23edo: Difference between revisions
Wikispaces>guest **Imported revision 243908233 - Original comment: ** |
Wikispaces>igliashon **Imported revision 248695117 - 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:igliashon|igliashon]] and made on <tt>2011-08-26 15:23:49 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>248695117</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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=<span style="font-size: 1.4em;">Intervals</span>= | =<span style="font-size: 1.4em;">Intervals</span>= | ||
|| <span style="color: #660000;">[[Degree]]</span> || [[Cent]]s value ||= Approximate | || <span style="color: #660000;">[[Degree]]</span> || [[Cent]]s value ||= Approximate | ||
Ratios* || | Ratios* ||= Armodue | ||
|| 0 || 0 ||= 1/1 || | Notation || | ||
|| 1 || 52.1739 ||= 33/32, 34/33 || | || 0 || 0 ||= 1/1 ||= 1 || | ||
|| 2 || 104.3478 ||= 17/16, 16/15, 18/17 || | || 1 || 52.1739 ||= 33/32, 34/33 ||= 2b || | ||
|| 3 || 156.5217 ||= 11/10, 12/11, 35/32 || | || 2 || 104.3478 ||= 17/16, 16/15, 18/17 ||= 1# || | ||
|| 4· || 208.6957 ||= 9/8, 44/39 || | || 3 || 156.5217 ||= 11/10, 12/11, 35/32 ||= 2 || | ||
|| 5 || 260.8696 ||= 7/6, 15/13, 29/25 || | || 4· || 208.6957 ||= 9/8, 44/39 ||= 3b || | ||
|| 6 || 313.0435 ||= 6/5 || | || 5 || 260.8696 ||= 7/6, 15/13, 29/25 ||= 2# || | ||
|| 7· || 365.2174 ||= 16/13, 21/17, 26/21 || | || 6 || 313.0435 ||= 6/5 ||= 3 || | ||
|| 8 || 417.3913 ||= 14/11, 33/26 || | || 7· || 365.2174 ||= 16/13, 21/17, 26/21 ||= 4b || | ||
|| 9 || 469.5652 ||= 21/16, 17/13 || | || 8 || 417.3913 ||= 14/11, 33/26 ||= 3# || | ||
|| 10· || 521.7391 ||= 23/17, 88/65, 256/189 || | || 9 || 469.5652 ||= 21/16, 17/13 ||= 4 || | ||
|| 11 || 573.913 ||= 7/5, 32/23, 46/33 || | || 10· || 521.7391 ||= 23/17, 88/65, 256/189 ||= 5 || | ||
|| 12 || 626.087 ||= 10/7, 23/16, 33/23 || | || 11 || 573.913 ||= 7/5, 32/23, 46/33 ||= 6b || | ||
|| 13· || 678.2609 ||= 34/23, 65/44, 189/128 || | || 12 || 626.087 ||= 10/7, 23/16, 33/23 ||= 5# || | ||
|| 14 || 730.4348 ||= 32/21, 26/17 || | || 13· || 678.2609 ||= 34/23, 65/44, 189/128 ||= 6 || | ||
|| 15 || 782.6087 ||= 11/7, 52/33 || | || 14 || 730.4348 ||= 32/21, 26/17 ||= 7b || | ||
|| 16· || 834.7826 ||= 13/8, 34/21, 21/13 || | || 15 || 782.6087 ||= 11/7, 52/33 ||= 6# || | ||
|| 17 || 886.9565 ||= 5/3 || | || 16· || 834.7826 ||= 13/8, 34/21, 21/13 ||= 7 || | ||
|| 18 || 939.1304 ||= 12/7, 26/15, 50/29 || | || 17 || 886.9565 ||= 5/3 ||= 8b || | ||
|| 19· || 991.3043 ||= 16/9, 39/22 || | || 18 || 939.1304 ||= 12/7, 26/15, 50/29 ||= 7# || | ||
|| 20 || 1043.4783 ||= 11/6, 20/11, 64/35 || | || 19· || 991.3043 ||= 16/9, 39/22 ||= 8 || | ||
|| 21 || 1095.6522 ||= 15/8, 17/9, 32/17 || | || 20 || 1043.4783 ||= 11/6, 20/11, 64/35 ||= 9b || | ||
|| 22 || 1147.8261 ||= 33/17, 64/33 || | || 21 || 1095.6522 ||= 15/8, 17/9, 32/17 ||= 8# || | ||
|| 23·· || 1200 ||= 2/1 || | || 22 || 1147.8261 ||= 33/17, 64/33 ||= 9 || | ||
|| 23·· || 1200 ||= 2/1 ||= 1 || | |||
*based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible. | *based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible. | ||
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23-EDO is also significant in that it is the largest EDO that fails to approximate the 3rd, 5th, 7th, and 11th harmonics within 20 cents, which makes it well-suited for musicians seeking to explore harmonic territory that is unusual even for the average microtonalist. Oddly, despite the fact that it fails to approximate these harmonics, it approximates the intervals between them (5/3, 7/3, 11/3, 7/5, 11/7, and 11/5) very well. The lowest harmonics well-approximated by 23-EDO are 13, 17, 21, and 23. | 23-EDO is also significant in that it is the largest EDO that fails to approximate the 3rd, 5th, 7th, and 11th harmonics within 20 cents, which makes it well-suited for musicians seeking to explore harmonic territory that is unusual even for the average microtonalist. Oddly, despite the fact that it fails to approximate these harmonics, it approximates the intervals between them (5/3, 7/3, 11/3, 7/5, 11/7, and 11/5) very well. The lowest harmonics well-approximated by 23-EDO are 13, 17, 21, and 23. | ||
