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220 lines
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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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<TITLE>Wavetable lookup in general</TITLE>
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<B> Next:</B> <A NAME="tex2html1051"
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HREF="node35.html">Using a wavetable as</A>
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<B> Up:</B> <A NAME="tex2html1045"
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HREF="node32.html">Examples</A>
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<B> Previous:</B> <A NAME="tex2html1039"
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HREF="node33.html">Wavetable oscillator</A>
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<B> <A NAME="tex2html1047"
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HREF="node4.html">Contents</A></B>
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<B> <A NAME="tex2html1049"
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HREF="node201.html">Index</A></B>
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<!--End of Navigation Panel-->
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<H2><A NAME="SECTION00662000000000000000">
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Wavetable lookup in general</A>
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</H2>
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<P>
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The <TT>tabosc4~</TT> class, while handy and efficient, is somewhat
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specialized and for many of the applications described in this chapter we need
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something more general. Example B03.tabread4.pd (Figure <A HREF="#fig02.13">2.13</A>) demonstrates
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the timbre stretching technique discussed in Section <A HREF="node30.html#sect2.stretching">2.4</A>.
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This is a simple example of a situation where <TT>tabosc4~</TT> would
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not have sufficed. There are new classes introduced here:
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig02.13"></A><A NAME="2412"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 2.13:</STRONG>
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A wavetable oscillator with variable duty cycle: B03.tabread4.pd.</CAPTION>
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<TR><TD><IMG
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WIDTH="407" HEIGHT="687" BORDER="0"
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SRC="img275.png"
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ALT="\begin{figure}\psfig{file=figs/fig02.13.ps}\end{figure}"></TD></TR>
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</TABLE>
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</DIV>
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<P>
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<BR><!-- MATH
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$\fbox{ $\mathrm{tabread4}\sim$\ }$
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-->
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<IMG
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WIDTH="102" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
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SRC="img276.png"
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ALT="\fbox{ $\mathrm{tabread4}\sim$\ }">:
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<A NAME="2555"></A>wavetable lookup. As in <TT>tabosc4~</TT> the table is read using
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4-point interpolation. But whereas <TT>tabosc4~</TT> takes a frequency
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as input and automatically reads the waveform in a repeating pattern, the
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simpler <TT>tabread4~</TT> expects the table lookup index as input.
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If you want to use it to do something repetitious, as in this example, the
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input itself has to be a repeating waveform. Like <TT>tabosc4~</TT> (and all the other table reading and writing objects),
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you can send messages to select which table to use.
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<P>
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<BR><!-- MATH
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$\fbox{ $\mathrm{tabwrite}\sim$\ }$
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-->
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<IMG
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WIDTH="99" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
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SRC="img277.png"
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ALT="\fbox{ $\mathrm{tabwrite}\sim$\ }">:
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<A NAME="2556"></A>record an audio signal into a wavetable. In this example the
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<TT>tabwrite~</TT> is used to display the output (although later
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on it will be used for all sorts of other things.) Whenever it receives a
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``bang" message from the pushbutton icon above it, <TT>tabwrite~</TT> begins
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writing successive samples of its input to the named table.
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<P>
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Example B03.tabread4.pd shows how to combine a <TT>phasor~</TT> and a <TT>tabread4~</TT> object to make a wavetable oscillator. The <TT>phasor~</TT>'s output ranges from
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0 to 1 in value. In this case the input wavetable, named ``waveform12", is 131
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elements long. The domain for the <TT>tabread4~</TT> object is thus from 1 to
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129. To adjust the range of the <TT>phasor~</TT> accordingly, we multiply it by
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the length of the domain (128) so that it reaches between 0 and 128, and then
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add 1, effectively sliding the interval to the right by one point. This
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rescaling is accomplished by the <TT>*~</TT> and <TT>+~</TT> objects
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between the <TT>phasor~</TT> and the <TT>tabread4~</TT>.
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<P>
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With only these four boxes we would have essentially reinvented the
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<TT>tabosc4~</TT> class. In this example, however, the multiplication
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is not by a constant 128 but by a variable amount controlled by the ``squeeze"
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parameter. The function of the four boxes at the right hand side of the patch
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is to supply the <TT>*~</TT> object with values to scale the
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<TT>phasor~</TT> by. This makes use of one more new object class:
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<P>
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<BR><!-- MATH
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$\fbox{ $\mathrm{pack}$\ }$
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-->
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<IMG
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WIDTH="56" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
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SRC="img278.png"
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ALT="\fbox{ $\mathrm{pack}$\ }">:
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<A NAME="2557"></A>compose a list of two or more elements. The creation arguments establish the
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number of arguments, their types (usually numbers) and their initial values.
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The inlets (there will be as many as you specified creation arguments) update
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the values of the message arguments, and, if the leftmost inlet is changed
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(or just triggered with a ``bang" message), the message is output.
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<A NAME="pdpack"></A>
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<P>
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In this patch the arguments are initially 0 and 50, but the number box will
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update the value of the first argument, so that, as pictured, the most recent
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message to leave the <TT>pack</TT> object was ``206 50". The effect of this
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on the <TT>line~</TT> object below is to ramp to 206 in 50 milliseconds; in
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general the output of the <TT>line~</TT> object is an audio signal that smoothly
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follows the sporadically changing values of the number box labeled ``squeeze".
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<P>
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Finally, 128 is added to the ``squeeze" value; if ``squeeze" takes non-negative
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values (as the number box in this patch enforces), the range-setting multiplier
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ranges the phasor by 128 or more. If the value is greater than 128, the effect
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is that the rescaled phasor spends some fraction of its cycle stuck at the end
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of the wavetable (which clips its input to 129). The result is that the
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waveform is scanned over some fraction of the cycle. As shown, the waveform
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is squeezed into 128/(128+206) of the cycle, so the spectrum is stretched by
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a factor of about 1/2.
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<P>
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For simplicity, this patch is subtly different from the example of Section
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<A HREF="node30.html#sect2.stretching">2.4</A> in that the waveforms are squeezed toward the beginning
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of each cycle and not toward the middle. This has the effect of slightly
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changing the phase of the various partials of the waveform as it is stretched
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and squeezed; if the squeezing factor changes quickly, the corresponding phase
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drift will sound like a slight wavering in pitch. This can be avoided by
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using a slightly more complicated arrangement: subtract 1/2 from the
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<TT>phasor~</TT>, multiply it by 128 or more, and then add 65 instead of one.
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<P>
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<B> Next:</B> <A NAME="tex2html1051"
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HREF="node35.html">Using a wavetable as</A>
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<B> Up:</B> <A NAME="tex2html1045"
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HREF="node32.html">Examples</A>
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<B> Previous:</B> <A NAME="tex2html1039"
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HREF="node33.html">Wavetable oscillator</A>
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<B> <A NAME="tex2html1047"
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HREF="node4.html">Contents</A></B>
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<B> <A NAME="tex2html1049"
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HREF="node201.html">Index</A></B>
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<ADDRESS>
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Miller Puckette
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2006-12-30
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