Semaphore and godzilla: Difference between revisions

Revision as of 16:06, 17 August 2011

IMPORTED REVISION FROM WIKISPACES

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

This revision was by author xenwolf and made on 2011-08-17 16:06:58 UTC.

The original revision id was 246547581.

The revision comment was: some links added

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

Original Wikitext content:

Semaphore, namesake of the [[Semaphore family]], is characterized by the vanishing of [[49_48|49/48]], so the generator represents [[8_7|8/7]] and [[7_6|7/6]] equally. This results in a very low [[complexity]] 2.3.7 [[temperament]], with the drawback that most intervals of 7 must be out of tune by at least half of 49/48, or about 18 [[cent]]s.

If 5 is mapped at all, it makes sense to map it to -8 [[generator]]s by [[tempering out]] [[81_80|81/80]], making it a [[meantone temperament]]. This temperament is called "[[godzilla]]".

==Interval chains== 
===Basic semaphore=== 
|| 198.46 || 448.85 || 699.23 || 949.62 || 0 || 250.38 || 500.77 || 751.15 || 1001.54 ||
|| [[9_8|9/8]] || [[9_7|9/7]] || [[3_2|3/2]] || 12/7~7/4 || [[1_1|1/1]] || 8/7~7/6 || [[4_3|4/3]] || [[14_9|14/9]] || [[16_9|16/9]] ||
===Godzilla=== 
|| 378.92 || 631.56 || 884.19 || 1136.83 || 189.46 || 442.10 || 694.73 || 947.37 || 0 || 252.63 || 505.27 || 757.90 || 1010.54 || 63.17 || 315.81 || 568.44 || 821.08 ||
|| [[5_4|5/4]] || [[10_7|10/7]] || [[5_3|5/3]] || 27/14 || 10/9~9/8 || 9/7 || 3/2 || 12/7~7/4 || 1/1 || 8/7~7/6 || 4/3 || 14/9 || 16/9~9/5 || 28/27~21/20 || [[6_5|6/5]] || [[7_5|7/5]] || [[8_5|8/5]] ||
==MOSes== 
===5-note (proper)=== 
|| Small ("minor") interval || 198.46 || 448.85 || 699.23 || 949.62 ||
|| [[JI]] intervals represented || 9/8 || 9/7 || 3/2 || 12/7~7/4 ||
|| Large ("major") interval || 250.38 || 500.77 || 751.15 || 1001.54 ||
|| JI intervals represented || 8/7~7/6 || 4/3 || 14/9 || 16/9 ||
===9-note (improper)=== 
|| Small ("minor") interval || 63.17 || 252.63 || 315.81 || 505.27 || 568.44 || 757.90 || 821.08 || 1010.54 ||
|| JI intervals represented ||   || 8/7~7/6 || 6/5 || 4/3 || 7/5 || 14/9 || 8/5 || 16/9~9/5 ||
|| Large ("major") interval || 189.46 || 378.92 || 442.10 || 631.56 || 694.73 || 884.19 || 947.37 || 1136.83 ||
|| JI intervals represented || 10/9~9/8 || 5/4 || 9/7 || 10/7 || 3/2 || 5/3 || 12/7~7/4 ||   ||

Original HTML content:

<html><head><title>Semaphore and Godzilla</title></head><body>Semaphore, namesake of the <a class="wiki_link" href="/Semaphore%20family">Semaphore family</a>, is characterized by the vanishing of <a class="wiki_link" href="/49_48">49/48</a>, so the generator represents <a class="wiki_link" href="/8_7">8/7</a> and <a class="wiki_link" href="/7_6">7/6</a> equally. This results in a very low <a class="wiki_link" href="/complexity">complexity</a> 2.3.7 <a class="wiki_link" href="/temperament">temperament</a>, with the drawback that most intervals of 7 must be out of tune by at least half of 49/48, or about 18 <a class="wiki_link" href="/cent">cent</a>s.<br />
<br />
If 5 is mapped at all, it makes sense to map it to -8 <a class="wiki_link" href="/generator">generator</a>s by <a class="wiki_link" href="/tempering%20out">tempering out</a> <a class="wiki_link" href="/81_80">81/80</a>, making it a <a class="wiki_link" href="/meantone%20temperament">meantone temperament</a>. This temperament is called &quot;<a class="wiki_link" href="/godzilla">godzilla</a>&quot;.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Interval chains"></a><!-- ws:end:WikiTextHeadingRule:0 -->Interval chains</h2>
 <!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x-Interval chains-Basic semaphore"></a><!-- ws:end:WikiTextHeadingRule:2 -->Basic semaphore</h3>
 

