17edo: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:igliashon|igliashon]] and made on <tt>2011-07-25 21:04:50 UTC</tt>.

: This revision was by author [[User:igliashon|igliashon]] and made on <tt>2011-09-21 16:32:39 UTC</tt>.

: The original revision id was <tt>~~242820745~~</tt>.

: The original revision id was <tt>256734802</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Line 14:

==As a temperament==

17-EDO ~~does not perform well as a 5- or 7-limit temperament, but is excellent~~ as a 2.3.11.13~~.25~~ subgroup temperament.

17-EDO can plausibly be treated as a 2.3.25.7.11.13 subgroup temperament, for which it is quite accurate (though the 7-limit ratios are generally not as well-represented as those of the other integers).

|| Degree || Cents ||= Approximate

Line 20:

|| 0 || 0 ||= 1/1 ||

|| 1 || 70.59 ||= 25/24, 26/25, 33/32 ||

|| 2 || 141.18 ||= 13/12, 12/11 ||

|| 2 || 141.18 ||= 13/12, 12/11, 14/13 ||

|| 3 || 211.76 ||= 9/8, 25/22, ||

|| 3 || 211.76 ||= 9/8, 25/22, 8/7, 28/25 ||

|| 4 || 282.35 ||= 13/11, 75/64 ||

|| 4 || 282.35 ||= 13/11, 75/64, 7/6 ||

|| 5 || 352.94 ||= 11/9, 16/13 ||

|| 6 || 423.53 ||= 32/25, 33/26 ||

|| 6 || 423.53 ||= 32/25, 33/26, 9/7, 14/11 ||

|| 7 || 494.12 ||= 4/3 ||

|| 8 || 564.71 ||= 11/8, 18/13 ||

|| 9 || 635.294 ||= 16/11, 13/9 ||

|| 10 || 705.88 ||= 3/2 ||

|| 11 || 776.47 ||= 25/16, 52/33 ||

|| 11 || 776.47 ||= 25/16, 52/33, 14/9, 11/7 ||

|| 12 || 847.06 ||= 13/8, 18/11 ||

|| 13 || 917.65 ||= 22/13, 128/75 ||

|| 13 || 917.65 ||= 22/13, 128/75, 12/7 ||

|| 14 || 988.24 ||= 16/9, 44/25 ||

|| 14 || 988.24 ||= 16/9, 44/25, 7/4, 25/14 ||

|| 15 || 1058.82 ||= 11/6, 24/13 ||

|| 15 || 1058.82 ||= 11/6, 24/13, 13/7 ||

|| 16 || 1129.41 ||= 25/13, 48/25, 64/33 ||

|| 17 || 1200 ||= 2/1 ||

Line 121:

<h2 id="toc2"><a name="x17 tone equal temperament-As a temperament"></a>As a temperament</h2>

17-EDO ~~does not perform well as a 5- or 7-limit temperament, but is excellent~~ as a 2.3.11.13~~.25~~ subgroup temperament.

17-EDO can plausibly be treated as a 2.3.25.7.11.13 subgroup temperament, for which it is quite accurate (though the 7-limit ratios are generally not as well-represented as those of the other integers).

Line 156:

<td>141.18

</td>

<td style="text-align: center;">13/12, 12/11

<td style="text-align: center;">13/12, 12/11, 14/13

</td>

</tr>

Line 164:

<td>211.76

</td>

<td style="text-align: center;">9/8, 25/22,

<td style="text-align: center;">9/8, 25/22, 8/7, 28/25

</td>

</tr>

Line 172:

<td>282.35

</td>

<td style="text-align: center;">13/11, 75/64

<td style="text-align: center;">13/11, 75/64, 7/6

</td>

</tr>

Line 188:

<td>423.53

</td>

<td style="text-align: center;">32/25, 33/26

<td style="text-align: center;">32/25, 33/26, 9/7, 14/11

</td>

</tr>

Line 228:

<td>776.47

</td>

<td style="text-align: center;">25/16, 52/33

<td style="text-align: center;">25/16, 52/33, 14/9, 11/7

</td>

</tr>

Line 244:

<td>917.65

</td>

<td style="text-align: center;">22/13, 128/75

<td style="text-align: center;">22/13, 128/75, 12/7

</td>

</tr>

Line 252:

<td>988.24

</td>

<td style="text-align: center;">16/9, 44/25

<td style="text-align: center;">16/9, 44/25, 7/4, 25/14

</td>

</tr>

Line 260:

