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<H2><A NAME="SECTION001052000000000000000">
Simple formant generator</A>
</H2>
<P>
The next three examples demonstrate the sound of the varying pulse
width, graph its spectrum, and contrast the waveshaping pulse generator.
Skipping to Example F05.ring.modulation.pd (Figure <A HREF="#fig06.14">6.15</A>), we show the
simplest way of combining the pulse generator with a ring modulating
oscillator to make a formant. The pulse train from the previous example is
contained in the <TT>pd pulse-train</TT> subpatch. It is multiplied
by an oscillator whose frequency is controlled as a multiple of the
fundamental frequency. If the multiple is an integer, a harmonic sound
results. No attempt is made to control the relative phases of the components
of the pulse train and of the carrier sinusoid.
<P>
<DIV ALIGN="CENTER"><A NAME="fig06.14"></A><A NAME="6976"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 6.15:</STRONG>
Excerpt from example F05.ring.modulation.pd combining ring modulation
with a stretched wavetable pulse generator</CAPTION>
<TR><TD><IMG
WIDTH="352" HEIGHT="285" BORDER="0"
SRC="img614.png"
ALT="\begin{figure}\psfig{file=figs/fig06.14.ps}\end{figure}"></TD></TR>
</TABLE>
</DIV>
<P>
The next example, F06.packets.pd (Figure <A HREF="#fig06.15">6.16</A>), shows how to
combine the stretched wavetable pulse train with a sampled sinusoid to realize
movable formants, as described in Section <A HREF="node95.html#sect6.carrier">6.3</A>. The pulse
generator is as before, but now the carrier signal is a broken sinusoid.
Since its phase is the fundamental phase times the center frequency quotient,
the sample-to-sample phase increment is the same as for a sinusoid at the
center frequency. However, when the phase wraps around, the carrier phase
jumps to a different place in the cycle, as was illustrated in Figure
<A HREF="node95.html#fig06.07">6.7</A>.
Although the bandwidth quotient <!-- MATH
${\omega_b}/\omega$
-->
<IMG
WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img588.png"
ALT="${\omega_b}/\omega$"> must be at least
one, the center
frequency quotient <!-- MATH
${\omega_c}/\omega$
-->
<IMG
WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img587.png"
ALT="${\omega_c}/\omega$"> may be
as low as zero if desired.
<P>
<DIV ALIGN="CENTER"><A NAME="fig06.15"></A><A NAME="6986"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 6.16:</STRONG>
Using stretched wavetable synthesis to make a formant with movable
center frequency.</CAPTION>
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<ADDRESS>
Miller Puckette
2006-12-30
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