34edo: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 601849852 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 601849994 - 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:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-10 13: | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-10 13:30:26 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>601849994</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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DMS || approx. ratios of | DMS || approx. ratios of | ||
2.3.5.13.17/1 [[xenharmonic/subgroup|subgroup]] || additional ratios | 2.3.5.13.17/1 [[xenharmonic/subgroup|subgroup]] || additional ratios | ||
of 7 and 11 | of 7 and 11 || | ||
|| 0 || do || 0.0 || 1/1 || || | |||
|| 0 || do || 0.0 || 1/1 || | |||
|| 1 || di || 35.294 | || 1 || di || 35.294 | ||
10°35'18" || 128/125 ([[128_125|diesis]]), 51/50 || 50/49, 49/48 | 10°35'18" || 128/125 ([[128_125|diesis]]), 51/50 || 50/49, 49/48 || | ||
|| 2 || rih || 70.588 | || 2 || rih || 70.588 | ||
21°10'35" || 25/24, 648/625 ([[648_625|large diesis]]) || | 21°10'35" || 25/24, 648/625 ([[648_625|large diesis]]) || || | ||
|| 3 || ra || 105.882 | || 3 || ra || 105.882 | ||
31°35'18" || 17/16, 18/17, 16/15 || 15/14 | 31°35'18" || 17/16, 18/17, 16/15 || 15/14 || | ||
|| 4 || ru || 141.176 | || 4 || ru || 141.176 | ||
42°21'11" || 13/12 || 14/13, 12/11 | 42°21'11" || 13/12 || 14/13, 12/11 || | ||
|| 5 || reh || 176.471 | || 5 || reh || 176.471 | ||
53°58'28" || 10/9 || 11/10 | 53°58'28" || 10/9 || 11/10 || | ||
|| 6 || re || 211.765 | || 6 || re || 211.765 | ||
63°31'46" || 9/8, 17/15 || | 63°31'46" || 9/8, 17/15 || || | ||
|| 7 || raw || 247.059 | || 7 || raw || 247.059 | ||
74°7'4" || 15/13 || 8/7 | 74°7'4" || 15/13 || 8/7 || | ||
|| 8 || meh || 282.353 | || 8 || meh || 282.353 | ||
84°42'21" || 20/17, 75/64 || 7/6, 13/11 | 84°42'21" || 20/17, 75/64 || 7/6, 13/11 || | ||
|| 9 || me || 317.647 | || 9 || me || 317.647 | ||
95°17'39" || 6/5 || 17/14 | 95°17'39" || 6/5 || 17/14 || | ||
|| 10 || mu || 352.941 | || 10 || mu || 352.941 | ||
105°52'56" || 16/13 || 11/9 | 105°52'56" || 16/13 || 11/9 || | ||
|| 11 || mi || 388.235 | || 11 || mi || 388.235 | ||
116°28'14" || 5/4 || | 116°28'14" || 5/4 || || | ||
|| 12 || maa || 423.529 | || 12 || maa || 423.529 | ||
127°3'32" || [[51_40|51/40]], 32/25 || 14/11, 9/7 | 127°3'32" || [[51_40|51/40]], 32/25 || 14/11, 9/7 || | ||
|| 13 || maw || 458.823 | || 13 || maw || 458.823 | ||
137°38'49" || 13/10, 17/13 || 22/17 | 137°38'49" || 13/10, 17/13 || 22/17 || | ||
|| 14 || fa || 494.118 | || 14 || fa || 494.118 | ||
148°14'7" || 4/3 || | 148°14'7" || 4/3 || || | ||
|| 15 || fih || 529.412 | || 15 || fih || 529.412 | ||
158°49'15" || || 15/11 | 158°49'15" || || 15/11 || | ||
|| 16 || fu || 564.706 | || 16 || fu || 564.706 | ||
169°24'42" || 18/13 || 11/8 | 169°24'42" || 18/13 || 11/8 || | ||
|| 17 || fi/se || 600 | || 17 || fi/se || 600 | ||
180° || 17/12, 24/17 || 7/5, 10/7 | 180° || 17/12, 24/17 || 7/5, 10/7 || | ||
|| 18 || su || 635.294 | || 18 || su || 635.294 | ||
190°35'18" || 13/9 || 16/11 | 190°35'18" || 13/9 || 16/11 || | ||
|| 19 || sih || 670.588 | || 19 || sih || 670.588 | ||
201°10'35" || || 22/15 | 201°10'35" || || 22/15 || | ||
|| 20 || sol || 705.882 | || 20 || sol || 705.882 | ||
211°45'53" || 3/2 || | 211°45'53" || 3/2 || || | ||
|| 21 || saw || 741.176 | || 21 || saw || 741.176 | ||
222°21'11" || 20/13, 26/17 || 17/11 | 222°21'11" || 20/13, 26/17 || 17/11 || | ||
|| 22 || leh || 776.471 | || 22 || leh || 776.471 | ||
233°58'28" || 25/16, 80/51 || 14/9 | 233°58'28" || 25/16, 80/51 || 14/9 || | ||
|| 23 || le || 811.765 | || 23 || le || 811.765 | ||
