34edo: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 600628440 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 600630016 - 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>2016-11-28 12: | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-11-28 12:37:55 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>600630016</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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of 7 and 11 || pseudo-traditional | of 7 and 11 || pseudo-traditional | ||
notation || | notation || | ||
|| 0 || do || 0.0 || 1/1 || || C = B^^ = | || 0 || do || 0.0 || 1/1 || || C = B^^ = Ax || | ||
|| 1 || di || 35.294 | || 1 || di || 35.294 | ||
10°35'18" || 128/125 ([[128_125|diesis]]) || | 10°35'18" || 128/125 ([[128_125|diesis]]), 51/50 || 50/49, 49/48 || C ^ || | ||
|| 2 || rih || 70.588 | || 2 || rih || 70.588 | ||
21°10'35" || 25/24, 648/625 ([[648_625|large diesis]]) || || Db = C ^^ = B# || | 21°10'35" || 25/24, 648/625 ([[648_625|large diesis]]) || || Db = C^^ = B# || | ||
|| 3 || ra || 105.882 | || 3 || ra || 105.882 | ||
31°35'18" || 17/16, 18/17, 16/15 || 15/14 || C#v = Db^ || | 31°35'18" || 17/16, 18/17, 16/15 || 15/14 || C#v = Db^ || | ||
| Line 73: | Line 73: | ||
105°52'56" || 16/13 || 11/9 || D# || | 105°52'56" || 16/13 || 11/9 || D# || | ||
|| 11 || mi || 388.235 | || 11 || mi || 388.235 | ||
116°28'14" || 5/4 || || D#^=Ev || | 116°28'14" || 5/4 || || D#^ = Ev || | ||
|| 12 || maa || 423.529 | || 12 || maa || 423.529 | ||
127°3'32" || [[51_40|51/40]], 32/25 || 14/11, 9/7 || E || | 127°3'32" || [[51_40|51/40]], 32/25 || 14/11, 9/7 || E || | ||
| Line 81: | Line 81: | ||
148°14'7" || 4/3 || || F || | 148°14'7" || 4/3 || || F || | ||
|| 15 || fih || 529.412 | || 15 || fih || 529.412 | ||
158°49'15" || || 15/11 || F^ = E#v || | 158°49'15" || || 15/11 || F^ = E#v = Gbv || | ||
|| 16 || fu || 564.706 | || 16 || fu || 564.706 | ||
169°24'42" || 18/13 || 11/8 || Gb || | 169°24'42" || 18/13 || 11/8 || E# = F^^ = Gb || | ||
|| 17 || fi/se || 600 | || 17 || fi/se || 600 | ||
180° || 17/12, 24/17 || 7/5, 10/7 || Gb^ || | 180° || 17/12, 24/17 || 7/5, 10/7 || Gb^ || | ||
| Line 95: | Line 95: | ||
222°21'11" || 20/13, 26/17 || 17/11 || G^ || | 222°21'11" || 20/13, 26/17 || 17/11 || G^ || | ||
|| 22 || leh || 776.471 | || 22 || leh || 776.471 | ||
233°58'28" || 25/16, 80/51 || 14/9 || Ab || | 233°58'28" || 25/16, 80/51 || 14/9 || Ab = Fx || | ||
|| 23 || le || 811.765 | || 23 || le || 811.765 | ||
243°31'46" || 8/5 || || Ab^ || | 243°31'46" || 8/5 || || Ab^ || | ||
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275°17'39" || [[17_10|17/10]] || 12/7, 22/13 || A || | 275°17'39" || [[17_10|17/10]] || 12/7, 22/13 || A || | ||
|| 27 || law || 952.941 | || 27 || law || 952.941 | ||
285°52'56" || 26/15 || 7/4 || A^ = Bbv = | 285°52'56" || 26/15 || 7/4 || A^ = Bbv = Gxv || | ||
|| 28 || teh || 988.235 | || 28 || teh || 988.235 | ||
296°28'14" || 16/9, 30/17 || || Bb || | 296°28'14" || 16/9, 30/17 || || Bb = Gx || | ||
|| 29 || te || 1023.529 | || 29 || te || 1023.529 | ||
307°3'32" || 9/5 || 20/11 || Bb^ || | 307°3'32" || 9/5 || 20/11 || Bb^ || | ||
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328°14'7" || 32/17, 17/9, 15/8 || 28/15 || A#^ = Bv || | 328°14'7" || 32/17, 17/9, 15/8 || 28/15 || A#^ = Bv || | ||
|| 32 || taa || 1129.412 | || 32 || taa || 1129.412 | ||
338°49'15" || 48/25 || || B || | 338°49'15" || 48/25, 625/324 || || B || | ||
|| 33 || da || 1164.706 | || 33 || da || 1164.706 | ||
349°24'42" || | 349°24'42" || 125/64, 100/51 || 49/25, 96/49 || B^ = Axv =Cv || | ||
==Selected just intervals by error== | ==Selected just intervals by error== | ||
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* [[https://myspace.com/microstick]]</pre></div> | * [[https://myspace.com/microstick]]</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>34edo</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>34edo</title></head><body><!-- ws:start:WikiTextTocRule:20:&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:20 --><!-- ws:start:WikiTextTocRule:21: --><a href="#Approximations to Just Intonation">Approximations to Just Intonation</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#x34edo and phi">34edo and phi</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> | <a href="#Rank two temperaments">Rank two temperaments</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | <a href="#F^^"> F^^ </a><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> | <a href="#Notations">Notations</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --> | <a href="#Listen">Listen</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Links">Links</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:31 --><hr /> | ||
<br /> | <br /> | ||
