2022-04-12 22:02:59 -03:00
|
|
|
<!DOCTYPE html>
|
2022-04-12 21:54:18 -03:00
|
|
|
|
|
|
|
|
<!--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>
|
2022-04-12 22:02:59 -03:00
|
|
|
|
|
|
|
|
<meta name="viewport" content="width=device-width, initial-scale=1.0">
|
|
|
|
|
|
|
|
|
|
|
2022-04-12 21:54:18 -03:00
|
|
|
<TITLE>More additive synthesis</TITLE>
|
|
|
|
|
<META NAME="description" CONTENT="More additive synthesis">
|
|
|
|
|
<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="previous" HREF="node23.html">
|
|
|
|
|
<LINK REL="up" HREF="node18.html">
|
|
|
|
|
<LINK REL="next" HREF="node25.html">
|
|
|
|
|
</HEAD>
|
|
|
|
|
|
|
|
|
|
<BODY >
|
|
|
|
|
<!--Navigation Panel-->
|
|
|
|
|
<A NAME="tex2html893"
|
|
|
|
|
HREF="node25.html">
|
|
|
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="next.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html887"
|
|
|
|
|
HREF="node18.html">
|
|
|
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="up.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html883"
|
|
|
|
|
HREF="node23.html">
|
|
|
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="prev.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html889"
|
|
|
|
|
HREF="node4.html">
|
|
|
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="contents.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html891"
|
|
|
|
|
HREF="node201.html">
|
|
|
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="index.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<BR>
|
|
|
|
|
<B> Next:</B> <A NAME="tex2html894"
|
|
|
|
|
HREF="node25.html">Exercises</A>
|
|
|
|
|
<B> Up:</B> <A NAME="tex2html888"
|
|
|
|
|
HREF="node18.html">Examples</A>
|
|
|
|
|
<B> Previous:</B> <A NAME="tex2html884"
|
|
|
|
|
HREF="node23.html">Conversion between frequency and</A>
|
|
|
|
|
<B> <A NAME="tex2html890"
|
|
|
|
|
HREF="node4.html">Contents</A></B>
|
|
|
|
|
<B> <A NAME="tex2html892"
|
|
|
|
|
HREF="node201.html">Index</A></B>
|
|
|
|
|
<BR>
|
|
|
|
|
<BR>
|
|
|
|
|
<!--End of Navigation Panel-->
|
|
|
|
|
|
|
|
|
|
<H2><A NAME="SECTION00596000000000000000">
|
|
|
|
|
More additive synthesis</A>
|
|
|
|
|
</H2>
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
The major triad (Example A06.frequency.pd, Page <A HREF="node22.html#sec1.triad"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="crossref.png"></A>)
|
2022-04-12 21:54:18 -03:00
|
|
|
shows one way to combine several sinusoids together by summing.
|
|
|
|
|
There are many other possible ways to organize collections of
|
|
|
|
|
sinusoids, of which we'll show two. Example A07.fusion.pd (Figure <A HREF="#fig01.14">1.14</A>) shows four oscillators,
|
|
|
|
|
whose frequencies are
|
|
|
|
|
tuned in the ratio 1:2:3:4, with relative amplitudes 1, 0.1, 0.2, and 0.5. The
|
|
|
|
|
amplitudes are set by multiplying the outputs of the oscillators (the
|
|
|
|
|
<TT>*~</TT> objects below the oscillators).
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
The second, third, and fourth oscillator are turned on and off using a
|
|
|
|
|
<A NAME="1318"></A><I>toggle switch</I>.
|
|
|
|
|
This is a graphical control, like the number box introduced earlier. The
|
|
|
|
|
toggle switch puts out 1 and 0 alternately when clicked on with the
|
|
|
|
|
mouse. This value is multiplied by the sum of the second, third, and fourth
|
|
|
|
|
oscillators, effectively turning them on and off.
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
Even when all four oscillators are combined (with the toggle switch in the
|
|
|
|
|
``1" position), the result fuses into a single tone,
|
|
|
|
|
heard at the pitch of the leftmost oscillator. In effect this patch sums a
|
|
|
|
|
four-term Fourier series to generate a complex, periodic waveform.
