29edo: Difference between revisions
Wikispaces>MasonGreen1 **Imported revision 599210802 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 601449880 - 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:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-05 15:17:09 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>601449880</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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|| 2 || 82.759, 99.310 | || 2 || 82.759, 99.310 | ||
24°49'39" || 21/20 || [[xenharmonic/Nautilus|Nautilus]] || | 24°49'39" || 21/20 || [[xenharmonic/Nautilus|Nautilus]] || | ||
|| 3 || 124.138, 148.9655 | || 3 || 124.138, [[tel:148.9655|148.9655]] | ||
37°14'29" || 16/15, 15/14, 14/13, 13/12 || [[xenharmonic/Negri|Negri]]/[[xenharmonic/Negril|Negril]] || | 37°14'29" || 16/15, 15/14, 14/13, 13/12 || [[xenharmonic/Negri|Negri]]/[[xenharmonic/Negril|Negril]] || | ||
|| 4 || 165.517, 198.621 | || 4 || 165.517, 198.621 | ||
| Line 44: | Line 44: | ||
|| 7· || 289.655, 347.586 | || 7· || 289.655, 347.586 | ||
86°53'48" || 13/11 || || | 86°53'48" || 13/11 || || | ||
|| 8 || 331.0345, 397.241 | || 8 || [[tel:331.0345|331.0345]], 397.241 | ||
99°18'37" || 6/5, 11/9 || || | 99°18'37" || 6/5, 11/9 || || | ||
|| 9 || 372.414, 446.896 | || 9 || 372.414, 446.896 | ||
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|| 20 || 827.586, 993.103 | || 20 || 827.586, 993.103 | ||
248°16'33* || 8/5, 13/8 || || | 248°16'33* || 8/5, 13/8 || || | ||
|| 21 || 868.9655, 1042.759 | || 21 || [[tel:868.9655|868.9655]], 1042.759 | ||
262°41'23" || 5/3, 18/11 || || | 262°41'23" || 5/3, 18/11 || || | ||
|| 22· || 910.345, 1092.414 | || 22· || 910.345, 1092.414 | ||
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=Commas= | =Commas= | ||
29 EDO tempers out the following commas. (Note: This assumes the val < 29 46 67 81 100 107 |, cent values rounded to 5 digits.) | 29 EDO tempers out the following commas. (Note: This assumes the val < [[tel:29 46 67 81 100 107|29 46 67 81 100 107]] |, cent values rounded to 5 digits.) | ||
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 || | ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 || | ||
||= 16875/16384 || | -14 3 4 > ||> 51.120 ||= Negri Comma ||= Double Augmentation Diesis || | ||= 16875/16384 || | -14 3 4 > ||> 51.120 ||= Negri Comma ||= Double Augmentation Diesis || | ||
| Line 132: | Line 132: | ||
||= 225/224 || | -5 2 2 -1 > ||> 7.7115 ||= Septimal Kleisma ||= Marvel Comma || | ||= 225/224 || | -5 2 2 -1 > ||> 7.7115 ||= Septimal Kleisma ||= Marvel Comma || | ||
||= 5120/5103 || | 10 -6 1 -1 > ||> 5.7578 ||= Hemifamity ||= || | ||= 5120/5103 || | 10 -6 1 -1 > ||> 5.7578 ||= Hemifamity ||= || | ||
||= | ||= || | 25 -14 0 -1 > ||> 3.8041 ||= Garischisma ||= || | ||
||= 100/99 || | 2 -2 2 0 -1 > ||> 17.399 ||= Ptolemisma ||= || | ||= 100/99 || | 2 -2 2 0 -1 > ||> 17.399 ||= Ptolemisma ||= || | ||
||= 121/120 || | -3 -1 -1 0 2 > ||> 14.367 ||= Biyatisma ||= || | ||= 121/120 || | -3 -1 -1 0 2 > ||> 14.367 ||= Biyatisma ||= || | ||
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A variant of porcupine supported in 29edo is [[xenharmonic/nautilus|nautilus]], which splits the porcupine generator in half (tempering out 50:49 in the process), thus resulting in a different mapping for 7 than standard porcupine. Nautilus also extends to the 13-limit much more easily than does standard porcupine. | A variant of porcupine supported in 29edo is [[xenharmonic/nautilus|nautilus]], which splits the porcupine generator in half (tempering out 50:49 in the process), thus resulting in a different mapping for 7 than standard porcupine. Nautilus also extends to the 13-limit much more easily than does standard porcupine. | ||