As with[[9edo| 9-EDO]], [[16edo|16-EDO]], and [[25edo|25-EDO]], one way to treat 23-EDO is as a Pelogic temperament, tempering out the "comma" of 135/128 and equating three 'acute [[4_3|4/3]]'s with 5/1 (related to the Armodue system). This means mapping '[[3_2|3/2]]' to 13 degrees of 23, and results in a 7 notes [[2L 5s|Anti-diatonic scale]] of 3 3 4 3 3 3 4 (in steps of 23-EDO), which extends to 9 notes [[7L 2s|Superdiatonic scale]] (3 3 3 1 3 3 3 3 1). | As with[[9edo| 9-EDO]], [[16edo|16-EDO]], and [[25edo|25-EDO]], one way to treat 23-EDO is as a Pelogic temperament, tempering out the "comma" of 135/128 and equating three 'acute [[4_3|4/3]]'s with 5/1 (related to the Armodue system). This means mapping '[[3_2|3/2]]' to 13 degrees of 23, and results in a 7 notes [[2L 5s|Anti-diatonic scale]] of 3 3 4 3 3 3 4 (in steps of 23-EDO), which extends to 9 notes [[7L 2s|Superdiatonic scale]] (3 3 3 1 3 3 3 3 1). One can notate 23-EDO using the Armodue system, but just like notating 17-EDO with familiar diatonic notation, sharps will be lower in pitch than enharmonic flats, because in 23-EDO, the "Armodue 6th" is sharper than it is in 16-EDO, just like the Diatonic 5th in 17-EDO is sharper than in 12-EDO. | ||
However, one can also map 3/2 to 14 degrees of 23-EDO without significantly increasing the error, taking us to a [[7-limit]] temperament where two 'broad 3/2's equals 7/3, meaning 28/27 is tempered out, and six 4/3's octave-reduced equals 5/4, meaning 4096/3645 is tempered out. Both of these are very large commas, so this is not at all an accurate temperament, but it is related to [[13edo|13-EDO]] and [[18edo|18-EDO]] and produces [[MOSScales|MOS scales]] of 5 and 8 notes: 5 5 4 5 4 (the [[3L 2s|"anti-pentatonic"]]) and 4 1 4 1 4 4 1 4 (the "quarter-tone" version of the Blackwood/[[http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29|Rapoport]]/Wilson 13-EDO "subminor" scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23-EDO a Sub-"4/3", we can call it 21/16. Here three 21/16's gets us to 9/4, meaning 1029/1024 is tempered out. This allows us to treat a triad of 0-4-9 degrees of 23-EDO as an approximation to 16:18:21, and 0-5-9 as 1/(16:18:21); both of these triads are abundant in the 8-note MOS scale. | However, one can also map 3/2 to 14 degrees of 23-EDO without significantly increasing the error, taking us to a [[7-limit]] temperament where two 'broad 3/2's equals 7/3, meaning 28/27 is tempered out, and six 4/3's octave-reduced equals 5/4, meaning 4096/3645 is tempered out. Both of these are very large commas, so this is not at all an accurate temperament, but it is related to [[13edo|13-EDO]] and [[18edo|18-EDO]] and produces [[MOSScales|MOS scales]] of 5 and 8 notes: 5 5 4 5 4 (the [[3L 2s|"anti-pentatonic"]]) and 4 1 4 1 4 4 1 4 (the "quarter-tone" version of the Blackwood/[[http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29|Rapoport]]/Wilson 13-EDO "subminor" scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23-EDO a Sub-"4/3", we can call it 21/16. Here three 21/16's gets us to 9/4, meaning 1029/1024 is tempered out. This allows us to treat a triad of 0-4-9 degrees of 23-EDO as an approximation to 16:18:21, and 0-5-9 as 1/(16:18:21); both of these triads are abundant in the 8-note MOS scale. | ||
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<span class="ymp-btn-page-play ymp-media-c0b7192b09da11ecea83384b2aad9c4b">[[http://clones.soonlabel.com/public/micro/23edo/daily20110619_23edo_23_chilled.mp3|23 Chilled]]</span> by [[Chris Vaisvil]] | <span class="ymp-btn-page-play ymp-media-c0b7192b09da11ecea83384b2aad9c4b">[[http://clones.soonlabel.com/public/micro/23edo/daily20110619_23edo_23_chilled.mp3|23 Chilled]]</span> by [[Chris Vaisvil]] | ||
