31edo: Difference between revisions
Wikispaces>guest **Imported revision 150596567 - Original comment: ** |
Wikispaces>guest **Imported revision 150596635 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:guest|guest]] and made on <tt>2010-06-26 01: | : This revision was by author [[User:guest|guest]] and made on <tt>2010-06-26 02:01:24 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>150596635</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | 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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The large tritone. | The large tritone. | ||
===17/31 octave | ===17/31 octave 18/31 octave 19/31 octave 20/31 octave 21/31 octave 22/31 octave 23/31 octave 24/31 octave 25/31 octave 26/31 octave 27/31 octave 28/31 octave=== | ||
===29/31 octave 30/31 octave perfect octave - 31/31 octave=== | |||
===29/31 octave | |||
=Modes= | =Modes= | ||
|||| ====31 tone equal modes:==== || | |||
|| {{**2 3 3 2 3 2 3 2 3 3 2 3**}} || Meantone Chromatic (53/220-comma) || | |||
|| {{**5 5 3 5 5 5 3**}} || Thirty-one tone Major, Intense Diatonic Lydian, M.Ionian || | |||
|| {{**5 3 5 5 3 5 5**}} || Thirty-one tone Natural Minor, Intense Diatonic Hypodorian, Aeolian || | |||
|| {{**5 3 5 5 5 5 3**}} || Thirty-one tone Melodic Minor || | |||
|| {{**5 3 5 5 3 7 3**}} || Thirty-one tone Harmonic Minor || | |||
|| {{**5 5 3 5 3 7 3**}} || Thirty-one tone Harmonic Major || | |||
|| {{**5 5 3 5 3 5 5**}} || Thirty-one tone Major-Minor || | |||
|| {{**5 8 5 13**}} || Genus primum || | |||
|| {{**10 3 5 5 5 3**}} || Genus secundum || | |||
|| {{**8 2 8 3 7 3**}} || Genus tertium || | |||
|| {{**10 10 10 1**}} || Genus quartum || | |||
|| {{**5 7 6 7 5 1**}} || Genus quintum || | |||
|| {{**4 6 2 6 4 3 3 3**}} || Genus sextum || | |||
|| {{**4 6 5 6 4 6**}} || Genus septimum || | |||
|| {{**6 6 6 1 6 6**}} || Genus octavum || | |||
|| {{**4 6 9 6 4 2**}} || Genus nonum || | |||
|| {{**13 6 6 6**}} || Genus decimum || | |||
|| {{**5 5 3 5 5 3 2 3**}} || Genus diatonicum || | |||
|| {{**3 5 2 3 5 3 2 5 3**}} || Genus chromaticum || | |||
|| {{**5 5 2 1 5 5 2 3 3**}} || Genus diatonicum cum septimis || | |||
|| {{**3 4 3 3 2 1 4 1 4 1 2 3**}} || Genus enharmonicum vocale || | |||
|| {{**2 2 4 2 2 3 3 3 1 3 3 3**}} || Genus enharmonicum instrumentale || | |||
|| {{**3 2 3 2 3 2 3 3 2 3 2 3**}} || Genus diatonico-chromaticum || | |||
|| {{**5 2 1 2 5 3 2 1 4 1 2 3**}} || Genus bichromaticum || | |||
|| {{**4 4 5 4 4 5 5**}} || Neutral Diatonic Mixolydian || | |||
|| {{**4 5 4 4 5 5 4**}} || Neutral Diatonic Lydian || | |||
|| {{**5 4 4 5 5 4 4**}} || Neutral Diatonic Phrygian || | |||
|| {{**4 4 5 5 4 4 5**}} || Neutral Diatonic Dorian || | |||
|| {{**4 5 5 4 4 5 4**}} || Neutral Diatonic Hypolydian || | |||
|| {{**5 5 4 4 5 4 4**}} || Neutral Diatonic Hypophrygian || | |||
|| {{**5 4 4 5 4 4 5**}} || Neutral Diatonic Hypodorian || | |||
|| {{**4 5 4 4 5 4 5**}} || Neutral Mixolydian || | |||
|| {{**5 4 4 5 4 5 4**}} || Neutral Lydian || | |||
|| {{**4 4 5 4 5 4 5**}} || Neutral Phrygian || | |||
|| {{**4 5 4 5 4 5 4**}} || Neutral Dorian || | |||
|| {{**5 4 5 4 5 4 4**}} || Neutral Hypolydian || | |||
|| {{**4 5 4 5 4 4 5**}} || Neutral Hypophrygian || | |||
|| {{**5 4 5 4 4 5 4**}} || Neutral Hypodorian || | |||
|| {{**2 2 9 2 2 9 5**}} || Hemiolic Chromatic Mixolydian || | |||
|| {{**2 9 2 2 9 5 2**}} || Hemiolic Chromatic Lydian || | |||
|| {{**9 2 2 9 5 2 2**}} || Hemiolic Chromatic Phrygian || | |||
|| {{**2 2 9 5 2 2 9**}} || Hemiolic Chromatic Dorian || | |||
