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