31edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 340672456 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 343227438 - 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: | : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2012-06-06 12:34:00 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>343227438</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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===12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth=== | ===12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth=== | ||
Exactly twice a supermajor second, thrice a neutral second, or four times a major second. In 7-limit tonal music, 12\31 functions as 21:16 (470.78¢). Generates semisept temperament. | Exactly twice a supermajor second, thrice a neutral second, or four times a major second. In 7-limit tonal music, 12\31 functions as 21:16 (470.78¢). Generates [[semisept]] temperament. | ||
====MOS Scales generated by 12\31:==== | ====MOS Scales generated by 12\31:==== | ||
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 || | ||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 || | ||
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===13\31 octave - approx. 503.23¢ - Perfect Fourth=== | ===13\31 octave - approx. 503.23¢ - Perfect Fourth=== | ||
A sharp perfect fourth (compare to 4:3 = 498.04¢). As such, it functions marvelously as a generator for meantone temperament. | A sharp perfect fourth (compare to 4:3 = 498.04¢). As such, it functions marvelously as a generator for [[meantone]] temperament. | ||
====MOS Scales generated by 13\31:==== | ====MOS Scales generated by 13\31:==== | ||
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 || | ||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 || | ||
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===15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth=== | ===15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth=== | ||
In 7-limit tonal music, functions as 7:5 (582.51¢). Exactly thrice a whole tone. Generates tritonic temperament. | In 7-limit tonal music, functions as 7:5 (582.51¢). Exactly thrice a whole tone. Generates [[tritonic]] temperament. | ||
====MOS Scales generated by 15\31:==== | ====MOS Scales generated by 15\31:==== | ||
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 || | ||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 || | ||
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31 EDO tempers out the following commas. (Note: This assumes the val < 31 49 72 87 107 115 |, comma values roundet to 5 significant digits.) | 31 EDO tempers out the following commas. (Note: This assumes the val < 31 49 72 87 107 115 |, comma values roundet to 5 significant digits.) | ||
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || | ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || | ||
||= 9931568/9752117 ||< | -25 7 6 > ||> 31.567 ||= Ampersand's Comma ||= ||= || | ||= 9931568/9752117 ||< | -25 7 6 > ||> 31.567 ||= [[ampersand|Ampersand's Comma]] ||= ||= || | ||
||= 81/80 ||< | -4 4 -1 > ||> 21.506 ||= Syntonic Comma ||= Didymos Comma ||= Meantone Comma || | ||= 81/80 ||< | -4 4 -1 > ||> 21.506 ||= [[Syntonic Comma]] ||= Didymos Comma ||= Meantone Comma || | ||
||= 393216/390625 ||< | 17 1 -8 > ||> 11.445 ||= | ||= 393216/390625 ||< | 17 1 -8 > ||> 11.445 ||= [[Würschmidt comma|Würschmidt Comma]] ||= ||= || | ||
||= 2109375/2097152 ||< | -21 3 7 > ||> 10.061 ||= Semicomma ||= Fokker Comma ||= || | ||= 2109375/2097152 ||< | -21 3 7 > ||> 10.061 ||= [[semicomma|Semicomma]] ||= Fokker Comma ||= || | ||
||= 6719816/6714445 ||< | 38 -2 -15 > ||> 1.3843 ||= Hemithirds Comma ||= ||= || | ||= 6719816/6714445 ||< | 38 -2 -15 > ||> 1.3843 ||= Hemithirds Comma ||= ||= || | ||
||= 9859966/9733137 ||< | -10 7 8 -7 > ||> 22.413 ||= Blackjackisma ||= ||= || | ||= 9859966/9733137 ||< | -10 7 8 -7 > ||> 22.413 ||= Blackjackisma ||= ||= || | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:46:&lt;h3&gt; --><h3 id="toc23"><a name="Intervals--12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth"></a><!-- ws:end:WikiTextHeadingRule:46 -->12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth</h3> | <!-- ws:start:WikiTextHeadingRule:46:&lt;h3&gt; --><h3 id="toc23"><a name="Intervals--12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth"></a><!-- ws:end:WikiTextHeadingRule:46 -->12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth</h3> | ||
Exactly twice a supermajor second, thrice a neutral second, or four times a major second. In 7-limit tonal music, 12\31 functions as 21:16 (470.78¢). Generates semisept temperament.<br /> | Exactly twice a supermajor second, thrice a neutral second, or four times a major second. In 7-limit tonal music, 12\31 functions as 21:16 (470.78¢). Generates <a class="wiki_link" href="/semisept">semisept</a> temperament.<br /> | ||
