34edo: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 601847494 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 601848148 - 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 12: | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-10 12:53:09 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>601848148</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> | ||
| Line 64: | Line 64: | ||
63°31'46" || 9/8, 17/15 || || D || | 63°31'46" || 9/8, 17/15 || || D || | ||
|| 7 || raw || 247.059 | || 7 || raw || 247.059 | ||
74°7'4" || 15/13 || 8/7 || D^ || | 74°7'4" || 15/13 || 8/7 || D^ = Ebv || | ||
|| 8 || meh || 282.353 | || 8 || meh || 282.353 | ||
84°42'21" || 20/17, 75/64 || 7/6, 13/11 || Eb || | 84°42'21" || 20/17, 75/64 || 7/6, 13/11 || D^^ = Eb || | ||
|| 9 || me || 317.647 | || 9 || me || 317.647 | ||
95°17'39" || 6/5 || 17/14 || D#v || | 95°17'39" || 6/5 || 17/14 || D#v = Eb^ || | ||
|| 10 || mu || 352.941 | || 10 || mu || 352.941 | ||
105°52'56" || 16/13 || 11/9 || D# || | 105°52'56" || 16/13 || 11/9 || D# = Evv = Fbv || | ||
|| 11 || mi || 388.235 | || 11 || mi || 388.235 | ||
116°28'14" || 5/4 || || D#^ = Ev || | 116°28'14" || 5/4 || || D#^ = Ev = Fb || | ||
|| 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 || Fvv = E || | ||
|| 13 || maw || 458.823 | || 13 || maw || 458.823 | ||
137°38'49" || 13/10, 17/13 || 22/17 || E^ = Fv || | 137°38'49" || 13/10, 17/13 || 22/17 || E^ = Fv || | ||
|| 14 || fa || 494.118 | || 14 || fa || 494.118 | ||
148°14'7" || 4/3 || || F || | 148°14'7" || 4/3 || || E^^ = F || | ||
|| 15 || fih || 529.412 | || 15 || fih || 529.412 | ||
158°49'15" || || 15/11 || F^ = E#v = Gbv || | 158°49'15" || || 15/11 || F^ = E#v = Gbv || | ||
| Line 84: | Line 84: | ||
169°24'42" || 18/13 || 11/8 || E# = F^^ = 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 || E#^ = F#v = Gb^ || | ||
|| 18 || su || 635.294 | || 18 || su || 635.294 | ||
190°35'18" || 13/9 || 16/11 || F# || | 190°35'18" || 13/9 || 16/11 || F# = Gvv || | ||
|| 19 || sih || 670.588 | || 19 || sih || 670.588 | ||
201°10'35" || || 22/15 || F#^ || | 201°10'35" || || 22/15 || F#^ = Gv || | ||
|| 20 || sol || 705.882 | || 20 || sol || 705.882 | ||
211°45'53" || 3/2 || || G || | 211°45'53" || 3/2 || || G || | ||
|| 21 || saw || 741.176 | || 21 || saw || 741.176 | ||
222°21'11" || 20/13, 26/17 || 17/11 || G^ || | 222°21'11" || 20/13, 26/17 || 17/11 || Fxv = G^ = Abv || | ||
|| 22 || leh || 776.471 | || 22 || leh || 776.471 | ||
233°58'28" || 25/16, 80/51 || 14/9 || Ab = Fx || | 233°58'28" || 25/16, 80/51 || 14/9 || Ab = G^^ = Fx || | ||
|| 23 || le || 811.765 | || 23 || le || 811.765 | ||
243°31'46" || 8/5 || || Ab^ || | 243°31'46" || 8/5 || || G#v = Ab^ || | ||
|| 24 || lu || 847.059 | || 24 || lu || 847.059 | ||
254°7'4" || 13/8 || 18/11 || G# || | 254°7'4" || 13/8 || 18/11 || G# = Avv || | ||
|| 25 || la || 882.353 | || 25 || la || 882.353 | ||
264°42'21" || 5/3 || 28/17 || Av || | 264°42'21" || 5/3 || 28/17 || Av || | ||
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285°52'56" || 26/15 || 7/4 || A^ = Bbv = Gxv || | 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 = Gx || | 296°28'14" || 16/9, 30/17 || || A^^ = 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 || A#v = Bb^ || | ||
|| 30 || tu || 1058.823 | || 30 || tu || 1058.823 | ||
317°38'49" || 24/13 || 13/7, 11/6 || A# || | 317°38'49" || 24/13 || 13/7, 11/6 || A# = Bvv = Cb || | ||
|| 31 || ti || 1094.118 | || 31 || ti || 1094.118 | ||
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, 625/324 || || B || | 338°49'15" || 48/25, 625/324 || || B = Cvv || | ||
|| 33 || da || 1164.706 | || 33 || da || 1164.706 | ||
349°24'42" || 125/64, 100/51 || 49/25, 96/49 || B^ = Axv =Cv || | 349°24'42" || 125/64, 100/51 || 49/25, 96/49 || B^ = Axv = Cv || | ||
==Selected just intervals by error== | ==Selected just intervals by error== | ||
| Line 518: | Line 518: | ||
<td>8/7<br /> | <td>8/7<br /> | ||
</td> | </td> | ||
<td>D^<br /> | <td>D^ = Ebv<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 533: | Line 533: | ||
<td>7/6, 13/11<br /> | <td>7/6, 13/11<br /> | ||
</td> | </td> | ||
<td>Eb<br /> | <td>D^^ = Eb<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 548: | Line 548: | ||
