43edo: Difference between revisions
Wikispaces>MasonGreen1 **Imported revision 578793765 - Original comment: ** |
Wikispaces>MasonGreen1 **Imported revision 578795311 - 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:MasonGreen1|MasonGreen1]] and made on <tt>2016-03-31 15: | : This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-03-31 15:54:00 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>578795311</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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43edo is the 14th [[prime numbers|prime]] edo, following [[41edo]] and coming before [[47edo]]. | 43edo is the 14th [[prime numbers|prime]] edo, following [[41edo]] and coming before [[47edo]]. | ||
Compared to [[31edo]], 43edo sacrifices some accuracy in the 7 | |||
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. | 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. | ||
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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, because the latter are enharmonically equivalent to simpler notes: blue Bb is actually just A#, for instance). | 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, because the latter are enharmonically equivalent to simpler notes: blue Bb is actually just A#, for instance). | ||
The diatonic semitone is four steps, so for the region between B and C (or, E and F), we can use: B, Cb, red Cb/blue B# (they are enharmonic equivalents), B#, and C. All of the notes in 43edo therefore have unambiguous names except for two: red Cb/blue B#, and red Fb/blue E#. It might also be possible to design special symbols for those two notes (resembling a cross between the letters B and C in the former case, and E and F in the latter). | The diatonic semitone is four steps, so for the region between B and C (or, E and F), we can use: B, Cb, red Cb/blue B# (//they are enharmonic equivalents//), B#, and C. All of the notes in 43edo therefore have unambiguous names except for two: red Cb/blue B#, and red Fb/blue E#. It might also be possible to design special symbols for those two notes (resembling a cross between the letters B and C in the former case, and E and F in the latter). | ||
If red Cb and blue B# (and red Fb/Blue E#) are instead forced to be distinct, but the requirement that all notes be equally spaced is maintained, then we end up with a //completely// unambiguous red-note/blue-note notation for [[45edo]], which is another meantone (actually, a [[flattone]]) system. | |||
[[file:xenharmonic/43 edo counterpoint.mid|43 edo counterpoint.mid]] //[[http://micro.soonlabel.com/gene_ward_smith/Others/Kosmorsky/43%20edo%20counterpoint.mp3|mp3]]// Peter Kosmorsky (late 2011) (in meantone)</pre></div> | [[file:xenharmonic/43 edo counterpoint.mid|43 edo counterpoint.mid]] //[[http://micro.soonlabel.com/gene_ward_smith/Others/Kosmorsky/43%20edo%20counterpoint.mp3|mp3]]// Peter Kosmorsky (late 2011) (in meantone)</pre></div> | ||
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<br /> | <br /> | ||
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 /> | 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 /> | |||
Compared to <a class="wiki_link" href="/31edo">31edo</a>, 43edo sacrifices some accuracy in the 7<br /> | |||
<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 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 /> | 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 /> | ||
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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, because the latter are enharmonically equivalent to simpler notes: blue Bb is actually just A#, for instance).<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, because the latter are enharmonically equivalent to simpler notes: blue Bb is actually just A#, for instance).<br /> | ||
<br /> | <br /> | ||
The diatonic semitone is four steps, so for the region between B and C (or, E and F), we can use: B, Cb, red Cb/blue B# (they are enharmonic equivalents), B#, and C. All of the notes in 43edo therefore have unambiguous names except for two: red Cb/blue B#, and red Fb/blue E#. It might also be possible to design special symbols for those two notes (resembling a cross between the letters B and C in the former case, and E and F in the latter).<br /> | The diatonic semitone is four steps, so for the region between B and C (or, E and F), we can use: B, Cb, red Cb/blue B# (<em>they are enharmonic equivalents</em>), B#, and C. All of the notes in 43edo therefore have unambiguous names except for two: red Cb/blue B#, and red Fb/blue E#. It might also be possible to design special symbols for those two notes (resembling a cross between the letters B and C in the former case, and E and F in the latter).<br /> | ||
<br /> | |||
If red Cb and blue B# (and red Fb/Blue E#) are instead forced to be distinct, but the requirement that all notes be equally spaced is maintained, then we end up with a <em>completely</em> unambiguous red-note/blue-note notation for <a class="wiki_link" href="/45edo">45edo</a>, which is another meantone (actually, a <a class="wiki_link" href="/flattone">flattone</a>) system.<br /> | |||
<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> | <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> | ||