|| {{**2 9 5 2 2 9 2**}} || Hemiolic Chromatic Hypolydian || | |||
|| {{**9 5 2 2 9 2 2**}} || Hemiolic Chromatic Hypophrygian || | |||
|| {{**5 2 2 9 2 2 9**}} || Hemiolic Chromatic Hypodorian || | |||
|| {{**2 3 8 2 3 8 5**}} || Ratio 2:3 Chromatic Mixolydian || | |||
|| {{**3 8 2 3 8 5 2**}} || Ratio 2:3 Chromatic Lydian || | |||
|| {{**8 2 3 8 5 2 3**}} || Ratio 2:3 Chromatic Phrygian || | |||
|| {{**2 3 8 5 2 3 8**}} || Ratio 2:3 Chromatic Dorian || | |||
|| {{**3 8 5 2 3 8 2**}} || Ratio 2:3 Chromatic Hypolydian || | |||
|| {{**8 5 2 3 8 2 3**}} || Ratio 2:3 Chromatic Hypophrygian || | |||
|| {{**5 2 3 8 2 3 8**}} || Ratio 2:3 Chromatic Hypodorian || | |||
|| {{**3 5 5 3 5 5 5**}} || Intense Diatonic Mixolydian, M.Locrian || | |||
|| {{**5 3 5 5 5 3 5**}} || Intense Diatonic Phrygian, M.Dorian || | |||
|| {{**3 5 5 5 3 5 5**}} || Intense Diatonic Dorian, M.Phrygian || | |||
|| {{**5 5 5 3 5 5 3**}} || Intense Diatonic Hypolydian, M.Lydian || | |||
|| {{**5 5 3 5 5 3 5**}} || Intense Diatonic Hypophrygian, M.Mixolydian || | |||
|| {{**2 5 6 2 5 6 5**}} || Soft Diatonic Mixolydian || | |||
|| {{**5 6 2 5 6 5 2**}} || Soft Diatonic Lydian || | |||
|| {{**6 2 5 6 5 2 5**}} || Soft Diatonic Phrygian || | |||
|| {{**2 5 6 5 2 5 6**}} || Soft Diatonic Dorian || | |||
|| {{**5 6 5 2 5 6 2**}} || Soft Diatonic Hypolydian || | |||
|| {{**6 5 2 5 6 2 5**}} || Soft Diatonic Hypophrygian || | |||
|| {{**5 2 5 6 2 5 6**}} || Soft Diatonic Hypodorian || | |||
|| {{**1 2 10 1 2 10 5**}} || Enharmonic Mixolydian || | |||
|| {{**2 10 1 2 10 5 1**}} || Enharmonic Lydian || | |||
|| {{**10 1 2 10 5 1 2**}} || Enharmonic Phrygian || | |||
|| {{**1 2 10 5 1 2 10**}} || Enharmonic Dorian || | |||
|| {{**2 10 5 1 2 10 1**}} || Enharmonic Hypolydian || | |||
|| {{**10 5 1 2 10 1 2**}} || Enharmonic Hypophrygian || | |||
|| {{**5 1 2 10 1 2 10**}} || Enharmonic Hypodorian || | |||
|| {{**6 6 7 6 6**}} || Quasi-equal Pentatonic || | |||
|| {{**3 2 2 3 3 2 3 3 2 2 3 3**}} || Fokker 12-tone || | |||
|| {{**5 3 5 3 5 2 5 3**}} || Modus conjunctus || | |||
|| {{**3 5 2 5 3 5 3 5**}} || Octatonic || | |||
|| {{**3 3 4 3 5 3 4 3 3**}} || Hahn symmetric pentachordal || | |||
|| {{**3 4 3 3 5 3 4 3 3**}} || Hahn pentachordal || | |||
|| {{**4 4 2 5 3 3 4 3 3**}} || Hahn Nonatonic || | |||
|| {{**5 1 5 1 5 1 5 1 5 1 1**}} || de Vries 11-tone || | |||
|| {{**4 1 4 4 4 1 4 4 1 4**}} || Breed 10-tone || | |||
|| {{**4 2 4 2 4 2 4 3 3 3**}} || Lumma Decatonic || | |||
|| {{**5 3 3 3 3 5 3 3 3**}} || Rothenberg Generalized Diatonic || | |||
|| {{**5 2 6 5 2 5 6**}} || "Septimal" Natural Minor || | |||
|| {{**4 3 4 3 4 3 4 3 3**}} || Thirty-one tone Orwell || | |||
|| {{**2 5 2 2 5 2 2 2 5 2 2**}} || Secor Sentinel || | |||
A large open list of modes (subsets) from 31-edo that people have named: [[31edo modes]]. See also [[31edo MOS scales]]. Some of the popular ones: | A large open list of modes (subsets) from 31-edo that people have named: [[31edo modes]]. See also [[31edo MOS scales]]. Some of the popular ones: | ||