<table class="wiki_table">
    <tr>
        <td>198.46<br />
</td>
        <td>448.85<br />
</td>
        <td>699.23<br />
</td>
        <td>949.62<br />
</td>
        <td>0<br />
</td>
        <td>250.38<br />
</td>
        <td>500.77<br />
</td>
        <td>751.15<br />
</td>
        <td>1001.54<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/9_8">9/8</a><br />
</td>
        <td><a class="wiki_link" href="/9_7">9/7</a><br />
</td>
        <td><a class="wiki_link" href="/3_2">3/2</a><br />
</td>
        <td>12/7~7/4<br />
</td>
        <td><a class="wiki_link" href="/1_1">1/1</a><br />
</td>
        <td>8/7~7/6<br />
</td>
        <td><a class="wiki_link" href="/4_3">4/3</a><br />
</td>
        <td><a class="wiki_link" href="/14_9">14/9</a><br />
</td>
        <td><a class="wiki_link" href="/16_9">16/9</a><br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Interval chains-Godzilla"></a><!-- ws:end:WikiTextHeadingRule:4 -->Godzilla</h3>
 

<table class="wiki_table">
    <tr>
        <td>378.92<br />
</td>
        <td>631.56<br />
</td>
        <td>884.19<br />
</td>
        <td>1136.83<br />
</td>
        <td>189.46<br />
</td>
        <td>442.10<br />
</td>
        <td>694.73<br />
</td>
        <td>947.37<br />
</td>
        <td>0<br />
</td>
        <td>252.63<br />
</td>
        <td>505.27<br />
</td>
        <td>757.90<br />
</td>
        <td>1010.54<br />
</td>
        <td>63.17<br />
</td>
        <td>315.81<br />
</td>
        <td>568.44<br />
</td>
        <td>821.08<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/5_4">5/4</a><br />
</td>
        <td><a class="wiki_link" href="/10_7">10/7</a><br />
</td>
        <td><a class="wiki_link" href="/5_3">5/3</a><br />
</td>
        <td>27/14<br />
</td>
        <td>10/9~9/8<br />
</td>
        <td>9/7<br />
</td>
        <td>3/2<br />
</td>
        <td>12/7~7/4<br />
</td>
        <td>1/1<br />
</td>
        <td>8/7~7/6<br />
</td>
        <td>4/3<br />
</td>
        <td>14/9<br />
</td>
        <td>16/9~9/5<br />
</td>
        <td>28/27~21/20<br />
</td>
        <td><a class="wiki_link" href="/6_5">6/5</a><br />
</td>
        <td><a class="wiki_link" href="/7_5">7/5</a><br />
</td>
        <td><a class="wiki_link" href="/8_5">8/5</a><br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-MOSes"></a><!-- ws:end:WikiTextHeadingRule:6 -->MOSes</h2>
 <!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x-MOSes-5-note (proper)"></a><!-- ws:end:WikiTextHeadingRule:8 -->5-note (proper)</h3>
 

<table class="wiki_table">
    <tr>
        <td>Small (&quot;minor&quot;) interval<br />
</td>
        <td>198.46<br />
</td>
        <td>448.85<br />
</td>
        <td>699.23<br />
</td>
        <td>949.62<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/JI">JI</a> intervals represented<br />
</td>
        <td>9/8<br />
</td>
        <td>9/7<br />
</td>
        <td>3/2<br />
</td>
        <td>12/7~7/4<br />
</td>
    </tr>
    <tr>
        <td>Large (&quot;major&quot;) interval<br />
</td>
        <td>250.38<br />
</td>
        <td>500.77<br />
</td>
        <td>751.15<br />
</td>
        <td>1001.54<br />
</td>
    </tr>
    <tr>
        <td>JI intervals represented<br />
</td>
        <td>8/7~7/6<br />
</td>
        <td>4/3<br />
</td>
        <td>14/9<br />
</td>
        <td>16/9<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="x-MOSes-9-note (improper)"></a><!-- ws:end:WikiTextHeadingRule:10 -->9-note (improper)</h3>
 

