Pseudo-semaphore
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author keenanpepper and made on 2011-08-17 15:45:22 UTC.
- The original revision id was 246543337.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
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.
==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 || || ||Original HTML content:
<html><head><title>Pseudo-semaphore</title></head><body>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.<br />
<br />
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 <a class="wiki_link" href="/Superpyth">superpyth</a> in which the 4/3 generator has been split in half forming a weird interval that's neither 8/7 nor 7/6.<br />
<!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Interval chain"></a><!-- ws:end:WikiTextHeadingRule:0 -->Interval chain</h2>
<table class="wiki_table">
<tr>
<td>204.<br />
</td>
<td>448.<br />
</td>
<td>692.<br />
</td>
<td>936.<br />
</td>
<td>1180.<br />
</td>
<td>224.<br />
</td>
<td>468.<br />
</td>
<td>712.<br />
</td>
<td>956.<br />
</td>
<td>0.<br />
</td>
<td>244.<br />
</td>
<td>488.<br />
</td>
<td>732.<br />
</td>
<td>976.<br />
</td>
<td>20.<br />
</td>
<td>264.<br />
</td>
<td>508.<br />
</td>
<td>752.<br />
</td>
<td>996.<br />
</td>
</tr>
<tr>
<td>9/8<br />
</td>
<td>9/7<br />
</td>
<td>3/2 (flat)<br />
</td>
<td>12/7<br />
</td>
<td><br />
</td>
<td>9/8~8/7<br />
</td>
<td><br />
</td>
<td>3/2 (sharp)<br />
</td>
<td><br />
</td>
<td>1/1<br />
</td>
<td><br />
</td>
<td>4/3 (flat)<br />
</td>
<td><br />
</td>
<td>7/4~16/9<br />
</td>
<td><br />
</td>
<td>7/6<br />
</td>
<td>4/3 (sharp)<br />
</td>
<td>14/9<br />
</td>
<td>16/9<br />
</td>
</tr>
</table>
<!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x-MOSes"></a><!-- ws:end:WikiTextHeadingRule:2 -->MOSes</h2>
<!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc2"><a name="x-MOSes-5-note (LLLLs, proper)"></a><!-- ws:end:WikiTextHeadingRule:4 -->5-note (LLLLs, proper)</h3>
The 5-note MOS is not much use because only one of the two different mappings shows up. You'd be better off using <a class="wiki_link" href="/semaphore">semaphore</a>[5] or <a class="wiki_link" href="/superpyth">superpyth</a>[5] (or <a class="wiki_link" href="/5edo">5edo</a>).<br />
<table class="wiki_table">
<tr>
<td>Small ("minor") interval<br />
</td>
<td>224.<br />
</td>
<td>468.<br />
</td>
<td>712.<br />
</td>
<td>956.<br />
</td>
</tr>
<tr>
<td>JI intervals represented<br />
</td>
<td>9/8~8/7<br />
</td>
<td><br />
</td>
<td>3/2<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>Large ("major") interval<br />
</td>
<td>244.<br />
</td>
<td>488.<br />
</td>
<td>732.<br />
</td>
<td>976.<br />
</td>
</tr>
<tr>
<td>JI intervals represented<br />
</td>
<td><br />
</td>
<td>4/3<br />
</td>
<td><br />
</td>
<td>7/4~16/9<br />
</td>
</tr>
</table>
<!-- ws:start:WikiTextHeadingRule:6:<h3> --><h3 id="toc3"><a name="x-MOSes-9-note (LLsLsLsLs, improper)"></a><!-- ws:end:WikiTextHeadingRule:6 -->9-note (LLsLsLsLs, improper)</h3>
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 <a class="wiki_link" href="/9edo">9edo</a>.<br />
<table class="wiki_table">
<tr>
<td>Small ("minor") interval<br />
</td>
<td>20.<br />
</td>
<td>244.<br />
</td>
<td>264.<br />
</td>
<td>488.<br />
</td>
<td>508.<br />
</td>
<td>732.<br />
</td>
<td>752.<br />
</td>
<td>976.<br />
</td>
</tr>
<tr>
<td>JI intervals represented<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>7/6<br />
</td>
<td>4/3 (flat)<br />
</td>
<td>4/3 (sharp)<br />
</td>
<td><br />
</td>
<td>14/9<br />
</td>
<td>7/4~16/9<br />
</td>
</tr>
<tr>
<td>Large ("major") interval<br />
</td>
<td>224.<br />
</td>
<td>448.<br />
</td>
<td>468.<br />
</td>
<td>692.<br />
</td>
<td>712.<br />
</td>
<td>936.<br />
</td>
<td>956.<br />
</td>
<td>1180.<br />
</td>
</tr>
<tr>
<td>JI intervals represented<br />
</td>
<td>9/8~8/7<br />
</td>
<td>9/7<br />
</td>
<td><br />
</td>
<td>3/2 (flat)<br />
</td>
<td>3/2 (sharp)<br />
</td>
<td>12/7<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
</table>
</body></html>