<span class="ymp-btn-page-play ymp-media-8ca0c9a378cc362bbcbc24ba13d6974b">[[http://www.seraph.it/dep/det/DesertWinds.mp3|Desert Winds]]</span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/926007c7483e4abc5a48d582c0667947-105.html|blog entry]]) | <span class="ymp-btn-page-play ymp-media-8ca0c9a378cc362bbcbc24ba13d6974b">[[http://www.seraph.it/dep/det/DesertWinds.mp3|Desert Winds]]</span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/926007c7483e4abc5a48d582c0667947-105.html|blog entry]]) | ||
[[http://www.seraph.it/dep/det/23Laments.mp3|23 Laments]]</span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/b2bf6f252efd467ee36ecc332a4872ac-106.html|blog entry]]) | <span class="ymp-btn-page-play ymp-media-2b9e61a2a9e271622ebe4a1311677936">[[http://www.seraph.it/dep/det/23Laments.mp3|23 Laments]]</span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/b2bf6f252efd467ee36ecc332a4872ac-106.html|blog entry]]) | ||
//Allegro Moderato// by Easley Blackwood | //Allegro Moderato// by Easley Blackwood | ||
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<td style="text-align: center;">Approximate<br /> | <td style="text-align: center;">Approximate<br /> | ||
Ratios*<br /> | Ratios*<br /> | ||
</td> | |||
<td style="text-align: center;">Armodue <br /> | |||
Notation<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 198: | Line 202: | ||
</td> | </td> | ||
<td style="text-align: center;">1/1<br /> | <td style="text-align: center;">1/1<br /> | ||
</td> | |||
<td style="text-align: center;">1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 206: | Line 212: | ||
</td> | </td> | ||
<td style="text-align: center;">33/32, 34/33<br /> | <td style="text-align: center;">33/32, 34/33<br /> | ||
</td> | |||
<td style="text-align: center;">2b<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 214: | Line 222: | ||
</td> | </td> | ||
<td style="text-align: center;">17/16, 16/15, 18/17<br /> | <td style="text-align: center;">17/16, 16/15, 18/17<br /> | ||
</td> | |||
<td style="text-align: center;">1#<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 222: | Line 232: | ||
</td> | </td> | ||
<td style="text-align: center;">11/10, 12/11, 35/32<br /> | <td style="text-align: center;">11/10, 12/11, 35/32<br /> | ||
</td> | |||
<td style="text-align: center;">2<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">9/8, 44/39<br /> | <td style="text-align: center;">9/8, 44/39<br /> | ||
</td> | |||
<td style="text-align: center;">3b<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">7/6, 15/13, 29/25<br /> | <td style="text-align: center;">7/6, 15/13, 29/25<br /> | ||
</td> | |||
<td style="text-align: center;">2#<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">6/5<br /> | <td style="text-align: center;">6/5<br /> | ||
</td> | |||
<td style="text-align: center;">3<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">16/13, 21/17, 26/21<br /> | <td style="text-align: center;">16/13, 21/17, 26/21<br /> | ||
</td> | |||
<td style="text-align: center;">4b<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">14/11, 33/26<br /> | <td style="text-align: center;">14/11, 33/26<br /> | ||
</td> | |||
<td style="text-align: center;">3#<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">21/16, 17/13<br /> | <td style="text-align: center;">21/16, 17/13<br /> | ||
</td> | |||
<td style="text-align: center;">4<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">23/17, 88/65, 256/189<br /> | <td style="text-align: center;">23/17, 88/65, 256/189<br /> | ||
</td> | |||
<td style="text-align: center;">5<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">7/5, 32/23, 46/33<br /> | <td style="text-align: center;">7/5, 32/23, 46/33<br /> | ||
</td> | |||
<td style="text-align: center;">6b<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">10/7, 23/16, 33/23<br /> | <td style="text-align: center;">10/7, 23/16, 33/23<br /> | ||
