17edo: Difference between revisions
Wikispaces>hearneg **Imported revision 598756378 - Original comment: ** |
Wikispaces>TallKite **Imported revision 599947404 - 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:TallKite|TallKite]] and made on <tt>2016-11-21 04:15:18 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>599947404</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"><span style="display: block; text-align: right;"><span style="color: #1300ff | <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"><span style="display: block; text-align: right;"><span style="color: #1300ff;">[[xenharmonie/17edo|Deutsch]] - [[17平均律|日本語]]</span> | ||
</span> | </span> | ||
=<span style="color: #1300ff | =<span style="color: #1300ff;">17 tone equal temperament</span>= | ||
[[toc]] | [[toc]] | ||
**17-EDO** divides the octave in 17 equal steps, each 70.588 [[cent|cents]] in size. It is the seventh [[prime numbers|prime]] edo, following [[13edo]] and coming before [[19edo]]. | **17-EDO** divides the octave in 17 equal steps, each 70.588 [[cent|cents]] in size. It is the seventh [[prime numbers|prime]] edo, following [[13edo]] and coming before [[19edo]]. | ||
| Line 24: | Line 24: | ||
=Intervals= | =Intervals= | ||
||~ Degree ||~ Names of Intervals ||~ Cents (coarse/fine) ||~ Approximate | ||~ Degree ||~ Names of | ||
Intervals ||~ [[Ups and Downs Notation|up/down ]] | |||
[[Ups and Downs Notation|name]] ||~ note | |||
names ||~ Cents (coarse/fine) ||~ Approximate | |||
Ratios* ||~ Temperament(s) | Ratios* ||~ Temperament(s) | ||
generated || | generated || | ||
|| 0 || Unison || 0 ||= 1/1 || || | || 0 || Unison || unison || C || 0 ||= 1/1 || || | ||
|| 1 || Super Unison/ | || 1 || Super Unison/ | ||
Minor Second || 70.59, 84.71 ||= [[25_24|25/24]], [[26_25|26/25]], [[33_32|33/32]] || || | Minor Second || min 2nd || Db || 70.59, 84.71 ||= [[25_24|25/24]], [[26_25|26/25]], [[33_32|33/32]] || || | ||
|| 2 || Augmented Unison/ | || 2 || Augmented Unison/ | ||
Neutral Second || 141.18, 169.41 ||= [[13_12|13/12]], [[12_11|12/11]], [[14_13|14/13]] || [[Bleu]] || | Neutral Second || mid 2nd || Dv || 141.18, 169.41 ||= [[13_12|13/12]], [[12_11|12/11]], [[14_13|14/13]] || [[Bleu]] || | ||
|| 3 || Major Second/ | || 3 || Major Second/ | ||
Sub Third || 211.765, 254.11 ||= [[9_8|9/8]], [[25_22|25/22]], [[8_7|8/7]], [[28_25|28/25]] || [[Machine]] || | Sub Third || maj 2nd || D || 211.765, 254.11 ||= [[9_8|9/8]], [[25_22|25/22]], [[8_7|8/7]], [[28_25|28/25]] || [[Machine]] || | ||
|| 4 || Minor Third/ | || 4 || Minor Third/ | ||
Super Second || 282.35, 338.82 ||= [[13_11|13/11]], [[75_64|75/64]], [[7_6|7/6]] || [[Huxley]] || | Super Second || min 3rd || Eb || 282.35, 338.82 ||= [[13_11|13/11]], [[75_64|75/64]], [[7_6|7/6]] || [[Huxley]] || | ||
|| 5 || Augmented Second/ | || 5 || Augmented Second/ | ||
Neutral Third/ | Neutral Third/ | ||
Diminished Fourth || 352.94, 423.53 ||= [[11_9|11/9]], [[16_13|16/13]] || [[Maqamic]]/[[hemif]] || | Diminished Fourth || mid 3rd || Ev || 352.94, 423.53 ||= [[11_9|11/9]], [[16_13|16/13]] || [[Maqamic]]/[[hemif]] || | ||
|| 6 || Major Third/ | || 6 || Major Third/ | ||
Sub Fourth || 423.53, 508.235 ||= [[32_25|32/25]], [[33_26|33/26]], [[9_7|9/7]], [[14_11|14/11]], [[51_40|51/40]] || [[Skwares]] || | Sub Fourth || maj 3rd || E || 423.53, 508.235 ||= [[32_25|32/25]], [[33_26|33/26]], [[9_7|9/7]], [[14_11|14/11]], [[51_40|51/40]] || [[Skwares]] || | ||
|| 7 || Perfect Fourth || 494.11, 592.94 ||= [[4_3|4/3]] || [[Supra]] || | || 7 || Perfect Fourth || perf 4th || F || 494.11, 592.94 ||= [[4_3|4/3]] || [[Supra]] || | ||