<td>17/14<br /> | <td>17/14<br /> | ||
</td> | </td> | ||
<td>D#v<br /> | <td>D#v = Eb^<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 563: | Line 563: | ||
<td>11/9<br /> | <td>11/9<br /> | ||
</td> | </td> | ||
<td>D#<br /> | <td>D# <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Evv"></a><!-- ws:end:WikiTextHeadingRule:8 --> Evv </h1> | ||
Fbv<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 578: | Line 579: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>D#^ = Ev<br /> | <td>D#^ = Ev = Fb<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 593: | Line 594: | ||
<td>14/11, 9/7<br /> | <td>14/11, 9/7<br /> | ||
</td> | </td> | ||
<td>E<br /> | <td>Fvv = E<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 623: | Line 624: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>F<br /> | <td>E^^ = F<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 653: | Line 654: | ||
<td>11/8<br /> | <td>11/8<br /> | ||
</td> | </td> | ||
<td>E# <!-- ws:start:WikiTextHeadingRule: | <td>E# <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="F^^"></a><!-- ws:end:WikiTextHeadingRule:10 --> F^^ </h1> | ||
Gb<br /> | Gb<br /> | ||
</td> | </td> | ||
| Line 669: | Line 670: | ||
<td>7/5, 10/7<br /> | <td>7/5, 10/7<br /> | ||
</td> | </td> | ||
<td>Gb^<br /> | <td>E#^ = F#v = Gb^<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 684: | Line 685: | ||
<td>16/11<br /> | <td>16/11<br /> | ||
</td> | </td> | ||
<td>F#<br /> | <td>F# = Gvv<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 699: | Line 700: | ||
<td>22/15<br /> | <td>22/15<br /> | ||
</td> | </td> | ||
<td>F#^<br /> | <td>F#^ = Gv<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 729: | Line 730: | ||
<td>17/11<br /> | <td>17/11<br /> | ||
</td> | </td> | ||
<td>G^<br /> | <td>Fxv = G^ = Abv<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 744: | Line 745: | ||
<td>14/9<br /> | <td>14/9<br /> | ||
</td> | </td> | ||
<td>Ab = Fx<br /> | <td>Ab = G^^ = Fx<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 759: | Line 760: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>Ab^<br /> | <td>G#v = Ab^<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 774: | Line 775: | ||
<td>18/11<br /> | <td>18/11<br /> | ||
</td> | </td> | ||
<td>G#<br /> | <td>G# = Avv<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 834: | Line 835: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>Bb = Gx<br /> | <td>A^^ = Bb = Gx<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 849: | Line 850: | ||
<td>20/11<br /> | <td>20/11<br /> | ||
</td> | </td> | ||
<td>Bb^<br /> | <td>A#v = Bb^<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 864: | Line 865: | ||
<td>13/7, 11/6<br /> | <td>13/7, 11/6<br /> | ||
</td> | </td> | ||
<td>A#<br /> | <td>A# <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Bvv"></a><!-- ws:end:WikiTextHeadingRule:12 --> Bvv </h1> | ||
Cb<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 894: | Line 896: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>B<br /> | <td>B = Cvv<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 909: | Line 911: | ||
<td>49/25, 96/49<br /> | <td>49/25, 96/49<br /> | ||
</td> | </td> | ||
<td>B^ = Axv =Cv<br /> | <td>B^ = Axv = Cv<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 915: | Line 917: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Bvv-Selected just intervals by error"></a><!-- ws:end:WikiTextHeadingRule:14 -->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 /> | ||
| Line 1,073: | Line 1,075: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Notations"></a><!-- ws:end:WikiTextHeadingRule:16 -->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:18:&lt;h1&gt; --><h1 id="toc9"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:18 -->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 1,234: | Line 1,236: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Listen"></a><!-- ws:end:WikiTextHeadingRule:20 -->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:22:&lt;h1&gt; --><h1 id="toc11"><a name="Links"></a><!-- ws:end:WikiTextHeadingRule:22 -->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> | ||