Pseudo-semaphore: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
Pseudo-semaphore is a weird temperament in which the third harmonic does not have a single consistent mapping. If you want to force it into the regular mapping paradigm you have to think of it as a 2.3.3'.7 temperament.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2012-05-19 04:24:02 UTC</tt>.<br>
: The original revision id was <tt>337248526</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>
<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">Pseudo-semaphore is a weird temperament in which the third harmonic does not have a single consistent mapping. If you want to force it into the regular mapping paradigm you have to think of it as a 2.3.3'.7 temperament.


It's called "pseudo-semaphore" because it has the same MOS structure as [[semaphore]], but 49/48 is not tempered out. Perhaps it's better to think of it as [[Superpyth|superpyth]] in which the 4/3 generator has been split in half forming a weird interval that's neither 8/7 nor 7/6.
It's called "pseudo-semaphore" because it has the same MOS structure as [[Semaphore|semaphore]], but 49/48 is not tempered out. Perhaps it's better to think of it as [[Superpyth|superpyth]] in which the 4/3 generator has been split in half forming a weird interval that's neither 8/7 nor 7/6.
==Interval chain==
|| 204. || 448. || 692. || 936. || 1180. || 224. || 468. || 712. || 956. || 0. || 244. || 488. || 732. || 976. || 20. || 264. || 508. || 752. || 996. ||
|| 9/8 || 9/7 || 3/2 (flat) || 12/7 ||  || 9/8~8/7 ||  || 3/2 (sharp) ||  || 1/1 ||  || 4/3 (flat) ||  || 7/4~16/9 ||  || 7/6 || 4/3 (sharp) || 14/9 || 16/9 ||
==MOSes==
===5-note (LLLLs, proper)===
The 5-note MOS is not much use because only one of the two different mappings shows up. You'd be better off using [[semaphore]][5] or [[superpyth]][5] (or [[5edo]]).
|| Small ("minor") interval || 224. || 468. || 712. || 956. ||
|| JI intervals represented || 9/8~8/7 ||  || 3/2 ||  ||
|| Large ("major") interval || 244. || 488. || 732. || 976. ||
|| JI intervals represented ||  || 4/3 ||  || 7/4~16/9 ||
===9-note (LLsLsLsLs, improper)===
Here's where all the action begins. Note that this nine-note scale contains nine 4/3s and nine 3/2s. The only way this is possible with a single mapping for 3 is an equal temperament, and all of these 4/3s and 3/2s are much more accurate than in [[9edo]].
|| Small ("minor") interval || 20. || 244. || 264. || 488. || 508. || 732. || 752. || 976. ||
|| JI intervals represented ||  ||  || 7/6 || 4/3 (flat) || 4/3 (sharp) ||  || 14/9 || 7/4~16/9 ||
|| Large ("major") interval || 224. || 448. || 468. || 692. || 712. || 936. || 956. || 1180. ||
|| JI intervals represented || 9/8~8/7 || 9/7 ||  || 3/2 (flat) || 3/2 (sharp) || 12/7 ||  ||  ||</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;Pseudo-semaphore&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Pseudo-semaphore is a weird temperament in which the third harmonic does not have a single consistent mapping. If you want to force it into the regular mapping paradigm you have to think of it as a 2.3.3'.7 temperament.&lt;br /&gt;
&lt;br /&gt;
It's called &amp;quot;pseudo-semaphore&amp;quot; because it has the same MOS structure as &lt;a class="wiki_link" href="/semaphore"&gt;semaphore&lt;/a&gt;, but 49/48 is not tempered out. Perhaps it's better to think of it as &lt;a class="wiki_link" href="/Superpyth"&gt;superpyth&lt;/a&gt; in which the 4/3 generator has been split in half forming a weird interval that's neither 8/7 nor 7/6.&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Interval chain"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Interval chain&lt;/h2&gt;


&lt;table class="wiki_table"&gt;
==Interval chain==
    &lt;tr&gt;
        &lt;td&gt;204.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;448.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;692.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;936.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1180.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;224.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;468.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;712.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;956.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;244.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;488.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;732.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;976.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;264.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;508.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;752.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;996.&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2 (flat)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/8~8/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2 (sharp)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/3 (flat)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/4~16/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/3 (sharp)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-MOSes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;MOSes&lt;/h2&gt;
{| class="wikitable"
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-MOSes-5-note (LLLLs, proper)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;5-note (LLLLs, proper)&lt;/h3&gt;
|-
The 5-note MOS is not much use because only one of the two different mappings shows up. You'd be better off using &lt;a class="wiki_link" href="/semaphore"&gt;semaphore&lt;/a&gt;[5] or &lt;a class="wiki_link" href="/superpyth"&gt;superpyth&lt;/a&gt;[5] (or &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt;).&lt;br /&gt;
| | 204.
| | 448.
| | 692.
| | 936.
| | 1180.
| | 224.
| | 468.
| | 712.
| | 956.
| | 0.
| | 244.
| | 488.
| | 732.
| | 976.
| | 20.
| | 264.
| | 508.
| | 752.
| | 996.
|-
| | 9/8
| | 9/7
| | 3/2 (flat)
| | 12/7
| |
| | 9/8~8/7
| |
| | 3/2 (sharp)
| |
| | 1/1
| |
| | 4/3 (flat)
| |
| | 7/4~16/9
| |
| | 7/6
| | 4/3 (sharp)
| | 14/9
| | 16/9
|}