|| 8 || Super Fourth | || 8 || Super Fourth | ||
Diminished Fifth || 564.71, 677.65 ||= [[11_8|11/8]], 18/13 || [[Progress]] || | Diminished Fifth || up 4th, | ||
dim 5th || F^, | |||
Gb || 564.71, 677.65 ||= [[11_8|11/8]], 18/13 || [[Progress]] || | |||
|| 9 || Augmented Fourth/ | || 9 || Augmented Fourth/ | ||
Sub Fifth || 635.29, 762.35 ||= [[16_11|16/11]], 13/9, [[23_16|23/16]] || Progress || | Sub Fifth || aug 4th, | ||
|| 10 || Perfect Fifth || 705.88, 847.06 ||= [[3_2|3/2]] || Supra || | down 5th || F#, | ||
Gv || 635.29, 762.35 ||= [[16_11|16/11]], 13/9, [[23_16|23/16]] || Progress || | |||
|| 10 || Perfect Fifth || perf 5th || G || 705.88, 847.06 ||= [[3_2|3/2]] || Supra || | |||
|| 11 || Super Fifth/ | || 11 || Super Fifth/ | ||
Minor Sixth || 776.47, 931.765 ||= 25/16, 52/33, 14/9, [[11_7|11/7]] || Skwares || | Minor Sixth || min 6th || Ab || 776.47, 931.765 ||= 25/16, 52/33, 14/9, [[11_7|11/7]] || Skwares || | ||
|| 12 || Augmented Fifth/ | || 12 || Augmented Fifth/ | ||
Neutral Sixth/ | Neutral Sixth/ | ||
Diminished Seventh || 847.06, 1016.47 ||= [[13_8|13/8]], 18/11 || Maqamic/hemif || | Diminished Seventh || mid 6th || Av || 847.06, 1016.47 ||= [[13_8|13/8]], 18/11 || Maqamic/hemif || | ||
|| 13 || Major Sixth/ | || 13 || Major Sixth/ | ||
Sub Seventh || 917.65, 1101.18 ||= [[17_10|17/10]], [[22_13|22/13]], 128/75, [[12_7|12/7]] || Huxley || | Sub Seventh || maj 6th || A || 917.65, 1101.18 ||= [[17_10|17/10]], [[22_13|22/13]], 128/75, [[12_7|12/7]] || Huxley || | ||
|| 14 || Minor Seventh/ | || 14 || Minor Seventh/ | ||
Super Sixth || 988.235, 1185.89 ||= [[16_9|16/9]], 44/25, 7/4, 25/14 || Machine || | Super Sixth || min 7th || Bb || 988.235, 1185.89 ||= [[16_9|16/9]], 44/25, 7/4, 25/14 || Machine || | ||
|| 15 || Augmented Sixth/ | || 15 || Augmented Sixth/ | ||
Neutral Seventh/ | Neutral Seventh/ | ||
Diminished Octave || 1058.82, 1270.59 ||= [[11_6|11/6]], 24/13, [[13_7|13/7]] || Bleu || | Diminished Octave || mid 7th || Bv || 1058.82, 1270.59 ||= [[11_6|11/6]], 24/13, [[13_7|13/7]] || Bleu || | ||
|| 16 || Major Seventh/ | || 16 || Major Seventh/ | ||
Sub Octave || 1129.41, 1355.29 ||= 25/13, 48/25, 64/33 || || | Sub Octave || maj 7th || B || 1129.41, 1355.29 ||= 25/13, 48/25, 64/33 || || | ||
|| 17 || Perfect Octave || 1200, 1440 ||= [[2_1|2/1]] || || | || 17 || Perfect Octave || 8ve || C || 1200, 1440 ||= [[2_1|2/1]] || || | ||
==Selected just intervals by error== | ==Selected just intervals by error== | ||
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[[image:17P1050829r.JPG]][[media type="custom" key="23473418"]]</pre></div> | [[image:17P1050829r.JPG]][[media type="custom" key="23473418"]]</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>17edo</title></head><body><span style="display: block; text-align: right;"><span style="color: #1300ff | <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>17edo</title></head><body><span style="display: block; text-align: right;"><span style="color: #1300ff;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/17edo">Deutsch</a> - <a class="wiki_link" href="/17%E5%B9%B3%E5%9D%87%E5%BE%8B">日本語</a></span><br /> | ||
</span><br /> | </span><br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc0"><a name="x17 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:2 --><span style="color: #1300ff | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc0"><a name="x17 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:2 --><span style="color: #1300ff;">17 tone equal temperament</span></h1> | ||
