209 lines
7.3 KiB
HTML
209 lines
7.3 KiB
HTML
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<!--Converted with LaTeX2HTML 2002-2-1 (1.71)
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original version by: Nikos Drakos, CBLU, University of Leeds
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* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
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* with significant contributions from:
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Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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<HTML>
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<HEAD>
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<TITLE>Automatic read point precession</TITLE>
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<META NAME="description" CONTENT="Automatic read point precession">
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<BR>
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<B> Next:</B> <A NAME="tex2html1105"
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HREF="node39.html">Exercises</A>
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<B> Up:</B> <A NAME="tex2html1099"
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HREF="node32.html">Examples</A>
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<B> Previous:</B> <A NAME="tex2html1095"
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HREF="node37.html">Overlapping sample looper</A>
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<B> <A NAME="tex2html1101"
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HREF="node4.html">Contents</A></B>
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<B> <A NAME="tex2html1103"
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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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<H2><A NAME="SECTION00666000000000000000">
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Automatic read point precession</A>
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</H2>
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<P>
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Example B11.sampler.rockafella.pd, shown in part (b) of Figure <A HREF="node37.html#fig02.16">2.16</A>, adapts the ideas
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shown above to a situation where the read point is computed automatically.
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Here we precess the read-point through the sample in a loop, permitting us
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to speed up or slow down the playback independently of the transposition.
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<P>
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This example addresses a weakness of the preceding one, which is that, if the
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relative precession speed is anywhere near one (i.e., the natural speed of
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listening to the recorded wavetable), and if there is not much transposition
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either, it becomes preferable to use larger grains and lower the frequency of
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repetition accordingly (keeping the product constant to achieve the desired
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transposition.) However, if the grain size is allowed to get large, it is no
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longer convenient to quantize control changes at phase wrappings, because
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they might be too far apart to allow for a reasonable response time to control
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changes.
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<P>
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In this patch we remove the <TT>samphold~</TT> object that had controlled
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the read point (but we leave in the one for chunk size which is much harder
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to change in mid-loop). Instead, we use the (known) rate of precession of the
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read point to correct the sawtooth frequency, so that we maintain the desired
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transposition. It turns out that, when transposition factor and precession
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are close to each other (so that we are nearly doing the same thing as simple
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speed change) the frequency will drop to a value close to zero, so we will
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have increased the naturalness of the result at the same time.
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<P>
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In this patch we switch from managing read points, chunk sizes, etc., in
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samples and use seconds instead, converting to samples (and shifting by
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one) only just before the <TT>tabread4~</TT> object.
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The wavetable holds one second of sound, and we'll assume here that the
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nominal chunk size will not exceed 0.1 second, so that we can safely let
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the read point range from 0 to 0.9; the ``real" chunk size will vary, and
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can become quite large, because of the moving read pointer.
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<P>
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The precession
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control sets the frequency of a phasor of amplitude 0.9, and therefore the
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precession must be multiplied by 0.9 to set the frequency of the phasor (so
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that, for a precession of one for instance, the amplitude and frequency of
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the read point are both 0.9, so that the slope, equal to amplitude over
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frequency, is one). The output of this is named ``read-pt" as before, and
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is used by both copies of the wavetable reader.
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<P>
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The precession <IMG
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WIDTH="11" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
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SRC="img57.png"
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ALT="$p$"> and the chunk size <IMG
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WIDTH="10" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img293.png"
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ALT="$c$"> being known, and if we denote
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the frequency of the upper (original) <TT>phasor~</TT> by <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="$f$">, the transposition factor is given by:
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<BR><P></P>
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<DIV ALIGN="CENTER">
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<!-- MATH
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\begin{displaymath}
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t = p + cf
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\end{displaymath}
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-->
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<IMG
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WIDTH="71" HEIGHT="27" BORDER="0"
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SRC="img294.png"
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ALT="\begin{displaymath}
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t = p + cf
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\end{displaymath}">
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</DIV>
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<BR CLEAR="ALL">
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<P></P>
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and solving for <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="$f$"> gives:
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<BR><P></P>
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<DIV ALIGN="CENTER">
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<!-- MATH
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\begin{displaymath}
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f = {{t - p} \over c} = {{{{2 ^ {h/12}}} - p} \over c}
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\end{displaymath}
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-->
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<IMG
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WIDTH="153" HEIGHT="42" BORDER="0"
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SRC="img295.png"
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ALT="\begin{displaymath}
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f = {{t - p} \over c} = {{{{2 ^ {h/12}}} - p} \over c}
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\end{displaymath}">
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</DIV>
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<BR CLEAR="ALL">
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<P></P>
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where <IMG
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WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img194.png"
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ALT="$h$"> is the desired transposition in half-steps. This is the formula
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used in the <TT>expr</TT> object.
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<P>
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<HR>
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<A NAME="tex2html1102"
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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="file:/usr/local/share/lib/latex2html/icons/index.png"></A>
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<BR>
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<B> Next:</B> <A NAME="tex2html1105"
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HREF="node39.html">Exercises</A>
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<B> Up:</B> <A NAME="tex2html1099"
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HREF="node32.html">Examples</A>
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<B> Previous:</B> <A NAME="tex2html1095"
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HREF="node37.html">Overlapping sample looper</A>
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<B> <A NAME="tex2html1101"
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HREF="node4.html">Contents</A></B>
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<B> <A NAME="tex2html1103"
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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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Miller Puckette
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2006-12-30
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</ADDRESS>
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