43edo: 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:MasonGreen1|MasonGreen1]] and made on <tt>2016-03-31 14:05:43 UTC</tt>.<br>

: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-03-31 14:46:42 UTC</tt>.<br>

: The original revision id was <tt>~~578782455~~</tt>.<br>

: The original revision id was <tt>578787405</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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43edo is the 14th [[prime numbers|prime]] edo, following [[41edo]] and coming before [[47edo]].

Although not [[consistency|consistent]], it performs quite decently in very high limits. It has unambiguous mappings for all prime harmonics up to //64//, with the sole exceptions of 23 and, perhaps, 41. The mappings for composite harmonics can then be derived from those for the primes, giving a version of mode 32 of the harmonic series, although the aforementioned lack of consistency will give some unusual results. Indeed, the step size of 43edo is very close to the septimal comma (64:63), while two steps is close to 32:31, and four steps to 16:15.

Although not [[consistency|consistent]], it performs quite decently in very high limits. It has unambiguous mappings for all prime harmonics up to //64//, with the sole exceptions of 23 and, perhaps, 41. The mappings for composite harmonics can then be derived from those for the primes, giving an almost-complete version of mode 32 of the harmonic series, although the aforementioned lack of consistency will give some unusual results. Indeed, the step size of 43edo is very close to the septimal comma (64:63), while two steps is close to 32:31, and four steps to 16:15.

==Intervals==

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|| 41 || 1144.186 || ||

|| 42 || 1172.093 || ||

==Notation of 43edo==

Because 43edo is a meantone system, this makes it easier to adapt traditional Western notation to it than to some other tunings. A# and Bb are distinct and the distance between them is one meride. The whole tone is divided into seven merides so this means we can use "third-sharps", "two-thirds-sharps", "third-flats", and "two-thirds-flats" to reach the remaining notes between A and B; notes elsewhere on the scale can be notated similarly.

Alternatively, a red-note/blue-note system (similar to that proposed for sixth-tones/[[36edo]]) can be used. Now we have the following sequence of notes, each separated by one meride: A, red A, blue A#, A#, Bb, red Bb, blue B, B. (Note that there are red flats and blue sharps, but no red sharps or blue flats).

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43edo is the 14th <a class="wiki_link" href="/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="/41edo">41edo</a> and coming before <a class="wiki_link" href="/47edo">47edo</a>.<br />

<br />

Although not <a class="wiki_link" href="/consistency">consistent</a>, it performs quite decently in very high limits. It has unambiguous mappings for all prime harmonics up to <em>64</em>, with the sole exceptions of 23 and, perhaps, 41. The mappings for composite harmonics can then be derived from those for the primes, giving a version of mode 32 of the harmonic series, although the aforementioned lack of consistency will give some unusual results. Indeed, the step size of 43edo is very close to the septimal comma (64:63), while two steps is close to 32:31, and four steps to 16:15.<br />

Although not <a class="wiki_link" href="/consistency">consistent</a>, it performs quite decently in very high limits. It has unambiguous mappings for all prime harmonics up to <em>64</em>, with the sole exceptions of 23 and, perhaps, 41. The mappings for composite harmonics can then be derived from those for the primes, giving an almost-complete version of mode 32 of the harmonic series, although the aforementioned lack of consistency will give some unusual results. Indeed, the step size of 43edo is very close to the septimal comma (64:63), while two steps is close to 32:31, and four steps to 16:15.<br />

<br />

<h2 id="toc2"><a name="x43 tone equal temperament-Intervals"></a>Intervals</h2>

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</table>

<br />

<h2 id="toc3"><a name="x43 tone equal temperament-Notation of 43edo"></a>Notation of 43edo</h2>

<br />

Because 43edo is a meantone system, this makes it easier to adapt traditional Western notation to it than to some other tunings. A# and Bb are distinct and the distance between them is one meride. The whole tone is divided into seven merides so this means we can use &quot;third-sharps&quot;, &quot;two-thirds-sharps&quot;, &quot;third-flats&quot;, and &quot;two-thirds-flats&quot; to reach the remaining notes between A and B; notes elsewhere on the scale can be notated similarly.<br />

<br />

Alternatively, a red-note/blue-note system (similar to that proposed for sixth-tones/<a class="wiki_link" href="/36edo">36edo</a>) can be used. Now we have the following sequence of notes, each separated by one meride: A, red A, blue A#, A#, Bb, red Bb, blue B, B. (Note that there are red flats and blue sharps, but no red sharps or blue flats).<br />

<br />

<a href="http://xenharmonic.wikispaces.com/file/view/43%20edo%20counterpoint.mid/311991536/43%20edo%20counterpoint.mid" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/43%20edo%20counterpoint.mid/311991536/43%20edo%20counterpoint.mid');">43 edo counterpoint.mid</a> <em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Kosmorsky/43%20edo%20counterpoint.mp3" rel="nofollow">mp3</a></em> Peter Kosmorsky (late 2011) (in meantone)</body></html></pre></div>

