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<H2><A NAME="SECTION007101000000000000000">
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Sampling and foldover</A>
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</H2>
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<P>
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Example C01.nyquist.pd (Figure <A HREF="#fig03.13">3.13</A>, part a) shows an oscillator
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playing a wavetable, sweeping through frequencies from 500 to 1423. The
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wavetable consists of only the 46th partial, which therefore varies from 23000
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to 65458 Hertz. At a sample rate of 44100 these two frequencies
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theoretically sound at 21100
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and 21358 Hertz, but sweeping from one to the other folds down through
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zero and back up.
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig03.13"></A><A NAME="3741"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 3.13:</STRONG>
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(a) sending an oscillator over the Nyquist frequency;
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(b) zipper noise from the <TT>line</TT> (control) object; (c) the
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<TT>line~</TT> and <TT>vline~</TT> objects compared.</CAPTION>
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<TR><TD><IMG
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ALT="\begin{figure}\psfig{file=figs/fig03.13.ps}\end{figure}"></TD></TR>
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</TABLE>
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</DIV>
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<P>
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Two other waveforms are provided to show the interesting effects of beating
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between partials which, although they ``should" have been far apart, find
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themselves neighbors through foldover. For instance, at 1423 Hertz, the second
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harmonic is 2846 Hertz whereas the 33rd harmonic sounds at 1423*33-44100 = 2859
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Hertz--a rude dissonance.
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<P>
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Other less extreme examples can still produce audible foldover in less striking
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forms. Usually it is still objectionable and it is worth learning to
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hear it. Example C02.sawtooth-foldover.pd (not pictured here) demonstrates this for a sawtooth
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(the <TT>phasor~</TT> object). For wavetables holding audio recordings,
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interpolation error can create extra foldover. The effects of this can
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vary widely; the sound is sometimes described as
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``crunchy" or ``splattering", depending on the recording, the transposition,
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and the interpolation algorithm.
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