Subgroup basis matrix: Difference between revisions
Wikispaces>genewardsmith **Imported revision 356334468 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 356334756 - 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:genewardsmith|genewardsmith]] and made on <tt>2012-08-04 13: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-08-04 13:09:00 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>356334756</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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**Subgroup Restriction** | **Subgroup Restriction** | ||
To restrict a val to the subgroup defined by the V-map, we'll left-multiply **V** by a val **W**. In this case, our val **W** will be the 7-limit patent val for [[12-EDO]]: | To restrict a val to the subgroup defined by the V-map, we'll left-multiply **V** by a val **W**. In this case, our val **W** will be the 7-limit patent val for [[12edo|12-EDO]]: | ||
[[math]] | [[math]] | ||
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which tells us that the restriction of the 12-EDO patent val to the 2.9/7.5/3 subgroup has a mapping of 12 steps for 2/1, a mapping of 4 steps for 9/7, and a mapping of 9 steps for 5/3. | which tells us that the restriction of the 12-EDO patent val to the 2.9/7.5/3 subgroup has a mapping of 12 steps for 2/1, a mapping of 4 steps for 9/7, and a mapping of 9 steps for 5/3. | ||
We can also send temperament mapping matrices into the V-map. For instance, here's 7-limit sensi: | We can also send temperament mapping matrices into the V-map. For instance, here's 7-limit [[Starling temperaments#Sensi temperament|sensi]]: | ||
[[math]] | [[math]] | ||
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<strong>Subgroup Restriction</strong><br /> | <strong>Subgroup Restriction</strong><br /> | ||
To restrict a val to the subgroup defined by the V-map, we'll left-multiply <strong>V</strong> by a val <strong>W</strong>. In this case, our val <strong>W</strong> will be the 7-limit patent val for <a class="wiki_link" href="/ | To restrict a val to the subgroup defined by the V-map, we'll left-multiply <strong>V</strong> by a val <strong>W</strong>. In this case, our val <strong>W</strong> will be the 7-limit patent val for <a class="wiki_link" href="/12edo">12-EDO</a>:<br /> | ||
<br /> | <br /> | ||
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which tells us that the restriction of the 12-EDO patent val to the 2.9/7.5/3 subgroup has a mapping of 12 steps for 2/1, a mapping of 4 steps for 9/7, and a mapping of 9 steps for 5/3.<br /> | which tells us that the restriction of the 12-EDO patent val to the 2.9/7.5/3 subgroup has a mapping of 12 steps for 2/1, a mapping of 4 steps for 9/7, and a mapping of 9 steps for 5/3.<br /> | ||
<br /> | <br /> | ||
We can also send temperament mapping matrices into the V-map. For instance, here's 7-limit sensi:<br /> | We can also send temperament mapping matrices into the V-map. For instance, here's 7-limit <a class="wiki_link" href="/Starling%20temperaments#Sensi temperament">sensi</a>:<br /> | ||
<br /> | <br /> | ||
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