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* <span class="wiki_link_ext">[[http://tonalsoft.com/enc/number/31edo.aspx|Tonalsoft Encyclopedia article]]</span></pre></div> | * <span class="wiki_link_ext">[[http://tonalsoft.com/enc/number/31edo.aspx|Tonalsoft Encyclopedia article]]</span></pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>31edo</title></head><body><!-- ws:start:WikiTextTocRule: | <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>31edo</title></head><body><!-- ws:start:WikiTextTocRule:50:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --> | <a href="#Modes">Modes</a><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --> | <a href="#Music in 31-edo">Music in 31-edo</a><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --> | <a href="#Practical Theory / Books">Practical Theory / Books</a><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --> | <a href="#Other Articles">Other Articles</a><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --> | ||
<!-- ws:end:WikiTextTocRule:76 --><hr /> | |||
<em>Thirty-one tone equal temperament</em>, also called <em>31-tET</em>, <em>31-EDO</em>, <em>31-et</em>, or <em>tricesimoprimal meantone temperament</em>, is the scale derived by dividing the octave into 31 <a class="wiki_link" href="/equal">equally</a> large steps. The term 'Tricesimoprimal' was first used by Adriaan Fokker. Each step is equivalent to a frequency ratio of the 31st root of 2, or 38.71 <a class="wiki_link" href="/cents">cents</a>. The fifth is flat (over five cents) as befits a tuning supporting meantone, but the major third is less than a cent sharp. The 7/4, a cent flat, is also very good. Because of these good values 31-et is relatively quite accurate and is in fact the sixth Zeta function integral tuning, <!-- ws:start:WikiTextUrlRule: | <em>Thirty-one tone equal temperament</em>, also called <em>31-tET</em>, <em>31-EDO</em>, <em>31-et</em>, or <em>tricesimoprimal meantone temperament</em>, is the scale derived by dividing the octave into 31 <a class="wiki_link" href="/equal">equally</a> large steps. The term 'Tricesimoprimal' was first used by Adriaan Fokker. Each step is equivalent to a frequency ratio of the 31st root of 2, or 38.71 <a class="wiki_link" href="/cents">cents</a>. The fifth is flat (over five cents) as befits a tuning supporting meantone, but the major third is less than a cent sharp. The 7/4, a cent flat, is also very good. Because of these good values 31-et is relatively quite accurate and is in fact the sixth Zeta function integral tuning, <!-- ws:start:WikiTextUrlRule:868:http://www.research.att.com/~njas/sequences/A117538 --><a class="wiki_link_ext" href="http://www.research.att.com/~njas/sequences/A117538" rel="nofollow">http://www.research.att.com/~njas/sequences/A117538</a><!-- ws:end:WikiTextUrlRule:868 -->.<br /> | ||
<br /> | <br /> | ||
For more encyclopedic info, see <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/31_equal_temperament" rel="nofollow">Wikipedia's article</a>.<br /> | For more encyclopedic info, see <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/31_equal_temperament" rel="nofollow">Wikipedia's article</a>.<br /> | ||
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The large tritone.<br /> | The large tritone.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:34:&lt;h3&gt; --><h3 id="toc17"><a name="Intervals--17/31 octave | <!-- ws:start:WikiTextHeadingRule:34:&lt;h3&gt; --><h3 id="toc17"><a name="Intervals--17/31 octave 18/31 octave 19/31 octave 20/31 octave 21/31 octave 22/31 octave 23/31 octave 24/31 octave 25/31 octave 26/31 octave 27/31 octave 28/31 octave"></a><!-- ws:end:WikiTextHeadingRule:34 -->17/31 octave 18/31 octave 19/31 octave 20/31 octave 21/31 octave 22/31 octave 23/31 octave 24/31 octave 25/31 octave 26/31 octave 27/31 octave 28/31 octave</h3> | ||
<!-- ws:start:WikiTextHeadingRule:36:&lt;h3&gt; --><h3 id="toc18"><a name="Intervals--29/31 octave 30/31 octave perfect octave - 31/31 octave"></a><!-- ws:end:WikiTextHeadingRule:36 -->29/31 octave 30/31 octave perfect octave - 31/31 octave</h3> | |||