==MOSes==


&lt;table class="wiki_table"&gt;
===5-note (LLLLs, proper)===
    &lt;tr&gt;
The 5-note MOS is not much use because only one of the two different mappings shows up. You'd be better off using [[Semaphore|semaphore]][5] or [[Superpyth|superpyth]][5] (or [[5edo|5edo]]).
        &lt;td&gt;Small (&amp;quot;minor&amp;quot;) interval&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;224.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;468.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;712.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;956.&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;JI intervals represented&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/8~8/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Large (&amp;quot;major&amp;quot;) interval&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;244.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;488.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;732.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;976.&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;JI intervals represented&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/4~16/9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-MOSes-9-note (LLsLsLsLs, improper)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;9-note (LLsLsLsLs, improper)&lt;/h3&gt;
{| class="wikitable"
Here's where all the action begins. Note that this nine-note scale contains nine 4/3s and nine 3/2s. The only way this is possible with a single mapping for 3 is an equal temperament, and all of these 4/3s and 3/2s are much more accurate than in &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt;.&lt;br /&gt;
|-
| | Small ("minor") interval
| | 224.
| | 468.
| | 712.
| | 956.
|-
| | JI intervals represented
| | 9/8~8/7
| |
| | 3/2
| |
|-
| | Large ("major") interval
| | 244.
| | 488.
| | 732.
| | 976.
|-
| | JI intervals represented
| |
| | 4/3
| |
| | 7/4~16/9
|}


===9-note (LLsLsLsLs, improper)===
Here's where all the action begins. Note that this nine-note scale contains nine 4/3s and nine 3/2s. The only way this is possible with a single mapping for 3 is an equal temperament, and all of these 4/3s and 3/2s are much more accurate than in [[9edo|9edo]].


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;td&gt;Small (&amp;quot;minor&amp;quot;) interval&lt;br /&gt;
| | Small ("minor") interval
&lt;/td&gt;
| | 20.
        &lt;td&gt;20.&lt;br /&gt;
| | 244.
&lt;/td&gt;
| | 264.
        &lt;td&gt;244.&lt;br /&gt;
| | 488.
&lt;/td&gt;
| | 508.
        &lt;td&gt;264.&lt;br /&gt;
| | 732.
&lt;/td&gt;
| | 752.
        &lt;td&gt;488.&lt;br /&gt;
| | 976.
&lt;/td&gt;
|-
        &lt;td&gt;508.&lt;br /&gt;
| | JI intervals represented
&lt;/td&gt;
| |
        &lt;td&gt;732.&lt;br /&gt;
| |
&lt;/td&gt;
| | 7/6
        &lt;td&gt;752.&lt;br /&gt;
| | 4/3 (flat)
&lt;/td&gt;
| | 4/3 (sharp)
        &lt;td&gt;976.&lt;br /&gt;
| |
&lt;/td&gt;
| | 14/9
    &lt;/tr&gt;
| | 7/4~16/9
    &lt;tr&gt;
|-
        &lt;td&gt;JI intervals represented&lt;br /&gt;
| | Large ("major") interval
&lt;/td&gt;
| | 224.
        &lt;td&gt;&lt;br /&gt;
| | 448.
&lt;/td&gt;
| | 468.
        &lt;td&gt;&lt;br /&gt;
| | 692.
&lt;/td&gt;
| | 712.
        &lt;td&gt;7/6&lt;br /&gt;
| | 936.
&lt;/td&gt;
| | 956.
        &lt;td&gt;4/3 (flat)&lt;br /&gt;
| | 1180.
&lt;/td&gt;
|-
        &lt;td&gt;4/3 (sharp)&lt;br /&gt;
| | JI intervals represented
&lt;/td&gt;
| | 9/8~8/7
        &lt;td&gt;&lt;br /&gt;
| | 9/7
&lt;/td&gt;
| |
        &lt;td&gt;14/9&lt;br /&gt;
| | 3/2 (flat)
&lt;/td&gt;
| | 3/2 (sharp)
        &lt;td&gt;7/4~16/9&lt;br /&gt;
| | 12/7
&lt;/td&gt;
| |
    &lt;/tr&gt;
| |
    &lt;tr&gt;
|}
        &lt;td&gt;Large (&amp;quot;major&amp;quot;) interval&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;224.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;448.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;468.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;692.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;712.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;936.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;956.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1180.&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;JI intervals represented&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/8~8/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2 (flat)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2 (sharp)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/body&gt;&lt;/html&gt;</pre></div>