The MOS nautilus[14] contains both "even" tetrads (approximating 4:5:6:7 or its inverse) as well as "odd" tetrads (approximating the "Bohlen-Pierce-like" chord 9:11:13:15, or its inverse). Both types are recognizable and consonant, if somewhat heavily tempered. Moreover, one of the four types of tetrads may be built on **each** scale degree of nautilus[14], thus there are as many chords as there are notes, so nautilus[14] has a "circulating" quality to it with as much freedom of modulation as possible. To be exact, there are 4 "major-even", 4 "minor-even", 3 "major-odd", and 3 "minor-odd" chords. | The MOS nautilus[14] contains both "even" tetrads (approximating 4:5:6:7 or its inverse) as well as "odd" tetrads (approximating the "Bohlen-Pierce-like" chord 9:11:13:15, or its inverse). Both types are recognizable and consonant, if somewhat heavily tempered. Moreover, one of the four types of tetrads may be built on **each** scale degree of nautilus[14], thus there are as many chords as there are notes, so nautilus[14] has a "circulating" quality to it with as much freedom of modulation as possible. To be exact, there are 4 "major-even", 4 "minor-even", 3 "major-odd", and 3 "minor-odd" chords. | ||
Fourteen-note MOSes are worth looking at because taking every other note of them gives a heptatonic, and in many cases diatonic-like, scale. Nautilus[14] is no exception; although the resulting porcupine "diatonic" scale sounds somewhat different from diatonic scales generated from fifths, it can still provide some degree of familiarity. Furthermore, every diatonic chord progression will have at least one loose analogue in nautilus[14], although the chord types might change (for instance, it is possible to have a I-IV-V chord progression where the I is major-odd, and the IV and V are both major-even; the V in this case being on a narrow or "odd" fifth rather than a perfect or "even" fifth). | Fourteen-note MOSes are worth looking at because taking every other note of them gives a heptatonic, and in many cases diatonic-like, scale. Nautilus[14] is no exception; although the resulting porcupine "diatonic" scale sounds somewhat different from diatonic scales generated from fifths, it can still provide some degree of familiarity. Furthermore, every diatonic chord progression will have at least one loose analogue in nautilus[14], although the chord types might change (for instance, it is possible to have a I-IV-V chord progression where the I is major-odd, and the IV and V are both major-even; the V in this case being on a narrow or "odd" fifth rather than a perfect or "even" fifth). | ||
| Line 246: | Line 246: | ||
<td>3<br /> | <td>3<br /> | ||
</td> | </td> | ||
<td>124.138, 148.9655<br /> | <td>124.138, <a class="wiki_link" href="http://tel.wikispaces.com/148.9655">148.9655</a><br /> | ||
37°14'29&quot;<br /> | 37°14'29&quot;<br /> | ||
</td> | </td> | ||
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<td>8<br /> | <td>8<br /> | ||
</td> | </td> | ||
<td>331.0345, 397.241<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/331.0345">331.0345</a>, 397.241<br /> | ||
99°18'37&quot;<br /> | 99°18'37&quot;<br /> | ||
</td> | </td> | ||
| Line 444: | Line 444: | ||
<td>21<br /> | <td>21<br /> | ||
</td> | </td> | ||
<td>868.9655, 1042.759<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/868.9655">868.9655</a>, 1042.759<br /> | ||
262°41'23&quot;<br /> | 262°41'23&quot;<br /> | ||
</td> | </td> | ||
| Line 693: | Line 693: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:6 -->Commas</h1> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:6 -->Commas</h1> | ||
29 EDO tempers out the following commas. (Note: This assumes the val &lt; 29 46 67 81 100 107 |, cent values rounded to 5 digits.)<br /> | 29 EDO tempers out the following commas. (Note: This assumes the val &lt; <a class="wiki_link" href="http://tel.wikispaces.com/29%2046%2067%2081%20100%20107">29 46 67 81 100 107</a> |, cent values rounded to 5 digits.)<br /> | ||
