Tenney–Euclidean temperament measures: Difference between revisions
Wikispaces>mbattaglia1 **Imported revision 386803398 - Original comment: ** |
Wikispaces>mbattaglia1 **Imported revision 386803464 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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:mbattaglia1|mbattaglia1]] and made on <tt>2012-11-28 03:17: | : This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2012-11-28 03:17:36 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>386803464</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> | ||
| Line 17: | Line 17: | ||
[[math]] | [[math]] | ||
\displaystyle | \displaystyle | ||
||M|| = ||v_1 \wedge v_2 \wedge ... \wedge v_r|| = \sqrt{\frac{det([v_i \cdot v_j])}{C(n, r)} | ||M|| = ||v_1 \wedge v_2 \wedge ... \wedge v_r|| = \sqrt{\frac{det([v_i \cdot v_j])}{C(n, r)}} | ||
[[math]] | [[math]] | ||
| Line 46: | Line 46: | ||
[[math]]&lt;br/&gt; | [[math]]&lt;br/&gt; | ||
\displaystyle&lt;br /&gt; | \displaystyle&lt;br /&gt; | ||
||M|| = ||v_1 \wedge v_2 \wedge ... \wedge v_r|| = \sqrt{\frac{det([v_i \cdot v_j])}{C(n, r)}&lt;br/&gt;[[math]] | ||M|| = ||v_1 \wedge v_2 \wedge ... \wedge v_r|| = \sqrt{\frac{det([v_i \cdot v_j])}{C(n, r)}}&lt;br/&gt;[[math]] | ||
--><script type="math/tex">\displaystyle | --><script type="math/tex">\displaystyle | ||
||M|| = ||v_1 \wedge v_2 \wedge ... \wedge v_r|| = \sqrt{\frac{det([v_i \cdot v_j])}{C(n, r)}</script><!-- ws:end:WikiTextMathRule:0 --><br /> | ||M|| = ||v_1 \wedge v_2 \wedge ... \wedge v_r|| = \sqrt{\frac{det([v_i \cdot v_j])}{C(n, r)}}</script><!-- ws:end:WikiTextMathRule:0 --><br /> | ||
<br /> | <br /> | ||
where C(n, r) is the number of combinations of n things taken r at a time, and vi.vj is the TE <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Symmetric_bilinear_form" rel="nofollow">symmetric form</a> on vals, which in weighted coordinates is simply the ordinary dot product. Here n is the number of primes up to the prime limit p, and r is the rank of the temperament, which equals the number of vals wedged together to compute the wedgie.<br /> | where C(n, r) is the number of combinations of n things taken r at a time, and vi.vj is the TE <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Symmetric_bilinear_form" rel="nofollow">symmetric form</a> on vals, which in weighted coordinates is simply the ordinary dot product. Here n is the number of primes up to the prime limit p, and r is the rank of the temperament, which equals the number of vals wedged together to compute the wedgie.<br /> | ||