<!-- ws:start:WikiTextHeadingRule: | |||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><h1 id="toc19"><a name="Modes"></a><!-- ws:end:WikiTextHeadingRule:38 -->Modes</h1> | ||
<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<td colspan="2"><!-- ws:start:WikiTextHeadingRule:40:&lt;h4&gt; --><h4 id="toc20"><a name="Modes---31 tone equal modes:"></a><!-- ws:end:WikiTextHeadingRule:40 -->31 tone equal modes:</h4> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>2 3 3 2 3 2 3 2 3 3 2 3</strong></tt><br /> | |||
</td> | |||
<td>Meantone Chromatic (53/220-comma)<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 5 3 5 5 5 3</strong></tt><br /> | |||
</td> | |||
<td>Thirty-one tone Major, Intense Diatonic Lydian, M.Ionian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 3 5 5 3 5 5</strong></tt><br /> | |||
</td> | |||
<td>Thirty-one tone Natural Minor, Intense Diatonic Hypodorian, Aeolian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 3 5 5 5 5 3</strong></tt><br /> | |||
</td> | |||
<td>Thirty-one tone Melodic Minor<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 3 5 5 3 7 3</strong></tt><br /> | |||
</td> | |||
<td>Thirty-one tone Harmonic Minor<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 5 3 5 3 7 3</strong></tt><br /> | |||
</td> | |||
<td>Thirty-one tone Harmonic Major<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 5 3 5 3 5 5</strong></tt><br /> | |||
</td> | |||
<td>Thirty-one tone Major-Minor<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 8 5 13</strong></tt><br /> | |||
</td> | |||
<td>Genus primum<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>10 3 5 5 5 3</strong></tt><br /> | |||
</td> | |||
<td>Genus secundum<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>8 2 8 3 7 3</strong></tt><br /> | |||
</td> | |||
<td>Genus tertium<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>10 10 10 1</strong></tt><br /> | |||
</td> | |||
<td>Genus quartum<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 7 6 7 5 1</strong></tt><br /> | |||
</td> | |||
<td>Genus quintum<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>4 6 2 6 4 3 3 3</strong></tt><br /> | |||
</td> | |||
<td>Genus sextum<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>4 6 5 6 4 6</strong></tt><br /> | |||
</td> | |||
<td>Genus septimum<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>6 6 6 1 6 6</strong></tt><br /> | |||
</td> | |||
<td>Genus octavum<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>4 6 9 6 4 2</strong></tt><br /> | |||
</td> | |||
<td>Genus nonum<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>13 6 6 6</strong></tt><br /> | |||
</td> | |||
<td>Genus decimum<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 5 3 5 5 3 2 3</strong></tt><br /> | |||
</td> | |||
<td>Genus diatonicum<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>3 5 2 3 5 3 2 5 3</strong></tt><br /> | |||
</td> | |||
<td>Genus chromaticum<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 5 2 1 5 5 2 3 3</strong></tt><br /> | |||
</td> | |||
<td>Genus diatonicum cum septimis<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>3 4 3 3 2 1 4 1 4 1 2 3</strong></tt><br /> | |||
</td> | |||
<td>Genus enharmonicum vocale<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>2 2 4 2 2 3 3 3 1 3 3 3</strong></tt><br /> | |||
</td> | |||
<td>Genus enharmonicum instrumentale<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>3 2 3 2 3 2 3 3 2 3 2 3</strong></tt><br /> | |||