</td> | |||
<td style="text-align: center;">5#<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">34/23, 65/44, 189/128<br /> | <td style="text-align: center;">34/23, 65/44, 189/128<br /> | ||
</td> | |||
<td style="text-align: center;">6<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">32/21, 26/17<br /> | <td style="text-align: center;">32/21, 26/17<br /> | ||
</td> | |||
<td style="text-align: center;">7b<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">11/7, 52/33<br /> | <td style="text-align: center;">11/7, 52/33<br /> | ||
</td> | |||
<td style="text-align: center;">6#<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">13/8, 34/21, 21/13<br /> | <td style="text-align: center;">13/8, 34/21, 21/13<br /> | ||
</td> | |||
<td style="text-align: center;">7<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">5/3<br /> | <td style="text-align: center;">5/3<br /> | ||
</td> | |||
<td style="text-align: center;">8b<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">12/7, 26/15, 50/29<br /> | <td style="text-align: center;">12/7, 26/15, 50/29<br /> | ||
</td> | |||
<td style="text-align: center;">7#<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">16/9, 39/22<br /> | <td style="text-align: center;">16/9, 39/22<br /> | ||
</td> | |||
<td style="text-align: center;">8<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">11/6, 20/11, 64/35<br /> | <td style="text-align: center;">11/6, 20/11, 64/35<br /> | ||
</td> | |||
<td style="text-align: center;">9b<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">15/8, 17/9, 32/17<br /> | <td style="text-align: center;">15/8, 17/9, 32/17<br /> | ||
</td> | |||
<td style="text-align: center;">8#<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">33/17, 64/33<br /> | <td style="text-align: center;">33/17, 64/33<br /> | ||
</td> | |||
<td style="text-align: center;">9<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td style="text-align: center;">2/1<br /> | <td style="text-align: center;">2/1<br /> | ||
</td> | |||
<td style="text-align: center;">1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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23-EDO is also significant in that it is the largest EDO that fails to approximate the 3rd, 5th, 7th, and 11th harmonics within 20 cents, which makes it well-suited for musicians seeking to explore harmonic territory that is unusual even for the average microtonalist. Oddly, despite the fact that it fails to approximate these harmonics, it approximates the intervals between them (5/3, 7/3, 11/3, 7/5, 11/7, and 11/5) very well. The lowest harmonics well-approximated by 23-EDO are 13, 17, 21, and 23.<br /> | 23-EDO is also significant in that it is the largest EDO that fails to approximate the 3rd, 5th, 7th, and 11th harmonics within 20 cents, which makes it well-suited for musicians seeking to explore harmonic territory that is unusual even for the average microtonalist. Oddly, despite the fact that it fails to approximate these harmonics, it approximates the intervals between them (5/3, 7/3, 11/3, 7/5, 11/7, and 11/5) very well. The lowest harmonics well-approximated by 23-EDO are 13, 17, 21, and 23.<br /> | ||
<br /> | <br /> | ||
As with<a class="wiki_link" href="/9edo"> 9-EDO</a>, <a class="wiki_link" href="/16edo">16-EDO</a>, and <a class="wiki_link" href="/25edo">25-EDO</a>, one way to treat 23-EDO is as a Pelogic temperament, tempering out the &quot;comma&quot; of 135/128 and equating three 'acute <a class="wiki_link" href="/4_3">4/3</a>'s with 5/1 (related to the Armodue system). This means mapping '<a class="wiki_link" href="/3_2">3/2</a>' to 13 degrees of 23, and results in a 7 notes <a class="wiki_link" href="/2L%205s">Anti-diatonic scale</a> of 3 3 4 3 3 3 4 (in steps of 23-EDO), which extends to 9 notes <a class="wiki_link" href="/7L%202s">Superdiatonic scale</a> (3 3 3 1 3 3 3 3 1).