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Wikispaces>genewardsmith **Imported revision 312141768 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 312142276 - Original comment: ** |
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| Line 1: | Line 1: | ||
<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>2012-03-18 15: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-03-18 15:21:58 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>312142276</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> | ||
| Line 20: | Line 20: | ||
|| Degrees of 43-EDO || Cents value || | || Degrees of 43-EDO || Cents value || | ||
|| 0 || 0 || | || 0 || 0 || | ||
|| 1 || 27 | || 1 || 27.907 || | ||
|| 2 || 55 | || 2 || 55.814 || | ||
|| 3 || 83 | || 3 || 83.721 || | ||
|| 4 || 111 | || 4 || 111.628 || | ||
|| 5 || 139 | || 5 || 139.535 || | ||
|| 6 || 167 | || 6 || 167.442 || | ||
|| 7 || 195 | || 7 || 195.349 || | ||
|| 8 || 223 | || 8 || 223.256 || | ||
|| 9 || 251 | || 9 || 251.163 || | ||
|| 10 || 279 | || 10 || 279.07 || | ||
|| 11 || 306 | || 11 || 306.977 || | ||
|| 12 || 334 | || 12 || 334.884 || | ||
|| 13 || 362 | || 13 || 362.791 || | ||
|| 14 || 390 | || 14 || 390.698 || | ||
|| 15 || 418 | || 15 || 418.605 || | ||
|| 16 || 446 | || 16 || 446.512 || | ||
|| 17 || 474 | || 17 || 474.419 || | ||
|| 18 || 502 | || 18 || 502.326 || | ||
|| 19 || 530 | || 19 || 530.233 || | ||
|| 20 || 558 | || 20 || 558.139 || | ||
|| 21 || 586 | || 21 || 586.046 || | ||
|| 22 || 613 | || 22 || 613.953 || | ||
|| 23 || 641 | || 23 || 641.86 || | ||
|| 24 || 669 | || 24 || 669.767 || | ||
|| 25 || 697 | || 25 || 697.674 || | ||
|| 26 || 725 | || 26 || 725.581 || | ||
|| 27 || 753 | || 27 || 753.488 || | ||
|| 28 || 781 | || 28 || 781.395 || | ||
|| 29 || 809 | || 29 || 809.302 || | ||
|| 30 || 837 | || 30 || 837.209 || | ||
|| 31 || 865 | || 31 || 865.116 || | ||
|| 32 || 893 | || 32 || 893.023 || | ||
|| 33 || 920 | || 33 || 920.93 || | ||
|| 34 || 948 | || 34 || 948.837 || | ||
|| 35 || 976 | || 35 || 976.744 || | ||
|| 36 || 1004 | || 36 || 1004.651 || | ||
|| 37 || 1032 | || 37 || 1032.558 || | ||
|| 38 || 1060 | || 38 || 1060.465 || | ||
|| 39 || 1088 | || 39 || 1088.372 || | ||
|| 40 || 1116 | || 40 || 1116.279 || | ||
|| 41 || 1144 | || 41 || 1144.186 || | ||
|| 42 || 1172 | || 42 || 1172.093 || | ||
| Line 96: | Line 96: | ||
<td>1<br /> | <td>1<br /> | ||
</td> | </td> | ||
<td>27 | <td>27.907<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 102: | Line 102: | ||
<td>2<br /> | <td>2<br /> | ||
</td> | </td> | ||
<td>55 | <td>55.814<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 108: | Line 108: | ||
<td>3<br /> | <td>3<br /> | ||
</td> | </td> | ||
<td>83 | <td>83.721<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 114: | Line 114: | ||
<td>4<br /> | <td>4<br /> | ||
</td> | </td> | ||
<td>111 | <td>111.628<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 120: | Line 120: | ||
<td>5<br /> | <td>5<br /> | ||
</td> | </td> | ||
<td>139 | <td>139.535<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 126: | Line 126: | ||
<td>6<br /> | <td>6<br /> | ||
</td> | </td> | ||
<td>167 | <td>167.442<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 132: | Line 132: | ||
<td>7<br /> | <td>7<br /> | ||
</td> | </td> | ||
<td>195 | <td>195.349<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 138: | Line 138: | ||
<td>8<br /> | <td>8<br /> | ||
</td> | </td> | ||
<td>223 | <td>223.256<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 144: | Line 144: | ||
<td>9<br /> | <td>9<br /> | ||
</td> | </td> | ||
<td>251 | <td>251.163<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 150: | Line 150: | ||
<td>10<br /> | <td>10<br /> | ||
</td> | </td> | ||
<td>279 | <td>279.07<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 156: | Line 156: | ||
<td>11<br /> | <td>11<br /> | ||
</td> | </td> | ||
<td>306 | <td>306.977<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 162: | Line 162: | ||
<td>12<br /> | <td>12<br /> | ||
</td> | </td> | ||
<td>334 | <td>334.884<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 168: | Line 168: | ||
<td>13<br /> | <td>13<br /> | ||
</td> | </td> | ||
<td>362 | <td>362.791<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 174: | Line 174: | ||