<td>1058.82

</td>

<td style="text-align: center;">11/6, 24/13

<td style="text-align: center;">11/6, 24/13, 13/7

</td>

</tr>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:igliashon|igliashon]] and made on <tt>2011-07-25 21:04:50 UTC</tt>.<br>
+: This revision was by author [[User:igliashon|igliashon]] and made on <tt>2011-09-21 16:32:39 UTC</tt>.<br>
-: The original revision id was <tt>242820745</tt>.<br>
+: The original revision id was <tt>256734802</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>
@@ Line 14: / Line 14: @@
 ==As a temperament==
--EDO does not perform well as a 5- or 7-limit temperament, but is excellent as a 2.3.11.13.25 subgroup temperament.
+-EDO can plausibly be treated as a 2.3.25.7.11.13 subgroup temperament, for which it is quite accurate (though the 7-limit ratios are generally not as well-represented as those of the other integers).
 || Degree || Cents ||= Approximate
@@ Line 20: / Line 20: @@
 || 0 || 0 ||= 1/1 ||
 || 1 || 70.59 ||= 25/24, 26/25, 33/32 ||
-|| 2 || 141.18 ||= 13/12, 12/11 ||
+|| 2 || 141.18 ||= 13/12, 12/11, 14/13 ||
-|| 3 || 211.76 ||= 9/8, 25/22, ||
+|| 3 || 211.76 ||= 9/8, 25/22, 8/7, 28/25 ||
-|| 4 || 282.35 ||= 13/11, 75/64 ||
+|| 4 || 282.35 ||= 13/11, 75/64, 7/6 ||
 || 5 || 352.94 ||= 11/9, 16/13 ||
-|| 6 || 423.53 ||= 32/25, 33/26 ||
+|| 6 || 423.53 ||= 32/25, 33/26, 9/7, 14/11 ||
 || 7 || 494.12 ||= 4/3 ||
 || 8 || 564.71 ||= 11/8, 18/13 ||
 || 9 || 635.294 ||= 16/11, 13/9 ||
 || 10 || 705.88 ||= 3/2 ||
-|| 11 || 776.47 ||= 25/16, 52/33 ||
+|| 11 || 776.47 ||= 25/16, 52/33, 14/9, 11/7 ||
 || 12 || 847.06 ||= 13/8, 18/11 ||
-|| 13 || 917.65 ||= 22/13, 128/75 ||
+|| 13 || 917.65 ||= 22/13, 128/75, 12/7 ||
-|| 14 || 988.24 ||= 16/9, 44/25 ||
+|| 14 || 988.24 ||= 16/9, 44/25, 7/4, 25/14 ||
-|| 15 || 1058.82 ||= 11/6, 24/13 ||
+|| 15 || 1058.82 ||= 11/6, 24/13, 13/7 ||
 || 16 || 1129.41 ||= 25/13, 48/25, 64/33 ||
 || 17 || 1200 ||= 2/1 ||
@@ Line 121: / Line 121: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x17 tone equal temperament-As a temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;As a temperament&lt;/h2&gt;
--EDO does not perform well as a 5- or 7-limit temperament, but is excellent as a 2.3.11.13.25 subgroup temperament.&lt;br /&gt;
+-EDO can plausibly be treated as a 2.3.25.7.11.13 subgroup temperament, for which it is quite accurate (though the 7-limit ratios are generally not as well-represented as those of the other integers).&lt;br /&gt;
 &lt;br /&gt;
@@ Line 156: / Line 156: @@
          &lt;td&gt;141.18&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;13/12, 12/11&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;13/12, 12/11, 14/13&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 164: / Line 164: @@
          &lt;td&gt;211.76&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;9/8, 25/22,&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;9/8, 25/22, 8/7, 28/25&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 172: / Line 172: @@
          &lt;td&gt;282.35&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;13/11, 75/64&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;13/11, 75/64, 7/6&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 188: / Line 188: @@
          &lt;td&gt;423.53&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;32/25, 33/26&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;32/25, 33/26, 9/7, 14/11&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 228: / Line 228: @@
          &lt;td&gt;776.47&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;25/16, 52/33&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;25/16, 52/33, 14/9, 11/7&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 244: / Line 244: @@
          &lt;td&gt;917.65&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;22/13, 128/75&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;22/13, 128/75, 12/7&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 252: / Line 252: @@
          &lt;td&gt;988.24&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;16/9, 44/25&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;16/9, 44/25, 7/4, 25/14&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 260: / Line 260: @@
          &lt;td&gt;1058.82&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;11/6, 24/13&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;11/6, 24/13, 13/7&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;