<!-- ws:start:WikiTextTocRule:30:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><div style="margin-left: 1em;"><a href="#x17 tone equal temperament">17 tone equal temperament</a></div> | <!-- ws:start:WikiTextTocRule:30:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><div style="margin-left: 1em;"><a href="#x17 tone equal temperament">17 tone equal temperament</a></div> | ||
<!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><div style="margin-left: 2em;"><a href="#x17 tone equal temperament-Theory">Theory</a></div> | <!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><div style="margin-left: 2em;"><a href="#x17 tone equal temperament-Theory">Theory</a></div> | ||
| Line 223: | Line 230: | ||
<th>Degree<br /> | <th>Degree<br /> | ||
</th> | </th> | ||
<th>Names of Intervals<br /> | <th>Names of <br /> | ||
Intervals<br /> | |||
</th> | |||
<th><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">up/down </a><br /> | |||
<a class="wiki_link" href="/Ups%20and%20Downs%20Notation">name</a><br /> | |||
</th> | |||
<th>note<br /> | |||
names<br /> | |||
</th> | </th> | ||
<th>Cents (coarse/fine)<br /> | <th>Cents (coarse/fine)<br /> | ||
| Line 238: | Line 252: | ||
</td> | </td> | ||
<td>Unison<br /> | <td>Unison<br /> | ||
</td> | |||
<td>unison<br /> | |||
</td> | |||
<td>C<br /> | |||
</td> | </td> | ||
<td>0<br /> | <td>0<br /> | ||
| Line 251: | Line 269: | ||
<td>Super Unison/<br /> | <td>Super Unison/<br /> | ||
Minor Second<br /> | Minor Second<br /> | ||
</td> | |||
<td>min 2nd<br /> | |||
</td> | |||
<td>Db<br /> | |||
</td> | </td> | ||
<td>70.59, 84.71<br /> | <td>70.59, 84.71<br /> | ||
| Line 264: | Line 286: | ||
<td>Augmented Unison/<br /> | <td>Augmented Unison/<br /> | ||
Neutral Second<br /> | Neutral Second<br /> | ||
</td> | |||
<td>mid 2nd<br /> | |||
</td> | |||
<td>Dv<br /> | |||
</td> | </td> | ||
<td>141.18, 169.41<br /> | <td>141.18, 169.41<br /> | ||
| Line 277: | Line 303: | ||
<td>Major Second/<br /> | <td>Major Second/<br /> | ||
Sub Third<br /> | Sub Third<br /> | ||
</td> | |||
<td>maj 2nd<br /> | |||
</td> | |||
<td>D<br /> | |||
</td> | </td> | ||
<td>211.765, 254.11<br /> | <td>211.765, 254.11<br /> | ||
| Line 290: | Line 320: | ||
<td>Minor Third/<br /> | <td>Minor Third/<br /> | ||
Super Second<br /> | Super Second<br /> | ||
</td> | |||
<td>min 3rd<br /> | |||
</td> | |||
<td>Eb<br /> | |||
</td> | </td> | ||
<td>282.35, 338.82<br /> | <td>282.35, 338.82<br /> | ||
| Line 304: | Line 338: | ||
Neutral Third/<br /> | Neutral Third/<br /> | ||
Diminished Fourth<br /> | Diminished Fourth<br /> | ||
</td> | |||
<td>mid 3rd<br /> | |||
</td> | |||
<td>Ev<br /> | |||
</td> | </td> | ||
<td>352.94, 423.53<br /> | <td>352.94, 423.53<br /> | ||
| Line 317: | Line 355: | ||
<td>Major Third/<br /> | <td>Major Third/<br /> | ||
Sub Fourth<br /> | Sub Fourth<br /> | ||
</td> | |||
<td>maj 3rd<br /> | |||
</td> | |||
<td>E<br /> | |||
</td> | </td> | ||
<td>423.53, 508.235<br /> | <td>423.53, 508.235<br /> | ||
| Line 329: | Line 371: | ||
</td> | </td> | ||
<td>Perfect Fourth<br /> | <td>Perfect Fourth<br /> | ||
</td> | |||
<td>perf 4th<br /> | |||
</td> | |||
<td>F<br /> | |||
</td> | </td> | ||
<td>494.11, 592.94<br /> | <td>494.11, 592.94<br /> | ||
| Line 342: | Line 388: | ||
<td>Super Fourth<br /> | <td>Super Fourth<br /> | ||
Diminished Fifth<br /> | Diminished Fifth<br /> | ||
</td> | |||
<td>up 4th,<br /> | |||
dim 5th<br /> | |||
</td> | |||
<td>F^, <br /> | |||
Gb<br /> | |||
</td> | </td> | ||
<td>564.71, 677.65<br /> | <td>564.71, 677.65<br /> | ||
| Line 355: | Line 407: | ||
<td>Augmented Fourth/<br /> | <td>Augmented Fourth/<br /> | ||
