You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
171 lines
5.6 KiB
171 lines
5.6 KiB
<!DOCTYPE html>
|
|
|
|
<!--Converted with LaTeX2HTML 2002-2-1 (1.71)
|
|
original version by: Nikos Drakos, CBLU, University of Leeds
|
|
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
|
|
* with significant contributions from:
|
|
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
|
|
<HTML>
|
|
<HEAD>
|
|
|
|
<meta name="viewport" content="width=device-width, initial-scale=1.0">
|
|
|
|
|
|
<TITLE>Waveshaping and difference tones</TITLE>
|
|
<META NAME="description" CONTENT="Waveshaping and difference tones">
|
|
<META NAME="keywords" CONTENT="book">
|
|
<META NAME="resource-type" CONTENT="document">
|
|
<META NAME="distribution" CONTENT="global">
|
|
|
|
<META NAME="Generator" CONTENT="LaTeX2HTML v2002-2-1">
|
|
<META HTTP-EQUIV="Content-Style-Type" CONTENT="text/css">
|
|
|
|
<LINK REL="STYLESHEET" HREF="book.css">
|
|
|
|
<LINK REL="next" HREF="node84.html">
|
|
<LINK REL="previous" HREF="node82.html">
|
|
<LINK REL="up" HREF="node80.html">
|
|
<LINK REL="next" HREF="node84.html">
|
|
</HEAD>
|
|
|
|
<BODY >
|
|
<!--Navigation Panel-->
|
|
<A ID="tex2html1788"
|
|
HREF="node84.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
|
SRC="next.png"></A>
|
|
<A ID="tex2html1782"
|
|
HREF="node80.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
|
SRC="up.png"></A>
|
|
<A ID="tex2html1776"
|
|
HREF="node82.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
|
SRC="prev.png"></A>
|
|
<A ID="tex2html1784"
|
|
HREF="node4.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
|
SRC="contents.png"></A>
|
|
<A ID="tex2html1786"
|
|
HREF="node201.html">
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
|
SRC="index.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A ID="tex2html1789"
|
|
HREF="node84.html">Waveshaping using Chebychev polynomials</A>
|
|
<B> Up:</B> <A ID="tex2html1783"
|
|
HREF="node80.html">Examples</A>
|
|
<B> Previous:</B> <A ID="tex2html1777"
|
|
HREF="node82.html">Octave divider and formant</A>
|
|
<B> <A ID="tex2html1785"
|
|
HREF="node4.html">Contents</A></B>
|
|
<B> <A ID="tex2html1787"
|
|
HREF="node201.html">Index</A></B>
|
|
<BR>
|
|
<BR>
|
|
<!--End of Navigation Panel-->
|
|
|
|
<H2><A ID="SECTION00953000000000000000">
|
|
Waveshaping and difference tones</A>
|
|
</H2>
|
|
|
|
<P>
|
|
Example E04.difference.tone.pd (Figure <A HREF="#fig05.11">5.11</A>) introduces waveshaping, demonstrating
|
|
the nonlinearity of the process. Two sinusoids (300 and 225 Hertz, or a ratio of
|
|
4 to 3) are summed and then clipped, using a new object class:
|
|
|
|
<P>
|
|
|
|
<DIV ALIGN="CENTER"><A ID="fig05.11"></A><A ID="5817"></A>
|
|
<TABLE>
|
|
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5.11:</STRONG>
|
|
Nonlinear distortion of a sum of two sinusoids to create a
|
|
difference tone.</CAPTION>
|
|
<TR><TD><IMG
|
|
WIDTH="394" HEIGHT="276" BORDER="0"
|
|
SRC="img490.png"
|
|
ALT="\begin{figure}\psfig{file=figs/fig05.11.ps}\end{figure}"></TD></TR>
|
|
</TABLE>
|
|
</DIV>
|
|
|
|
<P>
|
|
<BR><!-- MATH
|
|
$\fbox{ \texttt{clip\~}}$
|
|
-->
|
|
<IMG
|
|
WIDTH="61" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img491.png"
|
|
ALT="\fbox{ \texttt{clip\~}}">:
|
|
<A ID="5956"></A>signal clipper. When the signal lies between the limits specified by the
|
|
arguments to the <TT>clip~</TT> object, it is passed through unchanged; but
|
|
when it falls below the lower limit or rises above the upper limit, it is
|
|
replaced by the limit. The effect of
|
|
clipping a sinusoidal signal was shown graphically in Figure <A HREF="node78.html#fig05.06">5.6</A>.
|
|
|
|
<P>
|
|
As long as the amplitude of the sum of sinusoids is less than 50 percent, the
|
|
sum can't exceed one in absolute value and the <TT>clip~</TT> object passes the
|
|
pair of sinusoids through unchanged to the output. As soon as the amplitude
|
|
exceeds 50 percent, however, the nonlinearity of the <TT>clip~</TT> object
|
|
brings forth distortion products (at frequencies <IMG
|
|
WIDTH="94" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img493.png"
|
|
ALT="$300m+225n$"> for integers <IMG
|
|
WIDTH="17" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img111.png"
|
|
ALT="$m$">
|
|
and <IMG
|
|
WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img75.png"
|
|
ALT="$n$">), all of which happening to be multiples of 75, which is thus the
|
|
fundamental of the resulting tone. Seen another way, the shortest common
|
|
period of the two sinusoids is 1/75 second (which is four periods of the 300
|
|
Hertz, tone and three periods of the 225 Hertz tone), so the result repeats
|
|
75 times per second.
|
|
|
|
<P>
|
|
The frequency of the 225 Hertz tone in the patch may be varied. If it is moved
|
|
slightly away from 225, a beating sound results. Other values find other
|
|
common subharmonics, and still others give rise to rich, inharmonic tones.
|
|
|
|
<P>
|
|
<HR>
|
|
<!--Navigation Panel-->
|
|
<A ID="tex2html1788"
|
|
HREF="node84.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
|
SRC="next.png"></A>
|
|
<A ID="tex2html1782"
|
|
HREF="node80.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
|
SRC="up.png"></A>
|
|
<A ID="tex2html1776"
|
|
HREF="node82.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
|
SRC="prev.png"></A>
|
|
<A ID="tex2html1784"
|
|
HREF="node4.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
|
SRC="contents.png"></A>
|
|
<A ID="tex2html1786"
|
|
HREF="node201.html">
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
|
SRC="index.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A ID="tex2html1789"
|
|
HREF="node84.html">Waveshaping using Chebychev polynomials</A>
|
|
<B> Up:</B> <A ID="tex2html1783"
|
|
HREF="node80.html">Examples</A>
|
|
<B> Previous:</B> <A ID="tex2html1777"
|
|
HREF="node82.html">Octave divider and formant</A>
|
|
<B> <A ID="tex2html1785"
|
|
HREF="node4.html">Contents</A></B>
|
|
<B> <A ID="tex2html1787"
|
|
HREF="node201.html">Index</A></B>
|
|
<!--End of Navigation Panel-->
|
|
<ADDRESS>
|
|
Miller Puckette
|
|
2006-12-30
|
|
</ADDRESS>
|
|
</BODY>
|
|
</HTML>
|
|
|