Height: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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>2013-08-31 06:47:50 UTC</tt>.<br>

: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2013-08-31 06:49:09 UTC</tt>.<br>

: The original revision id was <tt>~~447781820~~</tt>.<br>

: The original revision id was <tt>447781960</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>

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\dfrac {\sqrt{q}} {\left( {q + 1} \right)} 2^{\large{\frac{1}{2} {\|q\|_{T1}}}}

[[math]] || [[math]]

\|q\|_{T1} ~~\right)~~ - 2 \log_2 \left( {q + 1} \right) + \log_2 \left( {q} \right)

\|q\|_{T1} - 2 \log_2 \left( {q + 1} \right) + \log_2 \left( {q} \right)

[[math]] ||

|| [[Kees Height]] || Semi-Height || [[math]]

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\|{2^{-v_2 \left( {q} \right)} q}\|_{T1} + | \log_2 \left( {q} \right) - v_2 \left( {q} \right) |

[[math]] ||

Where T1~~(q)~~ is the [[xenharmonic/Generalized Tenney Norms and Tp Interval Space#The%20Tenney%20Norm%20(T1%20norm)|tenney norm]] of q in monzo form, and vp(x) is the [[http://en.wikipedia.org/wiki/P-adic_order|p-adic valuation]] of x.

Where ||q||<span style="font-size: 80%; vertical-align: sub;">T1</span> is the [[xenharmonic/Generalized Tenney Norms and Tp Interval Space#The%20Tenney%20Norm%20(T1%20norm)|tenney norm]] of q in monzo form, and v<span style="vertical-align: sub;">p</span>(x) is the [[http://en.wikipedia.org/wiki/P-adic_order|p-adic valuation]] of x.

Some useful identities:

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<td><!-- ws:start:WikiTextMathRule:15:

[[math]]&lt;br/&gt;

\|q\|_{T1} ~~\right)~~ - 2 \log_2 \left( {q + 1} \right) + \log_2 \left( {q} \right)&lt;br/&gt;[[math]]

\|q\|_{T1} - 2 \log_2 \left( {q + 1} \right) + \log_2 \left( {q} \right)&lt;br/&gt;[[math]]

--><script type="math/tex">\|q\|_{T1} ~~\right)~~ - 2 \log_2 \left( {q + 1} \right) + \log_2 \left( {q} \right)</script><br />

--><script type="math/tex">\|q\|_{T1} - 2 \log_2 \left( {q + 1} \right) + \log_2 \left( {q} \right)</script><br />

</td>

</tr>

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</table>

Where T1~~(q)~~ is the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Generalized%20Tenney%20Norms%20and%20Tp%20Interval%20Space#The%20Tenney%20Norm%20(T1%20norm)">tenney norm</a> of q in monzo form, and vp(x) is the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/P-adic_order" rel="nofollow">p-adic valuation</a> of x.<br />

Where ||q||<span style="font-size: 80%; vertical-align: sub;">T1</span> is the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Generalized%20Tenney%20Norms%20and%20Tp%20Interval%20Space#The%20Tenney%20Norm%20(T1%20norm)">tenney norm</a> of q in monzo form, and v<span style="vertical-align: sub;">p</span>(x) is the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/P-adic_order" rel="nofollow">p-adic valuation</a> of x.<br />

<br />

Some useful identities:<br />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2013-08-31 06:47:50 UTC</tt>.<br>
+: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2013-08-31 06:49:09 UTC</tt>.<br>
-: The original revision id was <tt>447781820</tt>.<br>
+: The original revision id was <tt>447781960</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>
@@ Line 66: / Line 66: @@
 \dfrac {\sqrt{q}} {\left( {q + 1} \right)} 2^{\large{\frac{1}{2} {\|q\|_{T1}}}}
 [[math]] || [[math]]
-\|q\|_{T1} \right) - 2 \log_2 \left( {q + 1} \right) + \log_2 \left( {q} \right)
+\|q\|_{T1} - 2 \log_2 \left( {q + 1} \right) + \log_2 \left( {q} \right)
 [[math]] ||
 || [[Kees Height]] || Semi-Height || [[math]]
@@ Line 76: / Line 76: @@
 \|{2^{-v_2 \left( {q} \right)} q}\|_{T1} + | \log_2 \left( {q} \right) - v_2 \left( {q} \right) |
 [[math]] ||
-Where T1(q) is the [[xenharmonic/Generalized Tenney Norms and Tp Interval Space#The%20Tenney%20Norm%20(T1%20norm)|tenney norm]] of q in monzo form, and vp(x) is the [[http://en.wikipedia.org/wiki/P-adic_order|p-adic valuation]] of x.
+Where ||q||&lt;span style="font-size: 80%; vertical-align: sub;"&gt;T1&lt;/span&gt; is the [[xenharmonic/Generalized Tenney Norms and Tp Interval Space#The%20Tenney%20Norm%20(T1%20norm)|tenney norm]] of q in monzo form, and v&lt;span style="vertical-align: sub;"&gt;p&lt;/span&gt;(x) is the [[http://en.wikipedia.org/wiki/P-adic_order|p-adic valuation]] of x.
 Some useful identities:
@@ Line 219: / Line 219: @@
          &lt;td&gt;&lt;!-- ws:start:WikiTextMathRule:15:
 [[math]]&amp;lt;br/&amp;gt;
-\|q\|_{T1} \right) - 2 \log_2 \left( {q + 1} \right) + \log_2 \left( {q} \right)&amp;lt;br/&amp;gt;[[math]]
+\|q\|_{T1} - 2 \log_2 \left( {q + 1} \right) + \log_2 \left( {q} \right)&amp;lt;br/&amp;gt;[[math]]
-  --&gt;&lt;script type="math/tex"&gt;\|q\|_{T1} \right) - 2 \log_2 \left( {q + 1} \right) + \log_2 \left( {q} \right)&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:15 --&gt;&lt;br /&gt;
+  --&gt;&lt;script type="math/tex"&gt;\|q\|_{T1} - 2 \log_2 \left( {q + 1} \right) + \log_2 \left( {q} \right)&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:15 --&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 248: / Line 248: @@
 &lt;/table&gt;
-Where T1(q) is the &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Generalized%20Tenney%20Norms%20and%20Tp%20Interval%20Space#The%20Tenney%20Norm%20(T1%20norm)"&gt;tenney norm&lt;/a&gt; of q in monzo form, and vp(x) is the &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/P-adic_order" rel="nofollow"&gt;p-adic valuation&lt;/a&gt; of x.&lt;br /&gt;
+Where ||q||&lt;span style="font-size: 80%; vertical-align: sub;"&gt;T1&lt;/span&gt; is the &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Generalized%20Tenney%20Norms%20and%20Tp%20Interval%20Space#The%20Tenney%20Norm%20(T1%20norm)"&gt;tenney norm&lt;/a&gt; of q in monzo form, and v&lt;span style="vertical-align: sub;"&gt;p&lt;/span&gt;(x) is the &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/P-adic_order" rel="nofollow"&gt;p-adic valuation&lt;/a&gt; of x.&lt;br /&gt;
 &lt;br /&gt;
 Some useful identities:&lt;br /&gt;