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 04:43:48 UTC</tt>.<br>

: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2013-08-31 06:47:50 UTC</tt>.<br>

: The original revision id was <tt>~~447773950~~</tt>.<br>

: The original revision id was <tt>447781820</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 {\left( {q + 1} \right)} {\sqrt{q}} 2^{\large{\frac{1}{2} {\|q\|_{T1}}}}

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

T1 \~~left(~~ {q} ~~\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]] ||

|| Harmonic Height || Semi-Height || [[math]]

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

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

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

\|q\|_{T1} \right) - 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( {d} \right)} d} \right)

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

~~<span style="line-height: 1.5;">~~2^{\large{\frac{1}{2}\|2^{-v_2 \left( {q} \right)} q\|_{T1} + \mid \log_2(2) - v_2(q) \mid}}~~</span>~~

2^{\large{\left(\frac{1}{2}\|2^{-v_2 \left( {q} \right)} q\|_{T1} + \mid \log_2(2) - v_2(q) \mid \right)}}

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

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

\|{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.

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<td><!-- ws:start:WikiTextMathRule:12:

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

T1 \~~left(~~ {q} ~~\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">T1 \~~left(~~ {q} ~~\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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<td><!-- ws:start:WikiTextMathRule:15:

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

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

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

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

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

</td>

</tr>

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<td><!-- ws:start:WikiTextMathRule:17:

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

~~&lt;span style=&quot;line-height: 1.5;&quot;&gt;~~2^{\large{\frac{1}{2}\|2^{-v_2 \left( {q} \right)} q\|_{T1} + \mid \log_2(2) - v_2(q) \mid}}~~&lt;/span&gt;~~&lt;br/&gt;[[math]]

2^{\large{\left(\frac{1}{2}\|2^{-v_2 \left( {q} \right)} q\|_{T1} + \mid \log_2(2) - v_2(q) \mid \right)}}&lt;br/&gt;[[math]]

--><script type="math/tex~~"><span style="line-height: 1.5;~~">2^{\large{\frac{1}{2}\|2^{-v_2 \left( {q} \right)} q\|_{T1} + \mid \log_2(2) - v_2(q) \mid}}~~</span>~~</script><br />

--><script type="math/tex">2^{\large{\left(\frac{1}{2}\|2^{-v_2 \left( {q} \right)} q\|_{T1} + \mid \log_2(2) - v_2(q) \mid \right)}}</script><br />

</td>

<td><!-- ws:start:WikiTextMathRule:18:

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

T1 \~~left(~~ {2^{-v_2 \left( {q} \right)} q} \~~right)~~ + | \log_2 \left( {q} \right) - v_2 \left( {q} \right) |&lt;br/&gt;[[math]]

\|{2^{-v_2 \left( {q} \right)} q}\|_{T1} + | \log_2 \left( {q} \right) - v_2 \left( {q} \right) |&lt;br/&gt;[[math]]

--><script type="math/tex">T1 \~~left(~~ {2^{-v_2 \left( {q} \right)} q} \~~right)~~ + | \log_2 \left( {q} \right) - v_2 \left( {q} \right) |</script><br />

--><script type="math/tex">\|{2^{-v_2 \left( {q} \right)} q}\|_{T1} + | \log_2 \left( {q} \right) - v_2 \left( {q} \right) |</script><br />