</td> | |||
<td>Genus diatonico-chromaticum<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 2 1 2 5 3 2 1 4 1 2 3</strong></tt><br /> | |||
</td> | |||
<td>Genus bichromaticum<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>4 4 5 4 4 5 5</strong></tt><br /> | |||
</td> | |||
<td>Neutral Diatonic Mixolydian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>4 5 4 4 5 5 4</strong></tt><br /> | |||
</td> | |||
<td>Neutral Diatonic Lydian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 4 4 5 5 4 4</strong></tt><br /> | |||
</td> | |||
<td>Neutral Diatonic Phrygian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>4 4 5 5 4 4 5</strong></tt><br /> | |||
</td> | |||
<td>Neutral Diatonic Dorian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>4 5 5 4 4 5 4</strong></tt><br /> | |||
</td> | |||
<td>Neutral Diatonic Hypolydian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 5 4 4 5 4 4</strong></tt><br /> | |||
</td> | |||
<td>Neutral Diatonic Hypophrygian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 4 4 5 4 4 5</strong></tt><br /> | |||
</td> | |||
<td>Neutral Diatonic Hypodorian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>4 5 4 4 5 4 5</strong></tt><br /> | |||
</td> | |||
<td>Neutral Mixolydian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 4 4 5 4 5 4</strong></tt><br /> | |||
</td> | |||
<td>Neutral Lydian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>4 4 5 4 5 4 5</strong></tt><br /> | |||
</td> | |||
<td>Neutral Phrygian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>4 5 4 5 4 5 4</strong></tt><br /> | |||
</td> | |||
<td>Neutral Dorian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 4 5 4 5 4 4</strong></tt><br /> | |||
</td> | |||
<td>Neutral Hypolydian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>4 5 4 5 4 4 5</strong></tt><br /> | |||
</td> | |||
<td>Neutral Hypophrygian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 4 5 4 4 5 4</strong></tt><br /> | |||
</td> | |||
<td>Neutral Hypodorian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>2 2 9 2 2 9 5</strong></tt><br /> | |||
</td> | |||
<td>Hemiolic Chromatic Mixolydian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>2 9 2 2 9 5 2</strong></tt><br /> | |||
</td> | |||
<td>Hemiolic Chromatic Lydian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>9 2 2 9 5 2 2</strong></tt><br /> | |||
</td> | |||
<td>Hemiolic Chromatic Phrygian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>2 2 9 5 2 2 9</strong></tt><br /> | |||
</td> | |||
<td>Hemiolic Chromatic Dorian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>2 9 5 2 2 9 2</strong></tt><br /> | |||
</td> | |||
<td>Hemiolic Chromatic Hypolydian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>9 5 2 2 9 2 2</strong></tt><br /> | |||
</td> | |||
<td>Hemiolic Chromatic Hypophrygian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 2 2 9 2 2 9</strong></tt><br /> | |||
</td> | |||
<td>Hemiolic Chromatic Hypodorian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>2 3 8 2 3 8 5</strong></tt><br /> | |||
</td> | |||
<td>Ratio 2:3 Chromatic Mixolydian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>3 8 2 3 8 5 2</strong></tt><br /> | |||
</td> | |||
<td>Ratio 2:3 Chromatic Lydian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>8 2 3 8 5 2 3</strong></tt><br /> | |||
</td> | |||
<td>Ratio 2:3 Chromatic Phrygian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>2 3 8 5 2 3 8</strong></tt><br /> | |||
</td> | |||
