ||= 6\13 ||= ||= 553.8 ||= 1 1 4 1 1 1 4 ||= 369.2 ||= 92.3 ||= 4.00 ||
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| ||= ||= ||= ||= ||= 7\15 ||= 560.0 ||= 1 1 5 1 1 1 5 ||= 400.0 ||= 80.0 ||= 5.00 ||
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| ||= 1\2 ||= ||= ||= ||= ||= 600.0 ||= 0 0 1 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 />
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| 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;<br />
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| <br />
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| Generalized form in seven modes:<br />
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| <br />
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| s s L s s s L<br />
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| s L s s s L s<br />
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| L s s s L s s<br />
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| s s s L s s L<br />
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| s s L s s L s<br />
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| s L s s L s s<br />
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| L s s L s s s<br />
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| <br />
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| | == Intervals == |
| | {{TAMNAMS use}} |
| | {{MOS intervals}} |
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| <table class="wiki_table">
| | == Notation == |
| <tr>
| | 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. |
| <th colspan="5">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>scale<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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| </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 style="text-align: center;">514.3<br />
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| </td>
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| <td style="text-align: center;">1 1 1 1 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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| </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 style="text-align: center;">520.0<br />
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| </td>
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| <td style="text-align: center;">4 4 5 4 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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| </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 style="text-align: center;">521.7<br />
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| </td>
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| <td style="text-align: center;">3 3 4 3 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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| </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 style="text-align: center;">523.1<br />
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| </td>
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| <td style="text-align: center;">5 5 7 5 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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| </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 style="text-align: center;">525.0<br />
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| </td>
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| <td style="text-align: center;">2 2 3 2 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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| </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 style="text-align: center;">526.8<br />
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| </td>
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| <td style="text-align: center;">5 5 8 5 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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| </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 style="text-align: center;">528.0<br />
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| </td>
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| <td style="text-align: center;">3 3 5 3 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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| </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 style="text-align: center;">529.4<br />
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| </td>
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| <td style="text-align: center;">4 4 7 4 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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| </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 style="text-align: center;">533.3<br />
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| </td>
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| <td style="text-align: center;">1 1 2 1 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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| </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 style="text-align: center;">537.9<br />
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| </td>
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| <td style="text-align: center;">3 3 7 3 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>
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| <td style="text-align: center;">2.33<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 style="text-align: center;">540.0<br />
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| </td>
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| <td style="text-align: center;">2 2 5 2 2 2 5<br />
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| </td>
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| <td style="text-align: center;">300.0<br />
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| </td>
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| <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 />
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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;">14\31<br />
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| </td>
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| <td style="text-align: center;">541.9<br />
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| </td>
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| <td style="text-align: center;">3 3 8 3 3 3 8<br />
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| </td>
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| <td style="text-align: center;">309.7<br />
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| </td>
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| <td style="text-align: center;">116.1<br />
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| </td>
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| <td style="text-align: center;">2.66<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;">5\11<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;">545.5<br />
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| </td>
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| <td style="text-align: center;">1 1 3 1 1 1 3<br />
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| </td>
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| <td style="text-align: center;">327.3<br />
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| </td>
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| <td style="text-align: center;">109.1<br />
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| </td>
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| <td style="text-align: center;">3.00<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;">11\24<br />
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| </td>
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| <td style="text-align: center;">550.0<br />
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| </td>
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| <td style="text-align: center;">2 2 7 2 2 2 7<br />
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| </td>
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| <td style="text-align: center;">350.0<br />
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| </td>
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| <td style="text-align: center;">100.0<br />
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| </td>
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| <td style="text-align: center;">3.50<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;">6\13<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;">553.8<br />
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| </td>
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| <td style="text-align: center;">1 1 4 1 1 1 4<br />
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| </td>
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| <td style="text-align: center;">369.2<br />
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| </td>
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| <td style="text-align: center;">92.3<br />
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| </td>
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| <td style="text-align: center;">4.00<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;">7\15<br />
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| </td>
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| <td style="text-align: center;">560.0<br />
| |
| </td>
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| <td style="text-align: center;">1 1 5 1 1 1 5<br />
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| </td>
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| <td style="text-align: center;">400.0<br />
| |
| </td>
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| <td style="text-align: center;">80.0<br />
| |
| </td>
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| <td style="text-align: center;">5.00<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;">1\2<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;">600.0<br />
| |
| </td>
| |
| <td style="text-align: center;">0 0 1 0 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>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| </body></html></pre></div> | | {{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 --> |