@@ 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:MasonGreen1|MasonGreen1]] and made on <tt>2016-03-31 14:05:43 UTC</tt>.<br>
+: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-03-31 14:46:42 UTC</tt>.<br>
-: The original revision id was <tt>578782455</tt>.<br>
+: The original revision id was <tt>578787405</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 16: / Line 16: @@
 edo is the 14th [[prime numbers|prime]] edo, following [[41edo]] and coming before [[47edo]].
-Although not [[consistency|consistent]], it performs quite decently in very high limits. It has unambiguous mappings for all prime harmonics up to //64//, with the sole exceptions of 23 and, perhaps, 41. The mappings for composite harmonics can then be derived from those for the primes, giving a version of mode 32 of the harmonic series, although the aforementioned lack of consistency will give some unusual results. Indeed, the step size of 43edo is very close to the septimal comma (64:63), while two steps is close to 32:31, and four steps to 16:15.
+Although not [[consistency|consistent]], it performs quite decently in very high limits. It has unambiguous mappings for all prime harmonics up to //64//, with the sole exceptions of 23 and, perhaps, 41. The mappings for composite harmonics can then be derived from those for the primes, giving an almost-complete version of mode 32 of the harmonic series, although the aforementioned lack of consistency will give some unusual results. Indeed, the step size of 43edo is very close to the septimal comma (64:63), while two steps is close to 32:31, and four steps to 16:15.
 ==Intervals==
@@ Line 64: / Line 64: @@
 || 41 || 1144.186 ||   ||
 || 42 || 1172.093 ||   ||
+==Notation of 43edo==
+Because 43edo is a meantone system, this makes it easier to adapt traditional Western notation to it than to some other tunings. A# and Bb are distinct and the distance between them is one meride. The whole tone is divided into seven merides so this means we can use "third-sharps", "two-thirds-sharps", "third-flats", and "two-thirds-flats" to reach the remaining notes between A and B; notes elsewhere on the scale can be notated similarly.
+Alternatively, a red-note/blue-note system (similar to that proposed for sixth-tones/[[36edo]]) can be used. Now we have the following sequence of notes, each separated by one meride: A, red A, blue A#, A#, Bb, red Bb, blue B, B. (Note that there are red flats and blue sharps, but no red sharps or blue flats).
@@ Line 78: / Line 84: @@
 edo is the 14th &lt;a class="wiki_link" href="/prime%20numbers"&gt;prime&lt;/a&gt; edo, following &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt; and coming before &lt;a class="wiki_link" href="/47edo"&gt;47edo&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
-Although not &lt;a class="wiki_link" href="/consistency"&gt;consistent&lt;/a&gt;, it performs quite decently in very high limits. It has unambiguous mappings for all prime harmonics up to &lt;em&gt;64&lt;/em&gt;, with the sole exceptions of 23 and, perhaps, 41. The mappings for composite harmonics can then be derived from those for the primes, giving a version of mode 32 of the harmonic series, although the aforementioned lack of consistency will give some unusual results. Indeed, the step size of 43edo is very close to the septimal comma (64:63), while two steps is close to 32:31, and four steps to 16:15.&lt;br /&gt;
+Although not &lt;a class="wiki_link" href="/consistency"&gt;consistent&lt;/a&gt;, it performs quite decently in very high limits. It has unambiguous mappings for all prime harmonics up to &lt;em&gt;64&lt;/em&gt;, with the sole exceptions of 23 and, perhaps, 41. The mappings for composite harmonics can then be derived from those for the primes, giving an almost-complete version of mode 32 of the harmonic series, although the aforementioned lack of consistency will give some unusual results. Indeed, the step size of 43edo is very close to the septimal comma (64:63), while two steps is close to 32:31, and four steps to 16:15.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x43 tone equal temperament-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Intervals&lt;/h2&gt;
@@ Line 439: / Line 445: @@
 &lt;/table&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x43 tone equal temperament-Notation of 43edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Notation of 43edo&lt;/h2&gt;
+ &lt;br /&gt;
+Because 43edo is a meantone system, this makes it easier to adapt traditional Western notation to it than to some other tunings. A# and Bb are distinct and the distance between them is one meride. The whole tone is divided into seven merides so this means we can use &amp;quot;third-sharps&amp;quot;, &amp;quot;two-thirds-sharps&amp;quot;, &amp;quot;third-flats&amp;quot;, and &amp;quot;two-thirds-flats&amp;quot; to reach the remaining notes between A and B; notes elsewhere on the scale can be notated similarly.&lt;br /&gt;
+&lt;br /&gt;
+Alternatively, a red-note/blue-note system (similar to that proposed for sixth-tones/&lt;a class="wiki_link" href="/36edo"&gt;36edo&lt;/a&gt;) can be used. Now we have the following sequence of notes, each separated by one meride: A, red A, blue A#, A#, Bb, red Bb, blue B, B. (Note that there are red flats and blue sharps, but no red sharps or blue flats).&lt;br /&gt;
 &lt;br /&gt;
 &lt;br /&gt;
 &lt;a href="http://xenharmonic.wikispaces.com/file/view/43%20edo%20counterpoint.mid/311991536/43%20edo%20counterpoint.mid" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/43%20edo%20counterpoint.mid/311991536/43%20edo%20counterpoint.mid');"&gt;43 edo counterpoint.mid&lt;/a&gt; &lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Kosmorsky/43%20edo%20counterpoint.mp3" rel="nofollow"&gt;mp3&lt;/a&gt;&lt;/em&gt; Peter Kosmorsky (late 2011) (in meantone)&lt;/body&gt;&lt;/html&gt;</pre></div>