<td>Ratio 2:3 Chromatic Dorian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>3 8 5 2 3 8 2</strong></tt><br /> | |||
</td> | |||
<td>Ratio 2:3 Chromatic Hypolydian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>8 5 2 3 8 2 3</strong></tt><br /> | |||
</td> | |||
<td>Ratio 2:3 Chromatic Hypophrygian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 2 3 8 2 3 8</strong></tt><br /> | |||
</td> | |||
<td>Ratio 2:3 Chromatic Hypodorian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>3 5 5 3 5 5 5</strong></tt><br /> | |||
</td> | |||
<td>Intense Diatonic Mixolydian, M.Locrian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 3 5 5 5 3 5</strong></tt><br /> | |||
</td> | |||
<td>Intense Diatonic Phrygian, M.Dorian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>3 5 5 5 3 5 5</strong></tt><br /> | |||
</td> | |||
<td>Intense Diatonic Dorian, M.Phrygian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 5 5 3 5 5 3</strong></tt><br /> | |||
</td> | |||
<td>Intense Diatonic Hypolydian, M.Lydian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 5 3 5 5 3 5</strong></tt><br /> | |||
</td> | |||
<td>Intense Diatonic Hypophrygian, M.Mixolydian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>2 5 6 2 5 6 5</strong></tt><br /> | |||
</td> | |||
<td>Soft Diatonic Mixolydian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 6 2 5 6 5 2</strong></tt><br /> | |||
</td> | |||
<td>Soft Diatonic Lydian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>6 2 5 6 5 2 5</strong></tt><br /> | |||
</td> | |||
<td>Soft Diatonic Phrygian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>2 5 6 5 2 5 6</strong></tt><br /> | |||
</td> | |||
<td>Soft Diatonic Dorian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 6 5 2 5 6 2</strong></tt><br /> | |||
</td> | |||
<td>Soft Diatonic Hypolydian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>6 5 2 5 6 2 5</strong></tt><br /> | |||
</td> | |||
<td>Soft Diatonic Hypophrygian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 2 5 6 2 5 6</strong></tt><br /> | |||
</td> | |||
<td>Soft Diatonic Hypodorian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>1 2 10 1 2 10 5</strong></tt><br /> | |||
</td> | |||
<td>Enharmonic Mixolydian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>2 10 1 2 10 5 1</strong></tt><br /> | |||
</td> | |||
<td>Enharmonic Lydian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>10 1 2 10 5 1 2</strong></tt><br /> | |||
</td> | |||
<td>Enharmonic Phrygian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>1 2 10 5 1 2 10</strong></tt><br /> | |||
</td> | |||
<td>Enharmonic Dorian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>2 10 5 1 2 10 1</strong></tt><br /> | |||
</td> | |||
<td>Enharmonic Hypolydian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>10 5 1 2 10 1 2</strong></tt><br /> | |||
</td> | |||
<td>Enharmonic Hypophrygian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 1 2 10 1 2 10</strong></tt><br /> | |||
</td> | |||
<td>Enharmonic Hypodorian<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>6 6 7 6 6</strong></tt><br /> | |||
</td> | |||
<td>Quasi-equal Pentatonic<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>3 2 2 3 3 2 3 3 2 2 3 3</strong></tt><br /> | |||
</td> | |||
<td>Fokker 12-tone<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 3 5 3 5 2 5 3</strong></tt><br /> | |||
</td> | |||
<td>Modus conjunctus<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>3 5 2 5 3 5 3 5</strong></tt><br /> | |||
</td> | |||