<table class="wiki_table">
    <tr>
        <td>Small (&quot;minor&quot;) interval<br />
</td>
        <td>63.17<br />
</td>
        <td>252.63<br />
</td>
        <td>315.81<br />
</td>
        <td>505.27<br />
</td>
        <td>568.44<br />
</td>
        <td>757.90<br />
</td>
        <td>821.08<br />
</td>
        <td>1010.54<br />
</td>
    </tr>
    <tr>
        <td>JI intervals represented<br />
</td>
        <td><br />
</td>
        <td>8/7~7/6<br />
</td>
        <td>6/5<br />
</td>
        <td>4/3<br />
</td>
        <td>7/5<br />
</td>
        <td>14/9<br />
</td>
        <td>8/5<br />
</td>
        <td>16/9~9/5<br />
</td>
    </tr>
    <tr>
        <td>Large (&quot;major&quot;) interval<br />
</td>
        <td>189.46<br />
</td>
        <td>378.92<br />
</td>
        <td>442.10<br />
</td>
        <td>631.56<br />
</td>
        <td>694.73<br />
</td>
        <td>884.19<br />
</td>
        <td>947.37<br />
</td>
        <td>1136.83<br />
</td>
    </tr>
    <tr>
        <td>JI intervals represented<br />
</td>
        <td>10/9~9/8<br />
</td>
        <td>5/4<br />
</td>
        <td>9/7<br />
</td>
        <td>10/7<br />
</td>
        <td>3/2<br />
</td>
        <td>5/3<br />
</td>
        <td>12/7~7/4<br />
</td>
        <td><br />
</td>
    </tr>
</table>

