16edo: Difference between revisions
Wikispaces>xenwolf **Imported revision 575540033 - Original comment: ** |
Wikispaces>Nickname2 **Imported revision 585437115 - 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:Nickname2|Nickname2]] and made on <tt>2016-06-15 09:56:56 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>585437115</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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The following table shows how [[Just-24|some prominent just intervals]] are represented in 16-EDO (ordered by absolute error). | The following table shows how [[Just-24|some prominent just intervals]] are represented in 16-EDO (ordered by absolute error). | ||
|| **Interval, complement** || **Error (abs., in [[cent|cents]])** || | || **Interval, complement** || **Error (abs., in [[cent|cents]])** || | ||
||= [[12_11|12/11]], [[11_6|11/6]] | ||= [[12_11|12/11]], [[11_6|11/6]] ||= 0.637 || | ||
||= [[13_10|13/10]], [[20_13|20/13]] ||= | ||= [[13_10|13/10]], [[20_13|20/13]] ||= 4.214 || | ||
||= [[8_7|8/7]], | ||= [[8_7|8/7]], [[7_4|7/4]] ||= 6.174 || | ||
||= [[13_11|13/11]], [[22_13|22/13]] ||= 10.790 || | ||= [[13_11|13/11]], [[22_13|22/13]] ||= 10.790 || | ||
||= [[5_4|5/4]], | ||= [[5_4|5/4]], [[8_5|8/5]] ||= 11.314 || | ||
||= [[13_12|13/12]], [[24_13|24/13]] ||= 11.427 || | ||= [[13_12|13/12]], [[24_13|24/13]] ||= 11.427 || | ||
||= [[15_11|15/11]], [[22_15|22/15]] ||= 11.951 || | ||= [[15_11|15/11]], [[22_15|22/15]] ||= 11.951 || | ||
||= [[9_7|9/7]], | ||= [[9_7|9/7]], [[14_9|14/9]] ||= 14.916 || | ||
||= [[11_10|11/10]], [[20_11|20/11]] ||= 15.004 || | ||= [[11_10|11/10]], [[20_11|20/11]] ||= 15.004 || | ||
||= [[16_13|16/13]], [[13_8|13/8]] | ||= [[16_13|16/13]], [[13_8|13/8]] ||= 15.528 || | ||
||= [[6_5|6/5]], | ||= [[6_5|6/5]], [[5_3|5/3]] ||= 15.641 || | ||
||= [[7_5|7/5]], | ||= [[7_5|7/5]], [[10_7|10/7]] ||= 17.488 || | ||
||= [[9_8|9/8]], | ||= [[9_8|9/8]], [[16_9|16/9]] ||= 21.090 || | ||
||= [[14_13|14/13]], [[13_7|13/7]] | ||= [[14_13|14/13]], [[13_7|13/7]] ||= 21.702 || | ||
||= [[15_13|15/13]], [[26_15|26/15]] ||= 22.741 || | ||= [[15_13|15/13]], [[26_15|26/15]] ||= 22.741 || | ||
||= [[11_8|11/8]], | ||= [[11_8|11/8]], [[16_11|16/11]] ||= 26.318 || | ||
||= [[4_3|4/3]], | ||= [[4_3|4/3]], [[3_2|3/2]] ||= 26.955 || | ||
||= [[11_9|11/9]], | ||= [[11_9|11/9]], [[18_11|18/11]] ||= 27.592 || | ||
||= [[15_14|15/14]], [[28_15|28/15]] ||= 30.557 || | ||= [[15_14|15/14]], [[28_15|28/15]] ||= 30.557 || | ||
||= [[10_9|10/9]], | ||= [[10_9|10/9]], [[9_5|9/5]] ||= 32.404 || | ||
||= [[14_11|14/11]], [[11_7|11/7]] | ||= [[14_11|14/11]], [[11_7|11/7]] ||= 32.492 || | ||
||= [[7_6|7/6]], | ||= [[7_6|7/6]], [[12_7|12/7]] ||= 33.129 || | ||
||= [[18_13|18/13]], [[13_9|13/9]] | ||= [[18_13|18/13]], [[13_9|13/9]] ||= 36.618 || | ||
||= [[16_15|16/15]], [[15_8|15/8]] | ||= [[16_15|16/15]], [[15_8|15/8]] ||= 36.731 || | ||
It's worth noting that the 525-cent interval is almost exactly halfway in between 4/3 and 11/8, making it EXTREMELY discordant. | |||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"><a class="wiki_link" href="/8_7">8/7</a>, | <td style="text-align: center;"><a class="wiki_link" href="/8_7">8/7</a>, <a class="wiki_link" href="/7_4">7/4</a><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">6.174<br /> | <td style="text-align: center;">6.174<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"><a class="wiki_link" href="/5_4">5/4</a>, | <td style="text-align: center;"><a class="wiki_link" href="/5_4">5/4</a>, <a class="wiki_link" href="/8_5">8/5</a><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">11.314<br /> | <td style="text-align: center;">11.314<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"><a class="wiki_link" href="/9_7">9/7</a>, | <td style="text-align: center;"><a class="wiki_link" href="/9_7">9/7</a>, <a class="wiki_link" href="/14_9">14/9</a><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">14.916<br /> | <td style="text-align: center;">14.916<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"><a class="wiki_link" href="/6_5">6/5</a>, | <td style="text-align: center;"><a class="wiki_link" href="/6_5">6/5</a>, <a class="wiki_link" href="/5_3">5/3</a><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">15.641<br /> | <td style="text-align: center;">15.641<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"><a class="wiki_link" href="/7_5">7/5</a>, | <td style="text-align: center;"><a class="wiki_link" href="/7_5">7/5</a>, <a class="wiki_link" href="/10_7">10/7</a><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">17.488<br /> | <td style="text-align: center;">17.488<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"><a class="wiki_link" href="/9_8">9/8</a>, | <td style="text-align: center;"><a class="wiki_link" href="/9_8">9/8</a>, <a class="wiki_link" href="/16_9">16/9</a><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">21.090<br /> | <td style="text-align: center;">21.090<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"><a class="wiki_link" href="/11_8">11/8</a>, | <td style="text-align: center;"><a class="wiki_link" href="/11_8">11/8</a>, <a class="wiki_link" href="/16_11">16/11</a><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">26.318<br /> | <td style="text-align: center;">26.318<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"><a class="wiki_link" href="/4_3">4/3</a>, | <td style="text-align: center;"><a class="wiki_link" href="/4_3">4/3</a>, <a class="wiki_link" href="/3_2">3/2</a><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">26.955<br /> | <td style="text-align: center;">26.955<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"><a class="wiki_link" href="/11_9">11/9</a>, | <td style="text-align: center;"><a class="wiki_link" href="/11_9">11/9</a>, <a class="wiki_link" href="/18_11">18/11</a><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">27.592<br /> | <td style="text-align: center;">27.592<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"><a class="wiki_link" href="/10_9">10/9</a>, | <td style="text-align: center;"><a class="wiki_link" href="/10_9">10/9</a>, <a class="wiki_link" href="/9_5">9/5</a><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">32.404<br /> | <td style="text-align: center;">32.404<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"><a class="wiki_link" href="/7_6">7/6</a>, | <td style="text-align: center;"><a class="wiki_link" href="/7_6">7/6</a>, <a class="wiki_link" href="/12_7">12/7</a><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">33.129<br /> | <td style="text-align: center;">33.129<br /> | ||
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</table> | </table> | ||
<br /> | It's worth noting that the 525-cent interval is almost exactly halfway in between 4/3 and 11/8, making it EXTREMELY discordant.<br /> | ||
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