243°31'46" || 8/5 || | 243°31'46" || 8/5 || || | ||
|| 24 || lu || 847.059 | || 24 || lu || 847.059 | ||
254°7'4" || 13/8 || 18/11 | 254°7'4" || 13/8 || 18/11 || | ||
|| 25 || la || 882.353 | || 25 || la || 882.353 | ||
264°42'21" || 5/3 || 28/17 | 264°42'21" || 5/3 || 28/17 || | ||
|| 26 || laa || 917.647 | || 26 || laa || 917.647 | ||
275°17'39" || [[17_10|17/10]] || 12/7, 22/13 | 275°17'39" || [[17_10|17/10]] || 12/7, 22/13 || | ||
|| 27 || law || 952.941 | || 27 || law || 952.941 | ||
285°52'56" || 26/15 || 7/4 | 285°52'56" || 26/15 || 7/4 || | ||
|| 28 || teh || 988.235 | || 28 || teh || 988.235 | ||
296°28'14" || 16/9, 30/17 || | 296°28'14" || 16/9, 30/17 || || | ||
|| 29 || te || 1023.529 | || 29 || te || 1023.529 | ||
307°3'32" || 9/5 || 20/11 | 307°3'32" || 9/5 || 20/11 || | ||
|| 30 || tu || 1058.823 | || 30 || tu || 1058.823 | ||
317°38'49" || 24/13 || 13/7, 11/6 | 317°38'49" || 24/13 || 13/7, 11/6 || | ||
|| 31 || ti || 1094.118 | || 31 || ti || 1094.118 | ||
328°14'7" || 32/17, 17/9, 15/8 || 28/15 | 328°14'7" || 32/17, 17/9, 15/8 || 28/15 || | ||
|| 32 || taa || 1129.412 | || 32 || taa || 1129.412 | ||
338°49'15" || 48/25, 625/324 || | 338°49'15" || 48/25, 625/324 || || | ||
|| 33 || da || 1164.706 | || 33 || da || 1164.706 | ||
349°24'42" || 125/64, 100/51 || 49/25, 96/49 | 349°24'42" || 125/64, 100/51 || 49/25, 96/49 || | ||
==Selected just intervals by error== | ==Selected just intervals by error== | ||
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<td>additional ratios<br /> | <td>additional ratios<br /> | ||
of 7 and 11<br /> | of 7 and 11<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 418: | Line 408: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 433: | Line 421: | ||
</td> | </td> | ||
<td>50/49, 49/48<br /> | <td>50/49, 49/48<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 448: | Line 434: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 463: | Line 447: | ||
</td> | </td> | ||
<td>15/14<br /> | <td>15/14<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 478: | Line 460: | ||
</td> | </td> | ||
<td>14/13, 12/11<br /> | <td>14/13, 12/11<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 493: | Line 473: | ||
</td> | </td> | ||
<td>11/10<br /> | <td>11/10<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 508: | Line 486: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 523: | Line 499: | ||
</td> | </td> | ||
<td>8/7<br /> | <td>8/7<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 538: | Line 512: | ||
</td> | </td> | ||
<td>7/6, 13/11<br /> | <td>7/6, 13/11<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 553: | Line 525: | ||
</td> | </td> | ||
<td>17/14<br /> | <td>17/14<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 568: | Line 538: | ||
</td> | </td> | ||
<td>11/9<br /> | <td>11/9<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 585: | Line 551: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 600: | Line 564: | ||
</td> | </td> | ||
<td>14/11, 9/7<br /> | <td>14/11, 9/7<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 615: | Line 577: | ||
</td> | </td> | ||
<td>22/17<br /> | <td>22/17<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 645: | Line 603: | ||
</td> | </td> | ||
<td>15/11<br /> | <td>15/11<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 660: | Line 616: | ||
</td> | </td> | ||
<td>11/8<br /> | <td>11/8<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 677: | Line 629: | ||
</td> | </td> | ||
<td>7/5, 10/7<br /> | <td>7/5, 10/7<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 692: | Line 642: | ||
</td> | </td> | ||
<td>16/11<br /> | <td>16/11<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 707: | Line 655: | ||
