172 lines
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172 lines
5.6 KiB
HTML
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<H2><A ID="SECTION00953000000000000000">
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Waveshaping and difference tones</A>
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</H2>
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<P>
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Example E04.difference.tone.pd (Figure <A HREF="#fig05.11">5.11</A>) introduces waveshaping, demonstrating
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the nonlinearity of the process. Two sinusoids (300 and 225 Hertz, or a ratio of
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4 to 3) are summed and then clipped, using a new object class:
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<P>
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<DIV ALIGN="CENTER"><A ID="fig05.11"></A><A ID="5817"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5.11:</STRONG>
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Nonlinear distortion of a sum of two sinusoids to create a
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difference tone.</CAPTION>
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<TR><TD><IMG
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WIDTH="394" HEIGHT="276" BORDER="0"
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SRC="img490.png"
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ALT="\begin{figure}\psfig{file=figs/fig05.11.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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$\fbox{ \texttt{clip\~}}$
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-->
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<IMG
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WIDTH="61" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
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SRC="img491.png"
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ALT="\fbox{ \texttt{clip\~}}">:
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<A ID="5956"></A>signal clipper. When the signal lies between the limits specified by the
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arguments to the <TT>clip~</TT> object, it is passed through unchanged; but
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when it falls below the lower limit or rises above the upper limit, it is
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replaced by the limit. The effect of
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clipping a sinusoidal signal was shown graphically in Figure <A HREF="node78.html#fig05.06">5.6</A>.
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<P>
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As long as the amplitude of the sum of sinusoids is less than 50 percent, the
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sum can't exceed one in absolute value and the <TT>clip~</TT> object passes the
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pair of sinusoids through unchanged to the output. As soon as the amplitude
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exceeds 50 percent, however, the nonlinearity of the <TT>clip~</TT> object
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brings forth distortion products (at frequencies <IMG
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WIDTH="94" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
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SRC="img493.png"
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ALT="$300m+225n$"> for integers <IMG
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WIDTH="17" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img111.png"
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ALT="$m$">
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and <IMG
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WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
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SRC="img75.png"
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ALT="$n$">), all of which happening to be multiples of 75, which is thus the
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fundamental of the resulting tone. Seen another way, the shortest common
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period of the two sinusoids is 1/75 second (which is four periods of the 300
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Hertz, tone and three periods of the 225 Hertz tone), so the result repeats
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75 times per second.
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<P>
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The frequency of the 225 Hertz tone in the patch may be varied. If it is moved
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slightly away from 225, a beating sound results. Other values find other
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common subharmonics, and still others give rise to rich, inharmonic tones.
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HREF="node84.html">Waveshaping using Chebychev polynomials</A>
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HREF="node80.html">Examples</A>
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<B> Previous:</B> <A ID="tex2html1777"
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HREF="node82.html">Octave divider and formant</A>
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<ADDRESS>
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Miller Puckette
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2006-12-30
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