33edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 448613110 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 448613220 - 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:genewardsmith|genewardsmith]] and made on <tt>2013-09-04 16: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-09-04 16:56:07 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>448613220</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The //33 equal division// divides the [[octave]] into 33 equal parts of 36.3636 [[cent]]s each. It is not especially good at representing all rational intervals in the [[7-limit]], but it does very well on the 7-limit [[k*N subgroups|3*33 subgroup]] 2.27.15.21.11.13. On this subgroup it tunes things to the same tuning as [[99edo]], and as a subgroup patent val it tempers out the same commas. The 99 equal temperaments hemififths, amity, parakleismic, hemiwuerschmidt, ennealimmal and hendecatonic can be reduced to this subgroup and give various possibilities for MOS scales, etc. In particular, the [[Chromatic | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The //33 equal division// divides the [[octave]] into 33 equal parts of 36.3636 [[cent]]s each. It is not especially good at representing all rational intervals in the [[7-limit]], but it does very well on the 7-limit [[k*N subgroups|3*33 subgroup]] 2.27.15.21.11.13. On this subgroup it tunes things to the same tuning as [[99edo]], and as a subgroup patent val it tempers out the same commas. The 99 equal temperaments hemififths, amity, parakleismic, hemiwuerschmidt, ennealimmal and hendecatonic can be reduced to this subgroup and give various possibilities for MOS scales, etc. In particular, the [[Chromatic pairs#Terrain|terrain]] subgroup temperament can be tuned via the 5\33 generator. The full system of harmony provides the optimal patent val for [[Mint temperaments#Slurpee|slurpee temperament]] in the 5, 7, 11 and 13 limits. | ||
While relatively uncommon, 33edo is actually quite an interesting system. As a multiple of [[11edo]], it approximates the 7th and 11th harmonics via Andrew Heathwaite's 4L+3s Orgone modes (see [[26edo]]). 33edo also tunes the 13th harmonic slightly flat, allowing it to approximate the 21st and 17th harmonics as well, having an [[3L 7s|3L+7s]] of L=4 s=3. It tunes the perfect fifth about 11 cent flat, leading to a near perfect 10/9. The <33 52 76| or 33c val tempers out 81/80 and so leads to a very flat meantone tuning where the major tone is approximately 10/9 in size. Leaving the scale be would result in a flattone [[5L 2s|5L+2s]] of L=5 s=4 | While relatively uncommon, 33edo is actually quite an interesting system. As a multiple of [[11edo]], it approximates the 7th and 11th harmonics via Andrew Heathwaite's 4L+3s Orgone modes (see [[26edo]]). 33edo also tunes the 13th harmonic slightly flat, allowing it to approximate the 21st and 17th harmonics as well, having an [[3L 7s|3L+7s]] of L=4 s=3. It tunes the perfect fifth about 11 cent flat, leading to a near perfect 10/9. The <33 52 76| or 33c val tempers out 81/80 and so leads to a very flat meantone tuning where the major tone is approximately 10/9 in size. Leaving the scale be would result in a flattone [[5L 2s|5L+2s]] of L=5 s=4 | ||
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[[http://chrisvaisvil.com/5-5-1-mode-of-33-equal-with-video/|5 5 1 mode of 33 equal (with video)]] [[http://micro.soonlabel.com/33edo/20130827_551of33.mp3|play]] by [[Chris Vaisvil]]</pre></div> | [[http://chrisvaisvil.com/5-5-1-mode-of-33-equal-with-video/|5 5 1 mode of 33 equal (with video)]] [[http://micro.soonlabel.com/33edo/20130827_551of33.mp3|play]] by [[Chris Vaisvil]]</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>33edo</title></head><body>The <em>33 equal division</em> divides the <a class="wiki_link" href="/octave">octave</a> into 33 equal parts of 36.3636 <a class="wiki_link" href="/cent">cent</a>s each. It is not especially good at representing all rational intervals in the <a class="wiki_link" href="/7-limit">7-limit</a>, but it does very well on the 7-limit <a class="wiki_link" href="/k%2AN%20subgroups">3*33 subgroup</a> 2.27.15.21.11.13. On this subgroup it tunes things to the same tuning as <a class="wiki_link" href="/99edo">99edo</a>, and as a subgroup patent val it tempers out the same commas. The 99 equal temperaments hemififths, amity, parakleismic, hemiwuerschmidt, ennealimmal and hendecatonic can be reduced to this subgroup and give various possibilities for MOS scales, etc. In particular, the | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>33edo</title></head><body>The <em>33 equal division</em> divides the <a class="wiki_link" href="/octave">octave</a> into 33 equal parts of 36.3636 <a class="wiki_link" href="/cent">cent</a>s each. It is not especially good at representing all rational intervals in the <a class="wiki_link" href="/7-limit">7-limit</a>, but it does very well on the 7-limit <a class="wiki_link" href="/k%2AN%20subgroups">3*33 subgroup</a> 2.27.15.21.11.13. On this subgroup it tunes things to the same tuning as <a class="wiki_link" href="/99edo">99edo</a>, and as a subgroup patent val it tempers out the same commas. The 99 equal temperaments hemififths, amity, parakleismic, hemiwuerschmidt, ennealimmal and hendecatonic can be reduced to this subgroup and give various possibilities for MOS scales, etc. In particular, the <a class="wiki_link" href="/Chromatic%20pairs#Terrain">terrain</a> subgroup temperament can be tuned via the 5\33 generator. The full system of harmony provides the optimal patent val for <a class="wiki_link" href="/Mint%20temperaments#Slurpee">slurpee temperament</a> in the 5, 7, 11 and 13 limits.<br /> | ||
<br /> | <br /> | ||
While relatively uncommon, 33edo is actually quite an interesting system. As a multiple of <a class="wiki_link" href="/11edo">11edo</a>, it approximates the 7th and 11th harmonics via Andrew Heathwaite's 4L+3s Orgone modes (see <a class="wiki_link" href="/26edo">26edo</a>). 33edo also tunes the 13th harmonic slightly flat, allowing it to approximate the 21st and 17th harmonics as well, having an <a class="wiki_link" href="/3L%207s">3L+7s</a> of L=4 s=3. It tunes the perfect fifth about 11 cent flat, leading to a near perfect 10/9. The &lt;33 52 76| or 33c val tempers out 81/80 and so leads to a very flat meantone tuning where the major tone is approximately 10/9 in size. Leaving the scale be would result in a flattone <a class="wiki_link" href="/5L%202s">5L+2s</a> of L=5 s=4<br /> | While relatively uncommon, 33edo is actually quite an interesting system. As a multiple of <a class="wiki_link" href="/11edo">11edo</a>, it approximates the 7th and 11th harmonics via Andrew Heathwaite's 4L+3s Orgone modes (see <a class="wiki_link" href="/26edo">26edo</a>). 33edo also tunes the 13th harmonic slightly flat, allowing it to approximate the 21st and 17th harmonics as well, having an <a class="wiki_link" href="/3L%207s">3L+7s</a> of L=4 s=3. It tunes the perfect fifth about 11 cent flat, leading to a near perfect 10/9. The &lt;33 52 76| or 33c val tempers out 81/80 and so leads to a very flat meantone tuning where the major tone is approximately 10/9 in size. Leaving the scale be would result in a flattone <a class="wiki_link" href="/5L%202s">5L+2s</a> of L=5 s=4<br /> | ||