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
|
|
|
|
|
<DIV ALIGN="CENTER"><A NAME="fig01.14"></A><A NAME="1322"></A>
|
|
|
|
|
<TABLE>
|
|
|
|
|
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 1.14:</STRONG>
|
|
|
|
|
Additive synthesis using harmonically tuned oscillators.</CAPTION>
|
|
|
|
|
<TR><TD><IMG
|
|
|
|
|
WIDTH="447" HEIGHT="301" BORDER="0"
|
|
|
|
|
SRC="img160.png"
|
|
|
|
|
ALT="\begin{figure}\psfig{file=figs/fig01.14.ps}\end{figure}"></TD></TR>
|
|
|
|
|
</TABLE>
|
|
|
|
|
</DIV>
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
Example A08.beating.pd (Figure <A HREF="#fig01.15">1.15</A>) shows another possibility, in which six
|
|
|
|
|
oscillators are tuned into three pairs of neighbors, for instance 330 and 330.2
|
|
|
|
|
Hertz. These pairs slip into and out of phase with each other, so that the
|
|
|
|
|
amplitude of the sum changes over time. Called
|
|
|
|
|
<A NAME="1326"></A><I>beating</I>,
|
|
|
|
|
this phenomenon is frequently used for musical effects.
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
|
|
|
|
|
<DIV ALIGN="CENTER"><A NAME="fig01.15"></A><A NAME="1330"></A>
|
|
|
|
|
<TABLE>
|
|
|
|
|
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 1.15:</STRONG>
|
|
|
|
|
Additive synthesis: six oscillators arranged into three beating pairs.</CAPTION>
|
|
|
|
|
<TR><TD><IMG
|
|
|
|
|
WIDTH="404" HEIGHT="172" BORDER="0"
|
|
|
|
|
SRC="img161.png"
|
|
|
|
|
ALT="\begin{figure}\psfig{file=figs/fig01.15.ps}\end{figure}"></TD></TR>
|
|
|
|
|
</TABLE>
|
|
|
|
|
</DIV>
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
Oscillators may be combined in other ways besides simply summing their output,
|
|
|
|
|
and a wide range of resulting sounds is available. Example A09.frequency.mod.pd (not
|
|
|
|
|
shown here) demonstrates
|
|
|
|
|
<A NAME="1333"></A><A NAME="1334"></A><I>frequency modulation</I>
|
|
|
|
|
synthesis, in which one oscillator
|
|
|
|
|
controls another's frequency. This will be more fully described in Chapter
|
|
|
|
|
<A HREF="node75.html#chapter-modulation">5</A>.
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
<HR>
|
|
|
|
|
<!--Navigation Panel-->
|
|
|
|
|
<A NAME="tex2html893"
|
|
|
|
|
HREF="node25.html">
|
|
|
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="next.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html887"
|
|
|
|
|
HREF="node18.html">
|
|
|
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="up.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html883"
|
|
|
|
|
HREF="node23.html">
|
|
|
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="prev.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html889"
|
|
|
|
|
HREF="node4.html">
|
|
|
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="contents.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html891"
|
|
|
|
|
HREF="node201.html">
|
|
|
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="index.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<BR>
|
|
|
|
|
<B> Next:</B> <A NAME="tex2html894"
|
|
|
|
|
HREF="node25.html">Exercises</A>
|
|
|
|
|
<B> Up:</B> <A NAME="tex2html888"
|
|
|
|
|
HREF="node18.html">Examples</A>
|
|
|
|
|
<B> Previous:</B> <A NAME="tex2html884"
|
|
|
|
|
HREF="node23.html">Conversion between frequency and</A>
|
|
|
|
|
<B> <A NAME="tex2html890"
|
|
|
|
|
HREF="node4.html">Contents</A></B>
|
|
|
|
|
<B> <A NAME="tex2html892"
|
|
|
|
|
HREF="node201.html">Index</A></B>
|
|
|
|
|
<!--End of Navigation Panel-->
|
|
|
|
|
<ADDRESS>
|
|
|
|
|
Miller Puckette
|
|
|
|
|
2006-12-30
|
|
|
|
|
</ADDRESS>
|
|
|
|
|
</BODY>
|
|
|
|
|
</HTML>
|