| Line 854: | Line 854: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td>| 25 -14 0 -1 &gt;<br /> | <td>| 25 -14 0 -1 &gt;<br /> | ||
| Line 956: | Line 956: | ||
A variant of porcupine supported in 29edo is <a class="wiki_link" href="http://xenharmonic.wikispaces.com/nautilus">nautilus</a>, which splits the porcupine generator in half (tempering out 50:49 in the process), thus resulting in a different mapping for 7 than standard porcupine. Nautilus also extends to the 13-limit much more easily than does standard porcupine.<br /> | A variant of porcupine supported in 29edo is <a class="wiki_link" href="http://xenharmonic.wikispaces.com/nautilus">nautilus</a>, which splits the porcupine generator in half (tempering out 50:49 in the process), thus resulting in a different mapping for 7 than standard porcupine. Nautilus also extends to the 13-limit much more easily than does standard porcupine.<br /> | ||
<br /> | <br /> | ||
The MOS nautilus[14] contains both &quot;even&quot; tetrads (approximating 4:5:6:7 or its inverse) as well as &quot;odd&quot; tetrads (approximating the &quot;Bohlen-Pierce-like&quot; chord 9:11:13:15, or its inverse). Both types are recognizable and consonant, if somewhat heavily tempered. Moreover, one of the four types of tetrads may be built on <strong>each</strong> scale degree of nautilus[14], thus there are as many chords as there are notes, so nautilus[14] has a &quot;circulating&quot; quality to it with as much freedom of modulation as possible. To be exact, there are 4 &quot;major-even&quot;, 4 &quot;minor-even&quot;, 3 &quot;major-odd&quot;, and 3 &quot;minor-odd&quot; chords. <br /> | The MOS nautilus[14] contains both &quot;even&quot; tetrads (approximating 4:5:6:7 or its inverse) as well as &quot;odd&quot; tetrads (approximating the &quot;Bohlen-Pierce-like&quot; chord 9:11:13:15, or its inverse). Both types are recognizable and consonant, if somewhat heavily tempered. Moreover, one of the four types of tetrads may be built on <strong>each</strong> scale degree of nautilus[14], thus there are as many chords as there are notes, so nautilus[14] has a &quot;circulating&quot; quality to it with as much freedom of modulation as possible. To be exact, there are 4 &quot;major-even&quot;, 4 &quot;minor-even&quot;, 3 &quot;major-odd&quot;, and 3 &quot;minor-odd&quot; chords.<br /> | ||
<br /> | <br /> | ||
Fourteen-note MOSes are worth looking at because taking every other note of them gives a heptatonic, and in many cases diatonic-like, scale. Nautilus[14] is no exception; although the resulting porcupine &quot;diatonic&quot; scale sounds somewhat different from diatonic scales generated from fifths, it can still provide some degree of familiarity. Furthermore, every diatonic chord progression will have at least one loose analogue in nautilus[14], although the chord types might change (for instance, it is possible to have a I-IV-V chord progression where the I is major-odd, and the IV and V are both major-even; the V in this case being on a narrow or &quot;odd&quot; fifth rather than a perfect or &quot;even&quot; fifth).<br /> | Fourteen-note MOSes are worth looking at because taking every other note of them gives a heptatonic, and in many cases diatonic-like, scale. Nautilus[14] is no exception; although the resulting porcupine &quot;diatonic&quot; scale sounds somewhat different from diatonic scales generated from fifths, it can still provide some degree of familiarity. Furthermore, every diatonic chord progression will have at least one loose analogue in nautilus[14], although the chord types might change (for instance, it is possible to have a I-IV-V chord progression where the I is major-odd, and the IV and V are both major-even; the V in this case being on a narrow or &quot;odd&quot; fifth rather than a perfect or &quot;even&quot; fifth).<br /> | ||