<td>14<br /> | <td>14<br /> | ||
</td> | </td> | ||
<td>390 | <td>390.698<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 180: | Line 180: | ||
<td>15<br /> | <td>15<br /> | ||
</td> | </td> | ||
<td>418 | <td>418.605<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 186: | Line 186: | ||
<td>16<br /> | <td>16<br /> | ||
</td> | </td> | ||
<td>446 | <td>446.512<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 192: | Line 192: | ||
<td>17<br /> | <td>17<br /> | ||
</td> | </td> | ||
<td>474 | <td>474.419<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 198: | Line 198: | ||
<td>18<br /> | <td>18<br /> | ||
</td> | </td> | ||
<td>502 | <td>502.326<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 204: | Line 204: | ||
<td>19<br /> | <td>19<br /> | ||
</td> | </td> | ||
<td>530 | <td>530.233<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 210: | Line 210: | ||
<td>20<br /> | <td>20<br /> | ||
</td> | </td> | ||
<td>558 | <td>558.139<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 216: | Line 216: | ||
<td>21<br /> | <td>21<br /> | ||
</td> | </td> | ||
<td>586 | <td>586.046<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 222: | Line 222: | ||
<td>22<br /> | <td>22<br /> | ||
</td> | </td> | ||
<td>613 | <td>613.953<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 228: | Line 228: | ||
<td>23<br /> | <td>23<br /> | ||
</td> | </td> | ||
<td>641 | <td>641.86<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 234: | Line 234: | ||
<td>24<br /> | <td>24<br /> | ||
</td> | </td> | ||
<td>669 | <td>669.767<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 240: | Line 240: | ||
<td>25<br /> | <td>25<br /> | ||
</td> | </td> | ||
<td>697 | <td>697.674<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 246: | Line 246: | ||
<td>26<br /> | <td>26<br /> | ||
</td> | </td> | ||
<td>725 | <td>725.581<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 252: | Line 252: | ||
<td>27<br /> | <td>27<br /> | ||
</td> | </td> | ||
<td>753 | <td>753.488<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 258: | Line 258: | ||
<td>28<br /> | <td>28<br /> | ||
</td> | </td> | ||
<td>781 | <td>781.395<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 264: | Line 264: | ||
<td>29<br /> | <td>29<br /> | ||
</td> | </td> | ||
<td>809 | <td>809.302<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 270: | Line 270: | ||
<td>30<br /> | <td>30<br /> | ||
</td> | </td> | ||
<td>837 | <td>837.209<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 276: | Line 276: | ||
<td>31<br /> | <td>31<br /> | ||
</td> | </td> | ||
<td>865 | <td>865.116<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 282: | Line 282: | ||
<td>32<br /> | <td>32<br /> | ||
</td> | </td> | ||
<td>893 | <td>893.023<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 288: | Line 288: | ||
<td>33<br /> | <td>33<br /> | ||
</td> | </td> | ||
<td>920 | <td>920.93<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 294: | Line 294: | ||
<td>34<br /> | <td>34<br /> | ||
</td> | </td> | ||
<td>948 | <td>948.837<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 300: | Line 300: | ||
<td>35<br /> | <td>35<br /> | ||
</td> | </td> | ||
<td>976 | <td>976.744<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 306: | Line 306: | ||
<td>36<br /> | <td>36<br /> | ||
</td> | </td> | ||
<td>1004 | <td>1004.651<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 312: | Line 312: | ||
<td>37<br /> | <td>37<br /> | ||
</td> | </td> | ||
<td>1032 | <td>1032.558<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 318: | Line 318: | ||
<td>38<br /> | <td>38<br /> | ||
</td> | </td> | ||
<td>1060 | <td>1060.465<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 324: | Line 324: | ||
<td>39<br /> | <td>39<br /> | ||
</td> | </td> | ||
<td>1088 | <td>1088.372<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 330: | Line 330: | ||
<td>40<br /> | <td>40<br /> | ||
</td> | </td> | ||
<td>1116 | <td>1116.279<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 336: | Line 336: | ||
<td>41<br /> | <td>41<br /> | ||
</td> | </td> | ||
<td>1144 | <td>1144.186<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 342: | Line 342: | ||
<td>42<br /> | <td>42<br /> | ||
</td> | </td> | ||