<td>Octatonic<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>3 3 4 3 5 3 4 3 3</strong></tt><br /> | |||
</td> | |||
<td>Hahn symmetric pentachordal<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>3 4 3 3 5 3 4 3 3</strong></tt><br /> | |||
</td> | |||
<td>Hahn pentachordal<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>4 4 2 5 3 3 4 3 3</strong></tt><br /> | |||
</td> | |||
<td>Hahn Nonatonic<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 1 5 1 5 1 5 1 5 1 1</strong></tt><br /> | |||
</td> | |||
<td>de Vries 11-tone<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>4 1 4 4 4 1 4 4 1 4</strong></tt><br /> | |||
</td> | |||
<td>Breed 10-tone<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>4 2 4 2 4 2 4 3 3 3</strong></tt><br /> | |||
</td> | |||
<td>Lumma Decatonic<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 3 3 3 3 5 3 3 3</strong></tt><br /> | |||
</td> | |||
<td>Rothenberg Generalized Diatonic<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>5 2 6 5 2 5 6</strong></tt><br /> | |||
</td> | |||
<td>&quot;Septimal&quot; Natural Minor<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>4 3 4 3 4 3 4 3 3</strong></tt><br /> | |||
</td> | |||
<td>Thirty-one tone Orwell<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><tt><strong>2 5 2 2 5 2 2 2 5 2 2</strong></tt><br /> | |||
</td> | |||
<td>Secor Sentinel<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | <br /> | ||
A large open list of modes (subsets) from 31-edo that people have named: <a class="wiki_link" href="/31edo%20modes">31edo modes</a>. See also <a class="wiki_link" href="/31edo%20MOS%20scales">31edo MOS scales</a>. Some of the popular ones:<br /> | A large open list of modes (subsets) from 31-edo that people have named: <a class="wiki_link" href="/31edo%20modes">31edo modes</a>. See also <a class="wiki_link" href="/31edo%20MOS%20scales">31edo MOS scales</a>. Some of the popular ones:<br /> | ||
<br /> | <br /> | ||
<ul><li>31-tone major: 5 5 3 5 5 5 3</li><li>1/4-comma meantone (Eb-G#): 2 3 3 2 3 2 3 2 3 3 2 3</li><li>Harmonic scale 8: 5 5 4 4 4 4 3 3</li><li>the <a class="wiki_link" href="/Euler-fokker%20genera">Euler-fokker genera</a> (technically <a class="wiki_link" href="/JI">JI</a> but representable in 31)</li></ul><br /> | <ul><li>31-tone major: 5 5 3 5 5 5 3</li><li>1/4-comma meantone (Eb-G#): 2 3 3 2 3 2 3 2 3 3 2 3</li><li>Harmonic scale 8: 5 5 4 4 4 4 3 3</li><li>the <a class="wiki_link" href="/Euler-fokker%20genera">Euler-fokker genera</a> (technically <a class="wiki_link" href="/JI">JI</a> but representable in 31)</li></ul><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:42:&lt;h1&gt; --><h1 id="toc21"><a name="Music in 31-edo"></a><!-- ws:end:WikiTextHeadingRule:42 -->Music in 31-edo</h1> | ||
<a class="wiki_link" href="/31-edo%20compositions">An alphabetical list of Tricesimoprimal Compositions</a>.<br /> | <a class="wiki_link" href="/31-edo%20compositions">An alphabetical list of Tricesimoprimal Compositions</a>.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Music in 31-edo-Thirty-one tone pedagogy"></a><!-- ws:end:WikiTextHeadingRule:44 -->Thirty-one tone pedagogy</h2> | ||
