5edo: Difference between revisions
Wikispaces>hstraub **Imported revision 25656259 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 144739479 - 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: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-05-25 22:35:35 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>144739479</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> | ||
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If 5-edo is regarded as a temperament, which is to say as 5-et, then the most salient fact is that 16/15 is tempered out. This means in 5-et the major third and the fourth, and the minor sixth and the fifth, are not distinguished. This is at the very edge what can sensibly be called temperament, but it does make sense and can be used. | If 5-edo is regarded as a temperament, which is to say as 5-et, then the most salient fact is that 16/15 is tempered out. This means in 5-et the major third and the fourth, and the minor sixth and the fifth, are not distinguished. This is at the very edge what can sensibly be called temperament, but it does make sense and can be used. | ||
Also tempered out is 27/25, leading to [[beep temperament]], which equates 10/9 with 6/5: it is a little more perverse even than [[father temperament|father]]. Because these intervals are so large, this sort of analysis is less significant with 5 than it becomes with larger and more accurate divisions, but it still plays a role. | Also tempered out is 27/25, leading to [[beep temperament]], which equates 10/9 with 6/5: it is a little more perverse even than [[father temperament|father]]. Because these intervals are so large, this sort of analysis is less significant with 5 than it becomes with larger and more accurate divisions, but it still plays a role. For example, I-IV-V-I is the same as 1-III-V-I and involves triads with common intervals because of fourth-thirds equivalence. | ||
// | Despite its lack of accuracy, 5EDO is the second Zeta function integral tuning, after 2EDO. See http://www.research.att.com/~njas/sequences/A117538 | ||
==Cycles, Divisions== | ==Cycles, Divisions== | ||
5 is a prime number | 5 is a prime number so 5-edo contains no sub-edos. Only simple cycles: | ||
Cycle of seconds: 0-1-2-3-4-0 | Cycle of seconds: 0-1-2-3-4-0 | ||
Cycle of fourths: 0-2-4-1-3-0 | Cycle of fourths: 0-2-4-1-3-0 | ||
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If 5-edo is regarded as a temperament, which is to say as 5-et, then the most salient fact is that 16/15 is tempered out. This means in 5-et the major third and the fourth, and the minor sixth and the fifth, are not distinguished. This is at the very edge what can sensibly be called temperament, but it does make sense and can be used.<br /> | If 5-edo is regarded as a temperament, which is to say as 5-et, then the most salient fact is that 16/15 is tempered out. This means in 5-et the major third and the fourth, and the minor sixth and the fifth, are not distinguished. This is at the very edge what can sensibly be called temperament, but it does make sense and can be used.<br /> | ||
<br /> | <br /> | ||
Also tempered out is 27/25, leading to <a class="wiki_link" href="/beep%20temperament">beep temperament</a>, which equates 10/9 with 6/5: it is a little more perverse even than <a class="wiki_link" href="/father%20temperament">father</a>. Because these intervals are so large, this sort of analysis is less significant with 5 than it becomes with larger and more accurate divisions, but it still plays a role.<br /> | Also tempered out is 27/25, leading to <a class="wiki_link" href="/beep%20temperament">beep temperament</a>, which equates 10/9 with 6/5: it is a little more perverse even than <a class="wiki_link" href="/father%20temperament">father</a>. Because these intervals are so large, this sort of analysis is less significant with 5 than it becomes with larger and more accurate divisions, but it still plays a role. For example, I-IV-V-I is the same as 1-III-V-I and involves triads with common intervals because of fourth-thirds equivalence.<br /> | ||
<br /> | <br /> | ||
< | Despite its lack of accuracy, 5EDO is the second Zeta function integral tuning, after 2EDO. See <!-- ws:start:WikiTextUrlRule:249:http://www.research.att.com/~njas/sequences/A117538 --><a class="wiki_link_ext" href="http://www.research.att.com/~njas/sequences/A117538" rel="nofollow">http://www.research.att.com/~njas/sequences/A117538</a><!-- ws:end:WikiTextUrlRule:249 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x5 Equal Divisions of the Octave: Theory-Cycles, Divisions"></a><!-- ws:end:WikiTextHeadingRule:10 -->Cycles, Divisions</h2> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x5 Equal Divisions of the Octave: Theory-Cycles, Divisions"></a><!-- ws:end:WikiTextHeadingRule:10 -->Cycles, Divisions</h2> | ||
5 is a prime number | 5 is a prime number so 5-edo contains no sub-edos. Only simple cycles:<br /> | ||
Cycle of seconds: 0-1-2-3-4-0<br /> | Cycle of seconds: 0-1-2-3-4-0<br /> | ||
Cycle of fourths: 0-2-4-1-3-0<br /> | Cycle of fourths: 0-2-4-1-3-0<br /> | ||