</body></html>

@@ 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:keenanpepper|keenanpepper]] and made on <tt>2011-08-17 05:33:33 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-08-17 16:06:58 UTC</tt>.<br>
-: The original revision id was <tt>246440399</tt>.<br>
+: The original revision id was <tt>246547581</tt>.<br>
-: The revision comment was: <tt></tt><br>
+: The revision comment was: <tt>some links added</tt><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>
-<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">Semaphore, namesake of the [[Semaphore family]], is characterized by the vanishing of 49/48, so the generator represents 8/7 and 7/6 equally. This results in a very low complexity 2.3.7 temperament, with the drawback that most intervals of 7 must be out of tune by at least half of 49/48, or about 18 cents.
+<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">Semaphore, namesake of the [[Semaphore family]], is characterized by the vanishing of [[49_48|49/48]], so the generator represents [[8_7|8/7]] and [[7_6|7/6]] equally. This results in a very low [[complexity]] 2.3.7 [[temperament]], with the drawback that most intervals of 7 must be out of tune by at least half of 49/48, or about 18 [[cent]]s.
-If 5 is mapped at all, it makes sense to map it to -8 generators by tempering out 81/80, making it a meantone temperament. This temperament is called "godzilla".
+If 5 is mapped at all, it makes sense to map it to -8 [[generator]]s by [[tempering out]] [[81_80|81/80]], making it a [[meantone temperament]]. This temperament is called "[[godzilla]]".
 ==Interval chains==
 ===Basic semaphore===
 || 198.46 || 448.85 || 699.23 || 949.62 || 0 || 250.38 || 500.77 || 751.15 || 1001.54 ||
-|| 9/8 || 9/7 || 3/2 || 12/7~7/4 || 1/1 || 8/7~7/6 || 4/3 || 14/9 || 16/9 ||
+|| [[9_8|9/8]] || [[9_7|9/7]] || [[3_2|3/2]] || 12/7~7/4 || [[1_1|1/1]] || 8/7~7/6 || [[4_3|4/3]] || [[14_9|14/9]] || [[16_9|16/9]] ||
 ===Godzilla===
 || 378.92 || 631.56 || 884.19 || 1136.83 || 189.46 || 442.10 || 694.73 || 947.37 || 0 || 252.63 || 505.27 || 757.90 || 1010.54 || 63.17 || 315.81 || 568.44 || 821.08 ||
-|| 5/4 || 10/7 || 5/3 || 27/14 || 10/9~9/8 || 9/7 || 3/2 || 12/7~7/4 || 1/1 || 8/7~7/6 || 4/3 || 14/9 || 16/9~9/5 || 28/27~21/20 || 6/5 || 7/5 || 8/5 ||
+|| [[5_4|5/4]] || [[10_7|10/7]] || [[5_3|5/3]] || 27/14 || 10/9~9/8 || 9/7 || 3/2 || 12/7~7/4 || 1/1 || 8/7~7/6 || 4/3 || 14/9 || 16/9~9/5 || 28/27~21/20 || [[6_5|6/5]] || [[7_5|7/5]] || [[8_5|8/5]] ||
 ==MOSes==
 ===5-note (proper)===
 || Small ("minor") interval || 198.46 || 448.85 || 699.23 || 949.62 ||
-|| JI intervals represented || 9/8 || 9/7 || 3/2 || 12/7~7/4 ||
+|| [[JI]] intervals represented || 9/8 || 9/7 || 3/2 || 12/7~7/4 ||
 || Large ("major") interval || 250.38 || 500.77 || 751.15 || 1001.54 ||
 || JI intervals represented || 8/7~7/6 || 4/3 || 14/9 || 16/9 ||
@@ Line 29: / Line 29: @@
 || JI intervals represented || 10/9~9/8 || 5/4 || 9/7 || 10/7 || 3/2 || 5/3 || 12/7~7/4 ||   ||</pre></div>
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Semaphore and Godzilla&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Semaphore, namesake of the &lt;a class="wiki_link" href="/Semaphore%20family"&gt;Semaphore family&lt;/a&gt;, is characterized by the vanishing of 49/48, so the generator represents 8/7 and 7/6 equally. This results in a very low complexity 2.3.7 temperament, with the drawback that most intervals of 7 must be out of tune by at least half of 49/48, or about 18 cents.&lt;br /&gt;
+<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Semaphore and Godzilla&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Semaphore, namesake of the &lt;a class="wiki_link" href="/Semaphore%20family"&gt;Semaphore family&lt;/a&gt;, is characterized by the vanishing of &lt;a class="wiki_link" href="/49_48"&gt;49/48&lt;/a&gt;, so the generator represents &lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt; and &lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt; equally. This results in a very low &lt;a class="wiki_link" href="/complexity"&gt;complexity&lt;/a&gt; 2.3.7 &lt;a class="wiki_link" href="/temperament"&gt;temperament&lt;/a&gt;, with the drawback that most intervals of 7 must be out of tune by at least half of 49/48, or about 18 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s.&lt;br /&gt;
 &lt;br /&gt;
-If 5 is mapped at all, it makes sense to map it to -8 generators by tempering out 81/80, making it a meantone temperament. This temperament is called &amp;quot;godzilla&amp;quot;.&lt;br /&gt;
+If 5 is mapped at all, it makes sense to map it to -8 &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt;s by &lt;a class="wiki_link" href="/tempering%20out"&gt;tempering out&lt;/a&gt; &lt;a class="wiki_link" href="/81_80"&gt;81/80&lt;/a&gt;, making it a &lt;a class="wiki_link" href="/meantone%20temperament"&gt;meantone temperament&lt;/a&gt;. This temperament is called &amp;quot;&lt;a class="wiki_link" href="/godzilla"&gt;godzilla&lt;/a&gt;&amp;quot;.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Interval chains"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Interval chains&lt;/h2&gt;
@@ Line 59: / Line 59: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;9/8&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;9/7&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;3/2&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;12/7~7/4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1/1&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/1_1"&gt;1/1&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;8/7~7/6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;4/3&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/4_3"&gt;4/3&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;14/9&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/14_9"&gt;14/9&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;16/9&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/16_9"&gt;16/9&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 121: / Line 121: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;5/4&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;10/7&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/10_7"&gt;10/7&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;5/3&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/5_3"&gt;5/3&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;27/14&lt;br /&gt;
@@ Line 149: / Line 149: @@
          &lt;td&gt;28/27~21/20&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;6/5&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;7/5&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;8/5&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/8_5"&gt;8/5&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 176: / Line 176: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;JI intervals represented&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/JI"&gt;JI&lt;/a&gt; intervals represented&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;9/8&lt;br /&gt;

Semaphore and godzilla: Difference between revisions

Revision as of 16:06, 17 August 2011

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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