The <a class="wiki_link" href="/MicroPedagogyCollective">MicroPedagogyCollective</a> is currently at work producing demonstrative material which will encourage and enable more people to learn this system. There have been two <a class="wiki_link" href="/ThirtyOneToneSinginCamp">ThirtyOneToneSinginCamp</a>s as well.<br /> | The <a class="wiki_link" href="/MicroPedagogyCollective">MicroPedagogyCollective</a> is currently at work producing demonstrative material which will encourage and enable more people to learn this system. There have been two <a class="wiki_link" href="/ThirtyOneToneSinginCamp">ThirtyOneToneSinginCamp</a>s as well.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:46:&lt;h1&gt; --><h1 id="toc23"><a name="Practical Theory / Books"></a><!-- ws:end:WikiTextHeadingRule:46 -->Practical Theory / Books</h1> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:619:&lt;a href=&quot;http://www.ronsword.com/books.html&quot; target=&quot;_blank&quot; rel=&quot;nofollow&quot;&gt;&lt;img src=&quot;http://ronsword.com/images/TSG_sm.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 116px; width: 87px;&quot; /&gt;&lt;/a&gt; --><a href="http://www.ronsword.com/books.html" target="_blank" rel="nofollow"><img src="http://ronsword.com/images/TSG_sm.jpg" alt="external image TSG_sm.jpg" title="external image TSG_sm.jpg" style="height: 116px; width: 87px;" /></a><!-- ws:end:WikiTextRemoteImageRule:619 --><a class="wiki_link_ext" href="http://www.ronsword.com/books.html" rel="nofollow" target="_blank">Sword, Ronald. &quot;Tricesimoprimal Scales for Guitar.&quot; IAAA Press, UK-USA. First Ed: March 2009.</a> - A comprehensive approach to 31-EDO and all the families associated for Guitar. Features over 300 scale charts / scale examples.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:48:&lt;h1&gt; --><h1 id="toc24"><a name="Other Articles"></a><!-- ws:end:WikiTextHeadingRule:48 -->Other Articles</h1> | ||
<ul><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.xs4all.nl/%7Ehuygensf/english/index.html" rel="nofollow">de Beer, Anton, ''The Development of 31-tone Music</a></span></li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.xs4all.nl/%7Ehuygensf/doc/fokkerorg.html" rel="nofollow">Fokker, Adriaan Daniël, ''Equal Temperament and the Thirty-one-keyed organ</a></span></li><li>Fokker, A.D., &quot;New Music with 31 Notes&quot; translated by Leigh Gerdine</li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.xs4all.nl/%7Ehuygensf/doc/rap31.html" rel="nofollow">Rapoport, Paul, ''About 31-tone Equal Temperament</a></span></li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.xs4all.nl/%7Ehuygensf/doc/terp31.html" rel="nofollow">Terpstra, Siemen, ''Toward a Theory of Meantone (and 31-et) Harmony''</a></span></li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/31edo.aspx" rel="nofollow">Tonalsoft Encyclopedia article</a></span></li></ul></body></html></pre></div> | <ul><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.xs4all.nl/%7Ehuygensf/english/index.html" rel="nofollow">de Beer, Anton, ''The Development of 31-tone Music</a></span></li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.xs4all.nl/%7Ehuygensf/doc/fokkerorg.html" rel="nofollow">Fokker, Adriaan Daniël, ''Equal Temperament and the Thirty-one-keyed organ</a></span></li><li>Fokker, A.D., &quot;New Music with 31 Notes&quot; translated by Leigh Gerdine</li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.xs4all.nl/%7Ehuygensf/doc/rap31.html" rel="nofollow">Rapoport, Paul, ''About 31-tone Equal Temperament</a></span></li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.xs4all.nl/%7Ehuygensf/doc/terp31.html" rel="nofollow">Terpstra, Siemen, ''Toward a Theory of Meantone (and 31-et) Harmony''</a></span></li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/31edo.aspx" rel="nofollow">Tonalsoft Encyclopedia article</a></span></li></ul></body></html></pre></div> | ||