<td>1172 | <td>1172.093<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Revision as of 15:21, 18 March 2012
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2012-03-18 15:21:58 UTC.
- The original revision id was 312142276.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
=<span style="color: #027bac; font-size: 103%;">43 tone equal temperament</span>= = = //43edo// divides the octave into 43 equal parts of 27.907 cents each. It is strongly associated with meantone temperament, particularly 1/5 comma meantone, being a good tuning system in the 5, 7, 11, and 13-limit. The version of 11-limit meantone is the one tempering out 99/98, 176/175 and 441/440 sometimes called Huygens. 43-equal has the first good 13-limit meantone available as an equal division of the octave. The baroque, french, ironically hearing and speech impaired acoustician [[@http://en.wikipedia.org/wiki/Joseph_Sauveur|Joseph Saveur]] based his system on 43 equal tones to the octave, calling them "merides". Further information: [[http://tonalsoft.com/enc/m/meride.aspx]] In the 13-limit, we get two versions of meantone equivalent in 43et, one, [[Meantone family#Septimal meantone-Unidecimal meantone aka Huygens-Meridetone|meridetone]], tempering out 78/77, the other, [[Meantone family#Septimal meantone-Unidecimal meantone aka Huygens-Grosstone|grosstone]], 144/143. Meridetone has generator mapping <0 1 4 10 18 27|, and grosstone <0 1 4 10 18 -16|; 43 supplies the optimal patent val for meridetone. The 43 patent val <43 68 100 121 149 169| maps 5 to 100 steps, allowing the divison of 5 into 20 equal parts, leading to [[Meantone family#Jerome|jerome temperament]], an interesting higher-limit system for which 43 supplies the optimal patent val in the 7, 11, 13, 17, 19 and 23 limits. It also provides the optimal patent val for 11- and 13-limit [[Marvel temperaments#Amavil|amavil temperament]], which is not a meantone temperament. 43edo is the 14th [[prime numbers|prime]] edo, following [[41edo]] and coming before [[47edo]]. ==Intervals== || Degrees of 43-EDO || Cents value || || 0 || 0 || || 1 || 27.907 || || 2 || 55.814 || || 3 || 83.721 || || 4 || 111.628 || || 5 || 139.535 || || 6 || 167.442 || || 7 || 195.349 || || 8 || 223.256 || || 9 || 251.163 || || 10 || 279.07 || || 11 || 306.977 || || 12 || 334.884 || || 13 || 362.791 || || 14 || 390.698 || || 15 || 418.605 || || 16 || 446.512 || || 17 || 474.419 || || 18 || 502.326 || || 19 || 530.233 || || 20 || 558.139 || || 21 || 586.046 || || 22 || 613.953 || || 23 || 641.86 || || 24 || 669.767 || || 25 || 697.674 || || 26 || 725.581 || || 27 || 753.488 || || 28 || 781.395 || || 29 || 809.302 || || 30 || 837.209 || || 31 || 865.116 || || 32 || 893.023 || || 33 || 920.93 || || 34 || 948.837 || || 35 || 976.744 || || 36 || 1004.651 || || 37 || 1032.558 || || 38 || 1060.465 || || 39 || 1088.372 || || 40 || 1116.279 || || 41 || 1144.186 || || 42 || 1172.093 || [[http://xenharmonic.wikispaces.com/file/view/43%20edo%20counterpoint.mid|43 edo counterpoint.mid]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Kosmorsky/43%20edo%20counterpoint.mp3|mp3]] Peter Kosmorsky (late 2011)
Original HTML content:
<html><head><title>43edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x43 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #027bac; font-size: 103%;">43 tone equal temperament</span></h1>
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><!-- ws:end:WikiTextHeadingRule:2 --> </h1>
<em>43edo</em> divides the octave into 43 equal parts of 27.907 cents each. It is strongly associated with meantone temperament, particularly 1/5 comma meantone, being a good tuning system in the 5, 7, 11, and 13-limit. The version of 11-limit meantone is the one tempering out 99/98, 176/175 and 441/440 sometimes called Huygens. 43-equal has the first good 13-limit meantone available as an equal division of the octave. The baroque, french, ironically hearing and speech impaired acoustician <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Joseph_Sauveur" rel="nofollow" target="_blank">Joseph Saveur</a> based his system on 43 equal tones to the octave, calling them "merides". Further information: <a class="wiki_link_ext" href="http://tonalsoft.com/enc/m/meride.aspx" rel="nofollow">http://tonalsoft.com/enc/m/meride.aspx</a><br />