Sub Fifth<br /> | Sub Fifth<br /> | ||
</td> | |||
<td>aug 4th,<br /> | |||
down 5th<br /> | |||
</td> | |||
<td>F#,<br /> | |||
Gv<br /> | |||
</td> | </td> | ||
<td>635.29, 762.35<br /> | <td>635.29, 762.35<br /> | ||
| Line 367: | Line 425: | ||
</td> | </td> | ||
<td>Perfect Fifth<br /> | <td>Perfect Fifth<br /> | ||
</td> | |||
<td>perf 5th<br /> | |||
</td> | |||
<td>G<br /> | |||
</td> | </td> | ||
<td>705.88, 847.06<br /> | <td>705.88, 847.06<br /> | ||
| Line 380: | Line 442: | ||
<td>Super Fifth/<br /> | <td>Super Fifth/<br /> | ||
Minor Sixth<br /> | Minor Sixth<br /> | ||
</td> | |||
<td>min 6th<br /> | |||
</td> | |||
<td>Ab<br /> | |||
</td> | </td> | ||
<td>776.47, 931.765<br /> | <td>776.47, 931.765<br /> | ||
| Line 394: | Line 460: | ||
Neutral Sixth/<br /> | Neutral Sixth/<br /> | ||
Diminished Seventh<br /> | Diminished Seventh<br /> | ||
</td> | |||
<td>mid 6th<br /> | |||
</td> | |||
<td>Av<br /> | |||
</td> | </td> | ||
<td>847.06, 1016.47<br /> | <td>847.06, 1016.47<br /> | ||
| Line 407: | Line 477: | ||
<td>Major Sixth/<br /> | <td>Major Sixth/<br /> | ||
Sub Seventh<br /> | Sub Seventh<br /> | ||
</td> | |||
<td>maj 6th<br /> | |||
</td> | |||
<td>A<br /> | |||
</td> | </td> | ||
<td>917.65, 1101.18<br /> | <td>917.65, 1101.18<br /> | ||
| Line 420: | Line 494: | ||
<td>Minor Seventh/<br /> | <td>Minor Seventh/<br /> | ||
Super Sixth<br /> | Super Sixth<br /> | ||
</td> | |||
<td>min 7th<br /> | |||
</td> | |||
<td>Bb<br /> | |||
</td> | </td> | ||
<td>988.235, 1185.89<br /> | <td>988.235, 1185.89<br /> | ||
| Line 434: | Line 512: | ||
Neutral Seventh/<br /> | Neutral Seventh/<br /> | ||
Diminished Octave<br /> | Diminished Octave<br /> | ||
</td> | |||
<td>mid 7th<br /> | |||
</td> | |||
<td>Bv<br /> | |||
</td> | </td> | ||
<td>1058.82, 1270.59<br /> | <td>1058.82, 1270.59<br /> | ||
| Line 447: | Line 529: | ||
<td>Major Seventh/<br /> | <td>Major Seventh/<br /> | ||
Sub Octave<br /> | Sub Octave<br /> | ||
</td> | |||
<td>maj 7th<br /> | |||
</td> | |||
<td>B<br /> | |||
</td> | </td> | ||
<td>1129.41, 1355.29<br /> | <td>1129.41, 1355.29<br /> | ||
| Line 459: | Line 545: | ||
</td> | </td> | ||
<td>Perfect Octave<br /> | <td>Perfect Octave<br /> | ||
</td> | |||
<td>8ve<br /> | |||
</td> | |||
<td>C<br /> | |||
</td> | </td> | ||
<td>1200, 1440<br /> | <td>1200, 1440<br /> | ||
| Line 629: | Line 719: | ||
<br /> | <br /> | ||
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<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc4"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:10 -->Commas</h1> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc4"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:10 -->Commas</h1> | ||
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<ul><li><!-- ws:start:WikiTextHeadingRule:22:&lt;h4&gt; --><h4 id="toc10"><a name="Instruments---Guitar Heptadecatonic from Peruvian - Charles Loli and Antonio Huamani"></a><!-- ws:end:WikiTextHeadingRule:22 --><strong><a class="wiki_link_ext" href="http://www.microtonalismo.com/proyecto-xvii" rel="nofollow">Guitar Heptadecatonic from Peruvian - Charles Loli and Antonio Huamani</a></strong></h4> | <ul><li><!-- ws:start:WikiTextHeadingRule:22:&lt;h4&gt; --><h4 id="toc10"><a name="Instruments---Guitar Heptadecatonic from Peruvian - Charles Loli and Antonio Huamani"></a><!-- ws:end:WikiTextHeadingRule:22 --><strong><a class="wiki_link_ext" href="http://www.microtonalismo.com/proyecto-xvii" rel="nofollow">Guitar Heptadecatonic from Peruvian - Charles Loli and Antonio Huamani</a></strong></h4> | ||
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