</td> | </td> | ||
<td>22/15<br /> | <td>22/15<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 722: | Line 668: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 737: | Line 681: | ||
</td> | </td> | ||
<td>17/11<br /> | <td>17/11<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 752: | Line 694: | ||
</td> | </td> | ||
<td>14/9<br /> | <td>14/9<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 767: | Line 707: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 782: | Line 720: | ||
</td> | </td> | ||
<td>18/11<br /> | <td>18/11<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 797: | Line 733: | ||
</td> | </td> | ||
<td>28/17<br /> | <td>28/17<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 812: | Line 746: | ||
</td> | </td> | ||
<td>12/7, 22/13<br /> | <td>12/7, 22/13<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 827: | Line 759: | ||
</td> | </td> | ||
<td>7/4<br /> | <td>7/4<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 842: | Line 772: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 857: | Line 785: | ||
</td> | </td> | ||
<td>20/11<br /> | <td>20/11<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 872: | Line 798: | ||
</td> | </td> | ||
<td>13/7, 11/6<br /> | <td>13/7, 11/6<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 889: | Line 811: | ||
</td> | </td> | ||
<td>28/15<br /> | <td>28/15<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 904: | Line 824: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 919: | Line 837: | ||
</td> | </td> | ||
<td>49/25, 96/49<br /> | <td>49/25, 96/49<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Intervals-Selected just intervals by error"></a><!-- ws:end:WikiTextHeadingRule:8 -->Selected just intervals by error</h2> | ||
The following table shows how <a class="wiki_link" href="/Just-24">some prominent just intervals</a> are represented in 34edo (ordered by absolute error).<br /> | The following table shows how <a class="wiki_link" href="/Just-24">some prominent just intervals</a> are represented in 34edo (ordered by absolute error).<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Notations"></a><!-- ws:end:WikiTextHeadingRule:10 -->Notations</h1> | ||
The chain of fifths gives you the seven naturals, and their sharps and flats. The sharp or flat of a note is (what is commonly called) a neutral second away - the double-sharp means a minor third away from the natural. This has led certain &quot;complainers&quot;, in seeking to notate 17 edo, to create an extra character to raise something a small step of which. To render this symbol philosophically harmonious with 34 tone equal temperament, a symbol indicating an adjustment of 1/34 up or down serves the purpose by using two of it, doubled laterally or vertically as composer. This however emphasizes certain aspects of 34edo which <em>may not be most efficient expressions of some musical purposes.</em> The reader can construct his own notation to the needs of the music and performer. As an example, a system with 15 &quot;nominals&quot; like A, B, C ... F, instead of seven, might be waste - of paper, or space, or memory if they aren't used consecutively frequently. The system spelled out here has familiarity as an advantage and disadvantage. The spacing of the nominals and lines is the same. Dense chords of certain types would be very impossible to notate. Finally, the table uses ^ and v for &quot;up&quot; and &quot;down&quot;, but these might be reserved for adjustments of 1/68th of an octave, being hollow, and filled in triangles are recommended.