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By Miller Puckette

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So if we denote the Fourier series of x50 [n] as: x50 [n] = b0 + b1 cos (ωn + θ1 ) + b2 cos (2ωn + θ2 ) + · · · and substitute the Fourier series for all three terms above, we get: a0 + a1 cos (2ωn + φ1 ) + a2 cos (4ωn + φ2 ) + · · · = b0 + b1 cos (ωn + θ1 ) + b2 cos (2ωn + θ2 ) + · · · +b0 + b1 cos (ωn + π + θ1 ) + b2 cos (2ωn + 2π + θ2 ) + · · · = 2b0 + 2b2 cos (2ωn + θ2 ) + 2b4 cos (4ωn + θ4 ) + · · · and so a0 = 2b0 , a1 = 2b2 , a2 = 2b4 and so on: the even partials of x50 , at least, are obtained by stretching the partials of x100 out twice as far.

7 gives us a way to to grab and stretch timbres from a recorded wavetable. 2, where we now reinterpret t as the factor by which the timbre is to be stretched. 5 Interpolation As mentioned before, interpolation schemes are often used to increase the accuracy of table lookup. Here we will give a somewhat simplified account of the effects of table sizes and interpolation schemes on the result of table lookup. To speak of error in table lookup, we must view the wavetable as a sampled version of an underlying function.

12, implements a wavetable oscillator, which plays back from a wavetable named “table10”. Two new Pd primitives are shown here. First is the wavetable itself, which appears at right in the figure. You can “mouse” on the wavetable to change its shape and hear the sound change as a result. Not shown in the figure but demonstrated in the patch is Pd’s facility for automatically calculating wavetables with specified partial amplitudes, which is often preferable to drawing waveforms by hand. You can also read and write tables to (text or sound) files for interchanging data with other programs.

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The Theory and Technique of Electronic Music DRAFT by Miller Puckette

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