<br /> | As with<a class="wiki_link" href="/9edo"> 9-EDO</a>, <a class="wiki_link" href="/16edo">16-EDO</a>, and <a class="wiki_link" href="/25edo">25-EDO</a>, one way to treat 23-EDO is as a Pelogic temperament, tempering out the &quot;comma&quot; of 135/128 and equating three 'acute <a class="wiki_link" href="/4_3">4/3</a>'s with 5/1 (related to the Armodue system). This means mapping '<a class="wiki_link" href="/3_2">3/2</a>' to 13 degrees of 23, and results in a 7 notes <a class="wiki_link" href="/2L%205s">Anti-diatonic scale</a> of 3 3 4 3 3 3 4 (in steps of 23-EDO), which extends to 9 notes <a class="wiki_link" href="/7L%202s">Superdiatonic scale</a> (3 3 3 1 3 3 3 3 1). One can notate 23-EDO using the Armodue system, but just like notating 17-EDO with familiar diatonic notation, sharps will be lower in pitch than enharmonic flats, because in 23-EDO, the &quot;Armodue 6th&quot; is sharper than it is in 16-EDO, just like the Diatonic 5th in 17-EDO is sharper than in 12-EDO.<br /> | ||
<br /> | <br /> | ||
However, one can also map 3/2 to 14 degrees of 23-EDO without significantly increasing the error, taking us to a <a class="wiki_link" href="/7-limit">7-limit</a> temperament where two 'broad 3/2's equals 7/3, meaning 28/27 is tempered out, and six 4/3's octave-reduced equals 5/4, meaning 4096/3645 is tempered out. Both of these are very large commas, so this is not at all an accurate temperament, but it is related to <a class="wiki_link" href="/13edo">13-EDO</a> and <a class="wiki_link" href="/18edo">18-EDO</a> and produces <a class="wiki_link" href="/MOSScales">MOS scales</a> of 5 and 8 notes: 5 5 4 5 4 (the <a class="wiki_link" href="/3L%202s">&quot;anti-pentatonic&quot;</a>) and 4 1 4 1 4 4 1 4 (the &quot;quarter-tone&quot; version of the Blackwood/<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29" rel="nofollow">Rapoport</a>/Wilson 13-EDO &quot;subminor&quot; scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23-EDO a Sub-&quot;4/3&quot;, we can call it 21/16. Here three 21/16's gets us to 9/4, meaning 1029/1024 is tempered out. This allows us to treat a triad of 0-4-9 degrees of 23-EDO as an approximation to 16:18:21, and 0-5-9 as 1/(16:18:21); both of these triads are abundant in the 8-note MOS scale.<br /> | However, one can also map 3/2 to 14 degrees of 23-EDO without significantly increasing the error, taking us to a <a class="wiki_link" href="/7-limit">7-limit</a> temperament where two 'broad 3/2's equals 7/3, meaning 28/27 is tempered out, and six 4/3's octave-reduced equals 5/4, meaning 4096/3645 is tempered out. Both of these are very large commas, so this is not at all an accurate temperament, but it is related to <a class="wiki_link" href="/13edo">13-EDO</a> and <a class="wiki_link" href="/18edo">18-EDO</a> and produces <a class="wiki_link" href="/MOSScales">MOS scales</a> of 5 and 8 notes: 5 5 4 5 4 (the <a class="wiki_link" href="/3L%202s">&quot;anti-pentatonic&quot;</a>) and 4 1 4 1 4 4 1 4 (the &quot;quarter-tone&quot; version of the Blackwood/<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29" rel="nofollow">Rapoport</a>/Wilson 13-EDO &quot;subminor&quot; scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23-EDO a Sub-&quot;4/3&quot;, we can call it 21/16. Here three 21/16's gets us to 9/4, meaning 1029/1024 is tempered out. This allows us to treat a triad of 0-4-9 degrees of 23-EDO as an approximation to 16:18:21, and 0-5-9 as 1/(16:18:21); both of these triads are abundant in the 8-note MOS scale.<br /> | ||
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<span class="ymp-btn-page-play ymp-media-c0b7192b09da11ecea83384b2aad9c4b"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/23edo/daily20110619_23edo_23_chilled.mp3" rel="nofollow">23 Chilled</a></span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br /> | <span class="ymp-btn-page-play ymp-media-c0b7192b09da11ecea83384b2aad9c4b"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/23edo/daily20110619_23edo_23_chilled.mp3" rel="nofollow">23 Chilled</a></span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br /> | ||
