34edo: Difference between revisions

: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2013-11-17 22:04:10 UTC</tt>.<br>

: The original revision id was <tt>469917004</tt>.<br>

Like [[xenharmonic/17edo|17edo]], 34edo contains good 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 -- as well as 17 -- including 17/16, 18/17, 17/12, 17/10, 17/13, 17/15 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 [[xenharmonic/meantone|meantone ]]system.

|| 0 || do || 0.0 || 1/1 ||  || C ||

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 adds up to a minor third away. This has led certain complainers, aiming to notate 17 edo (which is relatively popular), to want an extra modifying mark to raise something a small step of which. The 34 tone equal temperament, however, can be constructed from two equally spaced 17-note scales: a symbol indicating an adjustment of 1/34 up or down can also serves the purpose of the previous sentence, by using two of it. This of course emphasizes certain aspects of 34-edo which may not be most efficient for some musical purposes. The reader can easily construct a notation. One concern is that a system with 15 nominals for example, instead of seven, might be waste - of paper, space, brainmemory etc. if they aren't used consecutively and frequently. The system spelled out here has familiarity as an advantage or disadvantage. Tangentially, while the table uses ^ and v for "up" and "down", Kosmorosky prefers using filled in triangles because that's what I decided on years ago, and he's one of a handful of people worldwide who uses the tuning extensively, as far as I know, but whatever, I can't hit you through a computer if you use alternate symbols!

* [[@http://www.archive.org/details/Ascension_105|Ascension]] (drums, bass, and 34-tone guitar)

* [[http://www.microstick.net/34guitararticle.htm|34 Equal Guitar]] by [[xenharmonic/Larry Hanson|Larry Hanson]]</pre></div>

  Like &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/17edo"&gt;17edo&lt;/a&gt;, 34edo contains good 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 -- as well as 17 -- including 17/16, 18/17, 17/12, 17/10, 17/13, 17/15 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="http://xenharmonic.wikispaces.com/meantone"&gt;meantone &lt;/a&gt;system.&lt;br /&gt;

         &lt;td&gt;C&lt;br /&gt;

  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 adds up to a minor third away. This has led certain complainers, aiming to notate 17 edo (which is relatively popular), to want an extra modifying mark to raise something a small step of which. The 34 tone equal temperament, however, can be constructed from two equally spaced 17-note scales: a symbol indicating an adjustment of 1/34 up or down can also serves the purpose of the previous sentence, by using two of it. This of course emphasizes certain aspects of 34-edo which may not be most efficient for some musical purposes. The reader can easily construct a notation. One concern is that a system with 15 nominals for example, instead of seven, might be waste - of paper, space, brainmemory etc. if they aren't used consecutively and frequently. The system spelled out here has familiarity as an advantage or disadvantage. Tangentially, while the table uses ^ and v for &amp;quot;up&amp;quot; and &amp;quot;down&amp;quot;, Kosmorosky prefers using filled in triangles because that's what I decided on years ago, and he's one of a handful of people worldwide who uses the tuning extensively, as far as I know, but whatever, I can't hit you through a computer if you use alternate symbols!&lt;br /&gt;

  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.archive.org/details/Ascension_105" rel="nofollow" target="_blank"&gt;Ascension&lt;/a&gt; (drums, bass, and 34-tone guitar)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="https://www.youtube.com/watch?v=FXTM0HeuExk" rel="nofollow" target="_blank"&gt;Uncomfortable In Crowds (extended)&lt;/a&gt; by Robin Perry&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x-Links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Links&lt;/h2&gt;

  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.microstick.net/34guitararticle.htm" rel="nofollow"&gt;34 Equal Guitar&lt;/a&gt; by &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Larry%20Hanson"&gt;Larry Hanson&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>