34edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:~~guest~~|~~guest~~]] and made on <tt>2010-11-~~02 16~~:48:27 UTC</tt>.<br>

: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2010-11-03 04:29:40 UTC</tt>.<br>

: The original revision id was <tt>~~175825239~~</tt>.<br>

: The original revision id was <tt>175967555</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>

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===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.

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|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]])

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<br />

<h3 id="toc0"><a name="x--Approximations to Just Intonation"></a>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 />

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 <a class="wiki_link" href="/meantone">meantone </a>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 />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:guest|guest]] and made on <tt>2010-11-02 16:48:27 UTC</tt>.<br>
+: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2010-11-03 04:29:40 UTC</tt>.<br>
-: The original revision id was <tt>175825239</tt>.<br>
+: The original revision id was <tt>175967555</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>
@@ Line 10: / Line 10: @@
 ===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.
+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|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]])
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 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc0"&gt;&lt;a name="x--Approximations to Just Intonation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Approximations to Just Intonation&lt;/h3&gt;
-  Like &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt;, 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.&lt;br /&gt;
+  Like &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt;, 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 &lt;a class="wiki_link" href="/meantone"&gt;meantone &lt;/a&gt;system.&lt;br /&gt;
 &lt;br /&gt;
 &lt;em&gt;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.&lt;/em&gt; (&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/34_equal_temperament" rel="nofollow"&gt;Wikipedia&lt;/a&gt;)&lt;br /&gt;