<span class="ymp-btn-page-play ymp-media-8ca0c9a378cc362bbcbc24ba13d6974b"><a class="wiki_link_ext" href="http://www.seraph.it/dep/det/DesertWinds.mp3" rel="nofollow">Desert Winds</a></span> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/926007c7483e4abc5a48d582c0667947-105.html" rel="nofollow">blog entry</a>)<br /> | <span class="ymp-btn-page-play ymp-media-8ca0c9a378cc362bbcbc24ba13d6974b"><a class="wiki_link_ext" href="http://www.seraph.it/dep/det/DesertWinds.mp3" rel="nofollow">Desert Winds</a></span> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/926007c7483e4abc5a48d582c0667947-105.html" rel="nofollow">blog entry</a>)<br /> | ||
<a class="wiki_link_ext" href="http://www.seraph.it/dep/det/23Laments.mp3" rel="nofollow">23 Laments</a></span> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/b2bf6f252efd467ee36ecc332a4872ac-106.html" rel="nofollow">blog entry</a>)<br /> | <span class="ymp-btn-page-play ymp-media-2b9e61a2a9e271622ebe4a1311677936"><a class="wiki_link_ext" href="http://www.seraph.it/dep/det/23Laments.mp3" rel="nofollow">23 Laments</a></span> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/b2bf6f252efd467ee36ecc332a4872ac-106.html" rel="nofollow">blog entry</a>)<br /> | ||
<em>Allegro Moderato</em> by Easley Blackwood<br /> | <em>Allegro Moderato</em> by Easley Blackwood<br /> | ||
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<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:699:&lt;img src=&quot;/file/view/Ciclo_Icositrifon%C3%ADa.png/255957914/492x490/Ciclo_Icositrifon%C3%ADa.png&quot; alt=&quot;Intervallic Cycle of 23 steps Equal per Octave&quot; title=&quot;Intervallic Cycle of 23 steps Equal per Octave&quot; style=&quot;height: 490px; width: 492px;&quot; /&gt; --><table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/Ciclo_Icositrifon%C3%ADa.png/255957914/492x490/Ciclo_Icositrifon%C3%ADa.png" alt="Ciclo_Icositrifonía.png" title="Ciclo_Icositrifonía.png" style="height: 490px; width: 492px;" /></td></tr><tr><td class="imageCaption">Intervallic Cycle of 23 steps Equal per Octave</td></tr></table><!-- ws:end:WikiTextLocalImageRule:699 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc6"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:14 -->Commas</h1> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc6"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:14 -->Commas</h1> | ||
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<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc8"><a name="Books"></a><!-- ws:end:WikiTextHeadingRule:18 -->Books</h1> | <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc8"><a name="Books"></a><!-- ws:end:WikiTextHeadingRule:18 -->Books</h1> | ||
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<!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc9"><a name="Instruments"></a><!-- ws:end:WikiTextHeadingRule:20 -->Instruments</h1> | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc9"><a name="Instruments"></a><!-- ws:end:WikiTextHeadingRule:20 -->Instruments</h1> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:701:&lt;img src=&quot;/file/view/Icositriphonic_Bass.JPG/206711470/594x216/Icositriphonic_Bass.JPG&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 216px; width: 594px;&quot; /&gt; --><img src="/file/view/Icositriphonic_Bass.JPG/206711470/594x216/Icositriphonic_Bass.JPG" alt="Icositriphonic_Bass.JPG" title="Icositriphonic_Bass.JPG" style="height: 216px; width: 594px;" /><!-- ws:end:WikiTextLocalImageRule:701 --><br /> | ||
<em>An Icositriphonic Bass. 23-EDO Bass by Tútim Deft Wafil.</em><br /> | <em>An Icositriphonic Bass. 23-EDO Bass by Tútim Deft Wafil.</em><br /> | ||
