Vals and tuning space: Difference between revisions
Wikispaces>genewardsmith **Imported revision 307445566 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 307490906 - 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>2012-03-03 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-03-03 22:15:29 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>307490906</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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This tells us that in septimal 12 equal, represented by V, the interval 225/224, represented by M, is mapped to 0, which represents 1. Hence, 225/224 vanishes in septimal 12 equal; it is in the [[http://mathworld.wolfram.com/GroupKernel.html|kernel]] of V. One should note in particular that the coordinates of V represent where the successive primes 2, 3, 5 and 7 are mapped. | This tells us that in septimal 12 equal, represented by V, the interval 225/224, represented by M, is mapped to 0, which represents 1. Hence, 225/224 vanishes in septimal 12 equal; it is in the [[http://mathworld.wolfram.com/GroupKernel.html|kernel]] of V. One should note in particular that the coordinates of V represent where the successive primes 2, 3, 5 and 7 are mapped. | ||
By embedding the monzos into a suitable vector space, norms may be placed on the monzos in various ways, turning them into [[http://mathworld.wolfram.com/PointLattice.html|lattices]] in a vector space. Given a vector space norm on a space of ket vectors, the [[http://mathworld.wolfram.com/DualNormedSpace.html|dual vector space norm]] on the space of bra vectors is defined as the least quantity ||V|| making | |||
**|<V|M>| ≤ ||V|| ||M||** | **|<V|M>| ≤ ||V|| ||M||** | ||
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This tells us that in septimal 12 equal, represented by V, the interval 225/224, represented by M, is mapped to 0, which represents 1. Hence, 225/224 vanishes in septimal 12 equal; it is in the <a class="wiki_link_ext" href="http://mathworld.wolfram.com/GroupKernel.html" rel="nofollow">kernel</a> of V. One should note in particular that the coordinates of V represent where the successive primes 2, 3, 5 and 7 are mapped.<br /> | This tells us that in septimal 12 equal, represented by V, the interval 225/224, represented by M, is mapped to 0, which represents 1. Hence, 225/224 vanishes in septimal 12 equal; it is in the <a class="wiki_link_ext" href="http://mathworld.wolfram.com/GroupKernel.html" rel="nofollow">kernel</a> of V. One should note in particular that the coordinates of V represent where the successive primes 2, 3, 5 and 7 are mapped.<br /> | ||
<br /> | <br /> | ||
By embedding the monzos into a suitable vector space, norms may be placed on the monzos in various ways, turning them into <a class="wiki_link_ext" href="http://mathworld.wolfram.com/PointLattice.html" rel="nofollow">lattices</a> in a vector space. Given a vector space norm on a space of ket vectors, the <a class="wiki_link_ext" href="http://mathworld.wolfram.com/DualNormedSpace.html" rel="nofollow">dual vector space norm</a> on the space of bra vectors is defined as the least quantity ||V|| making<br /> | |||
<br /> | <br /> | ||
<strong>|&lt;V|M&gt;| ≤ ||V|| ||M||</strong><br /> | <strong>|&lt;V|M&gt;| ≤ ||V|| ||M||</strong><br /> | ||