34edo
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Original Wikitext content:
34edo divides the 2:1 octave into 34 equal steps of approximately 35.294117 cents. 34edo contains two [[17edo]]'s and the half-octave tritone of 600 cents. As a Fibonacci number, 34edo contains a close approximation to the irrational interval phi -- 21 degrees of 34edo, approximately 741.2 cents. Repeated iterations of this interval generates [[MOSScales|Moment of Symmetry]] scales with near-phi relationships between the step sizes. ===Approximations to Just Intonation=== Like [[17edo]], 34edo contains workable approximations of just intervals involving 13 and 3 -- specifically, 13/8, 13/12, 13/9 and their inversions -- while failing to closely approximate ratios of 7 or 11. 34edo adds ratios of 5 into the mix, including: 5/4, 6/5, 9/5, 15/8, 13/10, 15/13, and their inversions. Since it distinguishes between 9/8 and 10/9 (exaggerating the difference between them, the syntonic comma of 81/80, from 21.5 cents to 35.3 cents), it is suitable for 5-limit JI. It is not a meantone system. //Viewed in light of Western diatonic theory, the three extra steps (of 34-et compared to 31-et) in effect widen the intervals between C and D, F and G, and A and B, thus making a distinction between major tones, ratio 9/8 and minor tones, ratio 10/9.// ([[http://en.wikipedia.org/wiki/34_equal_temperament|Wikipedia]]) ===Intervals:=== || degrees of 34edo || cents || || 0 || 0.0 || || 1 || 35.3 || || 2 || 70.6 || || 3 || 105.9 || || 4 || 141.2 || || 5 || 176.5 || || 6 || 211.8 || || 7 || 247.1 || || 8 || 282.4 || || 9 || 317.6 || || 10 || 352.9 || || 11 || 388.2 || || 12 || 423.5 || || 13 || 458.8 || || 14 || 494.1 || || 15 || 529.4 || || 16 || 564.7 || || 17 || 600.0 || || 18 || 635.3 || || 19 || 670.6 || || 20 || 705.9 || || 21 || 741.2 || || 22 || 776.5 || || 23 || 811.8 || || 24 || 847.1 || || 25 || 882.4 || || 26 || 917.6 || || 27 || 952.9 || || 28 || 988.2 || || 29 || 1023.5 || || 30 || 1058.8 || || 31 || 1094.1 || || 32 || 1129.4 || || 33 || 1164.7 || ==Listen== * [[@http://www.archive.org/details/Ascension_105|Ascension]] Drums Bass and 34-tone guitar
Original HTML content:
<html><head><title>34edo</title></head><body>34edo divides the 2:1 octave into 34 equal steps of approximately 35.294117 cents. 34edo contains two <a class="wiki_link" href="/17edo">17edo</a>'s and the half-octave tritone of 600 cents. As a Fibonacci number, 34edo contains a close approximation to the irrational interval phi -- 21 degrees of 34edo, approximately 741.2 cents. Repeated iterations of this interval generates <a class="wiki_link" href="/MOSScales">Moment of Symmetry</a> scales with near-phi relationships between the step sizes.<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h3> --><h3 id="toc0"><a name="x--Approximations to Just Intonation"></a><!-- ws:end:WikiTextHeadingRule:0 -->Approximations to Just Intonation</h3>
Like <a class="wiki_link" href="/17edo">17edo</a>, 34edo contains workable approximations of just intervals involving 13 and 3 -- specifically, 13/8, 13/12, 13/9 and their inversions -- while failing to closely approximate ratios of 7 or 11. 34edo adds ratios of 5 into the mix, including: 5/4, 6/5, 9/5, 15/8, 13/10, 15/13, and their inversions. Since it distinguishes between 9/8 and 10/9 (exaggerating the difference between them, the syntonic comma of 81/80, from 21.5 cents to 35.3 cents), it is suitable for 5-limit JI. It is not a meantone system.<br />
<br />
<em>Viewed in light of Western diatonic theory, the three extra steps (of 34-et compared to 31-et) in effect widen the intervals between C and D, F and G, and A and B, thus making a distinction between major tones, ratio 9/8 and minor tones, ratio 10/9.</em> (<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/34_equal_temperament" rel="nofollow">Wikipedia</a>)<br />
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<!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x--Intervals:"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals:</h3>
<table class="wiki_table">
<tr>
<td>degrees of 34edo<br />
</td>
<td>cents<br />
</td>
</tr>
<tr>
<td>0<br />
</td>
<td>0.0<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>35.3<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>70.6<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>105.9<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>141.2<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>176.5<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>211.8<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>247.1<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>282.4<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>317.6<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>352.9<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>388.2<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>423.5<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>458.8<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>494.1<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>529.4<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>564.7<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>600.0<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>635.3<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>670.6<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>705.9<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>741.2<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>776.5<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>811.8<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>847.1<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>882.4<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>917.6<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>952.9<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>988.2<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>1023.5<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>1058.8<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>1094.1<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>1129.4<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>1164.7<br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x-Listen"></a><!-- ws:end:WikiTextHeadingRule:4 -->Listen</h2>
<ul><li><a class="wiki_link_ext" href="http://www.archive.org/details/Ascension_105" rel="nofollow" target="_blank">Ascension</a></li></ul>Drums Bass and 34-tone guitar</body></html>