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<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:702:&lt;img src=&quot;/file/view/Icositriphonic_Guitar.PNG/206712964/601x305/Icositriphonic_Guitar.PNG&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 305px; width: 601px;&quot; /&gt; --><img src="/file/view/Icositriphonic_Guitar.PNG/206712964/601x305/Icositriphonic_Guitar.PNG" alt="Icositriphonic_Guitar.PNG" title="Icositriphonic_Guitar.PNG" style="height: 305px; width: 601px;" /><!-- ws:end:WikiTextLocalImageRule:702 --><br /> | ||
<em>An Icositriphonic 8-string Guitar. 23-EDO Guitar by Ron Sword.</em><br /> | <em>An Icositriphonic 8-string Guitar. 23-EDO Guitar by Ron Sword.</em><br /> | ||
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<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:703:&lt;img src=&quot;/file/view/Teclado_Icositrif%C3%B3nico.PNG/258408436/591x326/Teclado_Icositrif%C3%B3nico.PNG&quot; alt=&quot;A classic visualization of an Alternative 1/3-tone Keyboard. Armodue-Hornbostel Family Musical Systems&quot; title=&quot;A classic visualization of an Alternative 1/3-tone Keyboard. Armodue-Hornbostel Family Musical Systems&quot; style=&quot;height: 326px; width: 591px;&quot; /&gt; --><table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/Teclado_Icositrif%C3%B3nico.PNG/258408436/591x326/Teclado_Icositrif%C3%B3nico.PNG" alt="Teclado_Icositrifónico.PNG" title="Teclado_Icositrifónico.PNG" style="height: 326px; width: 591px;" /></td></tr><tr><td class="imageCaption">A classic visualization of an Alternative 1/3-tone Keyboard. Armodue-Hornbostel Family Musical Systems</td></tr></table><!-- ws:end:WikiTextLocalImageRule:703 --><br /> | ||
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Chris Vaisvil made a do it yourself 23 edo electric guitar out of less than $50 of material. Here he is playing it.<br /> | Chris Vaisvil made a do it yourself 23 edo electric guitar out of less than $50 of material. Here he is playing it.<br /> | ||
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Here is a still shot of the completed instrument.<br /> | Here is a still shot of the completed instrument.<br /> | ||
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This movie is a series of still shots Chris took during the process of making a 23 edo guitar in a stick like form. At the end the guitar is played without effects etc. and the open string tuning is sounded - which starts with a normal E and then adjusted to the 9th / 7th fret unison, like a typical 12edo guitar fashion.<br /> | This movie is a series of still shots Chris took during the process of making a 23 edo guitar in a stick like form. At the end the guitar is played without effects etc. and the open string tuning is sounded - which starts with a normal E and then adjusted to the 9th / 7th fret unison, like a typical 12edo guitar fashion.<br /> | ||
<!-- ws:start:WikiTextMediaRule:1:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/youtube/K4iO7k152og?h=349&amp;w=560&quot; class=&quot;WikiMedia WikiMediaYoutube&quot; id=&quot;wikitext@@media@@type=&amp;quot;youtube&amp;quot; key=&amp;quot;K4iO7k152og&amp;quot; height=&amp;quot;349&amp;quot; width=&amp;quot;560&amp;quot;&quot; title=&quot;YouTube Video&quot;height=&quot;349&quot; width=&quot;560&quot;/&gt; --><iframe width="560" height="349" src="//www.youtube.com/embed/K4iO7k152og" frameborder="0" allowfullscreen></iframe><!-- ws:end:WikiTextMediaRule:1 --></body></html></pre></div> | <!-- ws:start:WikiTextMediaRule:1:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/youtube/K4iO7k152og?h=349&amp;w=560&quot; class=&quot;WikiMedia WikiMediaYoutube&quot; id=&quot;wikitext@@media@@type=&amp;quot;youtube&amp;quot; key=&amp;quot;K4iO7k152og&amp;quot; height=&amp;quot;349&amp;quot; width=&amp;quot;560&amp;quot;&quot; title=&quot;YouTube Video&quot;height=&quot;349&quot; width=&quot;560&quot;/&gt; --><iframe width="560" height="349" src="//www.youtube.com/embed/K4iO7k152og" frameborder="0" allowfullscreen></iframe><!-- ws:end:WikiTextMediaRule:1 --></body></html></pre></div> | ||