<br /> | The chain of fifths gives you the seven naturals, and their sharps and flats. The sharp or flat of a note is (what is commonly called) a neutral second away - the double-sharp means a minor third away from the natural. This has led certain &quot;complainers&quot;, in seeking to notate 17 edo, to create an extra character to raise something a small step of which. To render this symbol philosophically harmonious with 34 tone equal temperament, a symbol indicating an adjustment of 1/34 up or down serves the purpose by using two of it, doubled laterally or vertically as composer. This however emphasizes certain aspects of 34edo which <em>may not be most efficient expressions of some musical purposes.</em> The reader can construct his own notation to the needs of the music and performer. As an example, a system with 15 &quot;nominals&quot; like A, B, C ... F, instead of seven, might be waste - of paper, or space, or memory if they aren't used consecutively frequently. The system spelled out here has familiarity as an advantage and disadvantage. The spacing of the nominals and lines is the same. Dense chords of certain types would be very impossible to notate. Finally, the table uses ^ and v for &quot;up&quot; and &quot;down&quot;, but these might be reserved for adjustments of 1/68th of an octave, being hollow, and filled in triangles are recommended.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:12 -->Commas</h1> | ||
34-EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the <a class="wiki_link" href="/val">val</a> &lt; <a class="wiki_link" href="http://tel.wikispaces.com/34%2054%2079%2095%20118%20126">34 54 79 95 118 126</a>/1 |.)<br /> | 34-EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the <a class="wiki_link" href="/val">val</a> &lt; <a class="wiki_link" href="http://tel.wikispaces.com/34%2054%2079%2095%20118%20126">34 54 79 95 118 126</a>/1 |.)<br /> | ||
| Line 1,245: | Line 1,161: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Listen"></a><!-- ws:end:WikiTextHeadingRule:14 -->Listen</h1> | ||
<ul><li><a class="wiki_link_ext" href="http://www.archive.org/details/Ascension_105" rel="nofollow" target="_blank">Ascension</a></li><li><a class="wiki_link_ext" href="https://www.youtube.com/watch?v=FXTM0HeuExk" rel="nofollow" target="_blank">Uncomfortable In Crowds (extended)</a> by Robin Perry</li></ul><br /> | <ul><li><a class="wiki_link_ext" href="http://www.archive.org/details/Ascension_105" rel="nofollow" target="_blank">Ascension</a></li><li><a class="wiki_link_ext" href="https://www.youtube.com/watch?v=FXTM0HeuExk" rel="nofollow" target="_blank">Uncomfortable In Crowds (extended)</a> by Robin Perry</li></ul><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Links"></a><!-- ws:end:WikiTextHeadingRule:16 -->Links</h1> | ||
<ul><li><a class="wiki_link_ext" href="http://www.microstick.net/34guitararticle.htm" rel="nofollow">34 Equal Guitar</a> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Larry%20Hanson">Larry Hanson</a></li><li><a class="wiki_link_ext" href="https://microstick.net" rel="nofollow">http://microstick.net/</a> websites of Neil Haverstick</li><li><a class="wiki_link_ext" href="https://myspace.com/microstick" rel="nofollow">https://myspace.com/microstick</a></li></ul></body></html></pre></div> | <ul><li><a class="wiki_link_ext" href="http://www.microstick.net/34guitararticle.htm" rel="nofollow">34 Equal Guitar</a> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Larry%20Hanson">Larry Hanson</a></li><li><a class="wiki_link_ext" href="https://microstick.net" rel="nofollow">http://microstick.net/</a> websites of Neil Haverstick</li><li><a class="wiki_link_ext" href="https://myspace.com/microstick" rel="nofollow">https://myspace.com/microstick</a></li></ul></body></html></pre></div> | ||