</td>

</tr>

@@ 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 04:43:48 UTC</tt>.<br>
+: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2013-08-31 06:47:50 UTC</tt>.<br>
-: The original revision id was <tt>447773950</tt>.<br>
+: The original revision id was <tt>447781820</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 59: / Line 59: @@
 \dfrac {\left( {q + 1} \right)} {\sqrt{q}} 2^{\large{\frac{1}{2} {\|q\|_{T1}}}}
 [[math]] || [[math]]
-T1 \left( {q} \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]] ||
 || Harmonic Height || Semi-Height || [[math]]
@@ Line 66: / Line 66: @@
 \dfrac {\sqrt{q}} {\left( {q + 1} \right)} 2^{\large{\frac{1}{2} {\|q\|_{T1}}}}
 [[math]] || [[math]]
-T1 \left( {q} \right) - 2 \log_2 \left( {q + 1} \right) + \log_2 \left( {q} \right)
+\|q\|_{T1} \right) - 2 \log_2 \left( {q + 1} \right) + \log_2 \left( {q} \right)
 [[math]] ||
 || [[Kees Height]] || Semi-Height || [[math]]
@@ Line 72: / Line 72: @@
 ^{-v_2 \left( {d} \right)} d} \right)
 [[math]] || [[math]]
-&lt;span style="line-height: 1.5;"&gt;2^{\large{\frac{1}{2}\|2^{-v_2 \left( {q} \right)} q\|_{T1} + \mid \log_2(2) - v_2(q) \mid}}&lt;/span&gt;
+^{\large{\left(\frac{1}{2}\|2^{-v_2 \left( {q} \right)} q\|_{T1} + \mid \log_2(2) - v_2(q) \mid \right)}}
 [[math]] || [[math]]
-T1 \left( {2^{-v_2 \left( {q} \right)} q} \right) + | \log_2 \left( {q} \right) - v_2 \left( {q} \right) |
+\|{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.
@@ Line 198: / Line 198: @@
          &lt;td&gt;&lt;!-- ws:start:WikiTextMathRule:12:
 [[math]]&amp;lt;br/&amp;gt;
-T1 \left( {q} \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;T1 \left( {q} \right) + 2 \log_2 \left( {q + 1} \right) - \log_2 \left( {q} \right)&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:12 --&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:12 --&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 219: / Line 219: @@
          &lt;td&gt;&lt;!-- ws:start:WikiTextMathRule:15:
 [[math]]&amp;lt;br/&amp;gt;
-T1 \left( {q} \right) - 2 \log_2 \left( {q + 1} \right) + \log_2 \left( {q} \right)&amp;lt;br/&amp;gt;[[math]]
+\|q\|_{T1} \right) - 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;T1 \left( {q} \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} \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;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 237: / Line 237: @@
          &lt;td&gt;&lt;!-- ws:start:WikiTextMathRule:17:
 [[math]]&amp;lt;br/&amp;gt;
-&amp;lt;span style=&amp;quot;line-height: 1.5;&amp;quot;&amp;gt;2^{\large{\frac{1}{2}\|2^{-v_2 \left( {q} \right)} q\|_{T1} + \mid \log_2(2) - v_2(q) \mid}}&amp;lt;/span&amp;gt;&amp;lt;br/&amp;gt;[[math]]
+^{\large{\left(\frac{1}{2}\|2^{-v_2 \left( {q} \right)} q\|_{T1} + \mid \log_2(2) - v_2(q) \mid \right)}}&amp;lt;br/&amp;gt;[[math]]
-  --&gt;&lt;script type="math/tex"&gt;&lt;span style="line-height: 1.5;"&gt;2^{\large{\frac{1}{2}\|2^{-v_2 \left( {q} \right)} q\|_{T1} + \mid \log_2(2) - v_2(q) \mid}}&lt;/span&gt;&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:17 --&gt;&lt;br /&gt;
+  --&gt;&lt;script type="math/tex"&gt;2^{\large{\left(\frac{1}{2}\|2^{-v_2 \left( {q} \right)} q\|_{T1} + \mid \log_2(2) - v_2(q) \mid \right)}}&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:17 --&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;!-- ws:start:WikiTextMathRule:18:
 [[math]]&amp;lt;br/&amp;gt;
-T1 \left( {2^{-v_2 \left( {q} \right)} q} \right) + | \log_2 \left( {q} \right) - v_2 \left( {q} \right) |&amp;lt;br/&amp;gt;[[math]]
+\|{2^{-v_2 \left( {q} \right)} q}\|_{T1} + | \log_2 \left( {q} \right) - v_2 \left( {q} \right) |&amp;lt;br/&amp;gt;[[math]]
-  --&gt;&lt;script type="math/tex"&gt;T1 \left( {2^{-v_2 \left( {q} \right)} q} \right) + | \log_2 \left( {q} \right) - v_2 \left( {q} \right) |&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:18 --&gt;&lt;br /&gt;
+  --&gt;&lt;script type="math/tex"&gt;\|{2^{-v_2 \left( {q} \right)} q}\|_{T1} + | \log_2 \left( {q} \right) - v_2 \left( {q} \right) |&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:18 --&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;