<!-- ws:start:WikiTextHeadingRule:48:&lt;h4&gt; --><h4 id="toc24"><a name="Intervals--12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth-MOS Scales generated by 12\31:"></a><!-- ws:end:WikiTextHeadingRule:48 -->MOS Scales generated by 12\31:</h4> | <!-- ws:start:WikiTextHeadingRule:48:&lt;h4&gt; --><h4 id="toc24"><a name="Intervals--12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth-MOS Scales generated by 12\31:"></a><!-- ws:end:WikiTextHeadingRule:48 -->MOS Scales generated by 12\31:</h4> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:50:&lt;h3&gt; --><h3 id="toc25"><a name="Intervals--13\31 octave - approx. 503.23¢ - Perfect Fourth"></a><!-- ws:end:WikiTextHeadingRule:50 -->13\31 octave - approx. 503.23¢ - Perfect Fourth</h3> | <!-- ws:start:WikiTextHeadingRule:50:&lt;h3&gt; --><h3 id="toc25"><a name="Intervals--13\31 octave - approx. 503.23¢ - Perfect Fourth"></a><!-- ws:end:WikiTextHeadingRule:50 -->13\31 octave - approx. 503.23¢ - Perfect Fourth</h3> | ||
A sharp perfect fourth (compare to 4:3 = 498.04¢). As such, it functions marvelously as a generator for meantone temperament.<br /> | A sharp perfect fourth (compare to 4:3 = 498.04¢). As such, it functions marvelously as a generator for <a class="wiki_link" href="/meantone">meantone</a> temperament.<br /> | ||
<!-- ws:start:WikiTextHeadingRule:52:&lt;h4&gt; --><h4 id="toc26"><a name="Intervals--13\31 octave - approx. 503.23¢ - Perfect Fourth-MOS Scales generated by 13\31:"></a><!-- ws:end:WikiTextHeadingRule:52 -->MOS Scales generated by 13\31:</h4> | <!-- ws:start:WikiTextHeadingRule:52:&lt;h4&gt; --><h4 id="toc26"><a name="Intervals--13\31 octave - approx. 503.23¢ - Perfect Fourth-MOS Scales generated by 13\31:"></a><!-- ws:end:WikiTextHeadingRule:52 -->MOS Scales generated by 13\31:</h4> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:58:&lt;h3&gt; --><h3 id="toc29"><a name="Intervals--15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth"></a><!-- ws:end:WikiTextHeadingRule:58 -->15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth</h3> | <!-- ws:start:WikiTextHeadingRule:58:&lt;h3&gt; --><h3 id="toc29"><a name="Intervals--15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth"></a><!-- ws:end:WikiTextHeadingRule:58 -->15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth</h3> | ||
In 7-limit tonal music, functions as 7:5 (582.51¢). Exactly thrice a whole tone. Generates tritonic temperament.<br /> | In 7-limit tonal music, functions as 7:5 (582.51¢). Exactly thrice a whole tone. Generates <a class="wiki_link" href="/tritonic">tritonic</a> temperament.<br /> | ||
<!-- ws:start:WikiTextHeadingRule:60:&lt;h4&gt; --><h4 id="toc30"><a name="Intervals--15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth-MOS Scales generated by 15\31:"></a><!-- ws:end:WikiTextHeadingRule:60 -->MOS Scales generated by 15\31:</h4> | <!-- ws:start:WikiTextHeadingRule:60:&lt;h4&gt; --><h4 id="toc30"><a name="Intervals--15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth-MOS Scales generated by 15\31:"></a><!-- ws:end:WikiTextHeadingRule:60 -->MOS Scales generated by 15\31:</h4> | ||
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<td style="text-align: right;">31.567<br /> | <td style="text-align: right;">31.567<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Ampersand's Comma<br /> | <td style="text-align: center;"><a class="wiki_link" href="/ampersand">Ampersand's Comma</a><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 7,400: | Line 7,400: | ||
<td style="text-align: right;">21.506<br /> | <td style="text-align: right;">21.506<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Syntonic Comma<br /> | <td style="text-align: center;"><a class="wiki_link" href="/Syntonic%20Comma">Syntonic Comma</a><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Didymos Comma<br /> | <td style="text-align: center;">Didymos Comma<br /> | ||
| Line 7,414: | Line 7,414: | ||
<td style="text-align: right;">11.445<br /> | <td style="text-align: right;">11.445<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><a class="wiki_link" href="/W%C3%BCrschmidt%20comma">Würschmidt Comma</a><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 7,428: | Line 7,428: | ||
<td style="text-align: right;">10.061<br /> | <td style="text-align: right;">10.061<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Semicomma<br /> | <td style="text-align: center;"><a class="wiki_link" href="/semicomma">Semicomma</a><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Fokker Comma<br /> | <td style="text-align: center;">Fokker Comma<br /> | ||