34edo divides the octave into 34 equal steps of approximately 35.29412 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent">cent</a>s. 34edo contains two <a class="wiki_link" href="http://xenharmonic.wikispaces.com/17edo">17edo</a>'s and the half-octave tritone of 600 cents. It excels as a 5-limit system, with tuning even more accurate than <a class="wiki_link" href="/31edo">31edo</a>, but with a sharp fifth rather than a flat one, and supports hanson, srutal, tetracot, würschmidt and vishnu temperaments. It does less well in the 7-limit, with two mappings possible for 7/4: a flat one from the patent val, and a sharp one from the 34d val. By way of the patent val 34 supports keemun temperament, and 34d is an excellent alternative to <a class="wiki_link" href="/22edo">22edo</a> for 7-limit pajara temperament. In the 11-limit, 34de supports 11-limit pajaric, and in fact is quite close to the POTE tuning; it adds 4375/4374 to the commas of 11-limit pajaric. On the other hand, the 34d val supports pajara, vishnu and würschmidt, adding 4375/4374 to the commas of pajara. Among subgroup temperaments, the patent val supports semaphore on the 2.3.7 subgroup.<br /> | 34edo divides the octave into 34 equal steps of approximately 35.29412 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent">cent</a>s. 34edo contains two <a class="wiki_link" href="http://xenharmonic.wikispaces.com/17edo">17edo</a>'s and the half-octave tritone of 600 cents. It excels as a 5-limit system, with tuning even more accurate than <a class="wiki_link" href="/31edo">31edo</a>, but with a sharp fifth rather than a flat one, and supports hanson, srutal, tetracot, würschmidt and vishnu temperaments. It does less well in the 7-limit, with two mappings possible for 7/4: a flat one from the patent val, and a sharp one from the 34d val. By way of the patent val 34 supports keemun temperament, and 34d is an excellent alternative to <a class="wiki_link" href="/22edo">22edo</a> for 7-limit pajara temperament. In the 11-limit, 34de supports 11-limit pajaric, and in fact is quite close to the POTE tuning; it adds 4375/4374 to the commas of 11-limit pajaric. On the other hand, the 34d val supports pajara, vishnu and würschmidt, adding 4375/4374 to the commas of pajara. Among subgroup temperaments, the patent val supports semaphore on the 2.3.7 subgroup.<br /> | ||
| Line 415: | Line 415: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>C = B^^ = | <td>C = B^^ = Ax<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 426: | Line 426: | ||
10°35'18&quot;<br /> | 10°35'18&quot;<br /> | ||
</td> | </td> | ||
<td>128/125 (<a class="wiki_link" href="/128_125">diesis</a>)<br /> | <td>128/125 (<a class="wiki_link" href="/128_125">diesis</a>), 51/50<br /> | ||
</td> | </td> | ||
<td><br /> | <td>50/49, 49/48<br /> | ||
</td> | </td> | ||
<td>C ^<br /> | <td>C ^<br /> | ||
| Line 445: | Line 445: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>Db = C ^^ = B#<br /> | <td>Db = C^^ = B#<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 580: | Line 580: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>D#^=Ev<br /> | <td>D#^ = Ev<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 640: | Line 640: | ||
<td>15/11<br /> | <td>15/11<br /> | ||
</td> | </td> | ||
<td>F^ = E#v<br /> | <td>F^ = E#v = Gbv<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 655: | Line 655: | ||
<td>11/8<br /> | <td>11/8<br /> | ||
</td> | </td> | ||
<td>Gb<br /> | <td>E# <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="F^^"></a><!-- ws:end:WikiTextHeadingRule:8 --> F^^ </h1> | ||
Gb<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 745: | Line 746: | ||
<td>14/9<br /> | <td>14/9<br /> | ||
</td> | </td> | ||
<td>Ab<br /> | <td>Ab = Fx<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 820: | Line 821: | ||
<td>7/4<br /> | <td>7/4<br /> | ||
</td> | </td> | ||
<td>A^ = Bbv = | <td>A^ = Bbv = Gxv<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 835: | Line 836: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>Bb<br /> | <td>Bb = Gx<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 891: | Line 892: | ||
338°49'15&quot;<br /> | 338°49'15&quot;<br /> | ||
</td> | </td> | ||
<td>48/25<br /> | <td>48/25, 625/324<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 906: | Line 907: | ||
349°24'42&quot;<br /> | 349°24'42&quot;<br /> | ||
</td> | </td> | ||
<td><br /> | <td>125/64, 100/51<br /> | ||
</td> | </td> | ||
<td><br /> | <td>49/25, 96/49<br /> | ||
</td> | </td> | ||
<td>B^ = | <td>B^ = Axv =Cv<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="F^^-Selected just intervals by error"></a><!-- ws:end:WikiTextHeadingRule:10 -->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:12:&lt;h1&gt; --><h1 id="toc6"><a name="Notations"></a><!-- ws:end:WikiTextHeadingRule:12 -->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:14:&lt;h1&gt; --><h1 id="toc7"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:14 -->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> |.)<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> |.)<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Listen"></a><!-- ws:end:WikiTextHeadingRule:16 -->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:18:&lt;h1&gt; --><h1 id="toc9"><a name="Links"></a><!-- ws:end:WikiTextHeadingRule:18 -->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> | ||