34edo: Difference between revisions

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-03-28 21:32:52 UTC</tt>.<br>

: The original revision id was <tt>545669406</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. In layman's terms while no number of fifths (frequently ratios of ~3:2) land on major or minor thirds, an even number of major or minor thirds, technically will be the same pitch as something, somewhere upon the cycle of seventeen fifths.

*The sharpness of ~13 cents of 11/8 can fit somewhat with the 9/8 and 13/8 which both are about 7 cents sharp. Likewise the 16-cent flatness of the 27\34 approximation to 7/4 isn't impossible. The ability to tolerate these errors may depend on subtle natural changes in mood. [[68edo]], double 34, has both these intervals in more perfect form.

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 character 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 also serves the purpose of the previous sentence, by using two of it. This systemology of course emphasizes certain aspects of 34-edo which may not be most efficient expressions of some musical purposes: The reader can easily construct his own 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 to reserve /\ and \/ as adjustments by 1/68 octave.

  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 &amp;quot;syntonic comma&amp;quot; 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. In layman's terms while no number of fifths (frequently ratios of ~3:2) land on major or minor thirds, an even number of major or minor thirds, technically will be the same pitch as something, somewhere upon the cycle of seventeen fifths.&lt;br /&gt;

*The sharpness of ~13 cents of 11/8 can fit somewhat with the 9/8 and 13/8 which both are about 7 cents sharp. Likewise the 16-cent flatness of the 27\34 approximation to 7/4 isn't impossible. The ability to tolerate these errors may depend on subtle natural changes in mood. &lt;a class="wiki_link" href="/68edo"&gt;68edo&lt;/a&gt;, double 34, has both these intervals in more perfect form.&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 character 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 also serves the purpose of the previous sentence, by using two of it. This systemology of course emphasizes certain aspects of 34-edo which may not be most efficient expressions of some musical purposes: The reader can easily construct his own 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 to reserve /\ and \/ as adjustments by 1/68 octave.&lt;br /&gt;