replace '<A NAME=' with '<A ID='
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node11.html
54
node11.html
@@ -30,42 +30,42 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<BODY >
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<!--Navigation Panel-->
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<A NAME="tex2html707"
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<A ID="tex2html707"
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HREF="node12.html">
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<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
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SRC="next.png"></A>
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<A NAME="tex2html701"
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<A ID="tex2html701"
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HREF="node7.html">
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<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
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SRC="up.png"></A>
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<A NAME="tex2html695"
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<A ID="tex2html695"
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HREF="node10.html">
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<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
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SRC="prev.png"></A>
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<A NAME="tex2html703"
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<A ID="tex2html703"
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HREF="node4.html">
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<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
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SRC="contents.png"></A>
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<A NAME="tex2html705"
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<A ID="tex2html705"
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HREF="node201.html">
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<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
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SRC="index.png"></A>
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<BR>
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<B> Next:</B> <A NAME="tex2html708"
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<B> Next:</B> <A ID="tex2html708"
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HREF="node12.html">Synthesizing a sinusoid</A>
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<B> Up:</B> <A NAME="tex2html702"
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<B> Up:</B> <A ID="tex2html702"
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HREF="node7.html">Sinusoids, amplitude and frequency</A>
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<B> Previous:</B> <A NAME="tex2html696"
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<B> Previous:</B> <A ID="tex2html696"
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HREF="node10.html">Controlling Amplitude</A>
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<B> <A NAME="tex2html704"
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<B> <A ID="tex2html704"
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HREF="node4.html">Contents</A></B>
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<B> <A NAME="tex2html706"
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<B> <A ID="tex2html706"
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HREF="node201.html">Index</A></B>
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<BR>
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<BR>
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<!--End of Navigation Panel-->
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<H1><A NAME="SECTION00540000000000000000">
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<H1><A ID="SECTION00540000000000000000">
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Frequency</A>
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</H1>
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@@ -78,7 +78,7 @@ the musical interval between them.
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<P>
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The Western musical scale divides the
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<A NAME="1095"></A><I>octave</I> (the musical interval associated with a ratio of 2:1) into
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<A ID="1095"></A><I>octave</I> (the musical interval associated with a ratio of 2:1) into
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twelve equal sub-intervals, each of which therefore corresponds to a ratio
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of <!-- MATH
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${2 ^ {1/{12}}}$
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@@ -87,12 +87,12 @@ of <!-- MATH
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WIDTH="37" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
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SRC="img110.png"
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ALT="${2 ^ {1/{12}}}$">. For historical reasons this sub-interval is called a
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<A NAME="1098"></A><I>half-step</I>.
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<A ID="1098"></A><I>half-step</I>.
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A convenient logarithmic scale for pitch is simply to
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count the number of half-steps from a reference pitch--allowing fractions to
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permit us to specify pitches which don't fall on a note of the Western scale.
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The most commonly used logarithmic pitch scale is
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<A NAME="1100"></A>"MIDI pitch", in which the pitch 69 is assigned to a frequency of 440 cycles
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<A ID="1100"></A>"MIDI pitch", in which the pitch 69 is assigned to a frequency of 440 cycles
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per second--the A above middle C. To convert between a MIDI pitch <IMG
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WIDTH="17" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img111.png"
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@@ -102,10 +102,10 @@ in cycles per second <IMG
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WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img112.png"
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ALT="$f$">, apply the
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<A NAME="1101"></A>Pitch/Frequency Conversion formulas:
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<A ID="1101"></A>Pitch/Frequency Conversion formulas:
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<P>
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<A NAME="eq-pitchmidi"></A>
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<A ID="eq-pitchmidi"></A>
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<BR><P></P>
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<DIV ALIGN="CENTER">
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<!-- MATH
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@@ -162,7 +162,7 @@ description of MIDI, its capabilities and limitations, see
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<P>
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A half-step comes to a ratio of about 1.059 to 1, or about a six percent
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increase in frequency. Half-steps are further divided into <A NAME="1107"></A><I>cents</I>, each cent being one hundredth of a half-step. As a rule of
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increase in frequency. Half-steps are further divided into <A ID="1107"></A><I>cents</I>, each cent being one hundredth of a half-step. As a rule of
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thumb, it might take about three cents to make a discernible change in the
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pitch of a musical tone. At middle C this comes to a difference of about 1/2
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cycle per second. A graph of frequency as a function of MIDI pitch, over a
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@@ -171,36 +171,36 @@ two-octave range, is shown in Figure <A HREF="node10.html#fig01.04">1.4</A>.
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<P>
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<HR>
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<!--Navigation Panel-->
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<A NAME="tex2html707"
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<A ID="tex2html707"
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HREF="node12.html">
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<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
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SRC="next.png"></A>
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<A NAME="tex2html701"
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<A ID="tex2html701"
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HREF="node7.html">
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<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
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SRC="up.png"></A>
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<A NAME="tex2html695"
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<A ID="tex2html695"
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HREF="node10.html">
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<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
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SRC="prev.png"></A>
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<A NAME="tex2html703"
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<A ID="tex2html703"
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HREF="node4.html">
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<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
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SRC="contents.png"></A>
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<A NAME="tex2html705"
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<A ID="tex2html705"
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HREF="node201.html">
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<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
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SRC="index.png"></A>
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<BR>
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<B> Next:</B> <A NAME="tex2html708"
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<B> Next:</B> <A ID="tex2html708"
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HREF="node12.html">Synthesizing a sinusoid</A>
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<B> Up:</B> <A NAME="tex2html702"
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<B> Up:</B> <A ID="tex2html702"
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HREF="node7.html">Sinusoids, amplitude and frequency</A>
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<B> Previous:</B> <A NAME="tex2html696"
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<B> Previous:</B> <A ID="tex2html696"
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HREF="node10.html">Controlling Amplitude</A>
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<B> <A NAME="tex2html704"
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<B> <A ID="tex2html704"
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HREF="node4.html">Contents</A></B>
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<B> <A NAME="tex2html706"
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<B> <A ID="tex2html706"
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HREF="node201.html">Index</A></B>
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<!--End of Navigation Panel-->
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<ADDRESS>
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