<br />
In the 13-limit, we get two versions of meantone equivalent in 43et, one, <a class="wiki_link" href="/Meantone%20family#Septimal meantone-Unidecimal meantone aka Huygens-Meridetone">meridetone</a>, tempering out 78/77, the other, <a class="wiki_link" href="/Meantone%20family#Septimal meantone-Unidecimal meantone aka Huygens-Grosstone">grosstone</a>, 144/143. Meridetone has generator mapping <0 1 4 10 18 27|, and grosstone <0 1 4 10 18 -16|; 43 supplies the optimal patent val for meridetone.<br />
<br />
The 43 patent val <43 68 100 121 149 169| maps 5 to 100 steps, allowing the divison of 5 into 20 equal parts, leading to <a class="wiki_link" href="/Meantone%20family#Jerome">jerome temperament</a>, an interesting higher-limit system for which 43 supplies the optimal patent val in the 7, 11, 13, 17, 19 and 23 limits. It also provides the optimal patent val for 11- and 13-limit <a class="wiki_link" href="/Marvel%20temperaments#Amavil">amavil temperament</a>, which is not a meantone temperament.<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 />
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x43 tone equal temperament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h2>
<br />
<table class="wiki_table">
<tr>
<td>Degrees of 43-EDO<br />
</td>
<td>Cents value<br />
</td>
</tr>
<tr>
<td>0<br />
</td>
<td>0<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>27.907<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>55.814<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>83.721<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>111.628<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>139.535<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>167.442<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>195.349<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>223.256<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>251.163<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>279.07<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>306.977<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>334.884<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>362.791<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>390.698<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>418.605<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>446.512<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>474.419<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>502.326<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>530.233<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>558.139<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>586.046<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>613.953<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>641.86<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>669.767<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>697.674<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>725.581<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>753.488<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>781.395<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>809.302<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>837.209<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>865.116<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>893.023<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>920.93<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>948.837<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>976.744<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>1004.651<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>1032.558<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>1060.465<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>1088.372<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>1116.279<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>1144.186<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>1172.093<br />
</td>
</tr>
</table>
<br />
<br />
<a href="http://xenharmonic.wikispaces.com/file/view/43%20edo%20counterpoint.mid">43 edo counterpoint.mid</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Kosmorsky/43%20edo%20counterpoint.mp3" rel="nofollow">mp3</a> Peter Kosmorsky (late 2011)</body></html>