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+#X text 93 93 Fourier series;
+#X text 98 146 magnitude;
+#X text 96 131 calculate;
+#X text 21 3 This subpatch computes the spectrum of the incoming signal
+with a (rectangular windowed) FFT. FFTs aren't properly introduced
+until much later.;
+#X text 83 61 signal to analyze;
+#X text 192 166 delay two samples;
+#X text 191 182 for better graphing;
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+#X text 14 319 At load time \, calculate a good choice of fundamental
+frequency for showing spectra: the 16th bin in a 4096-point spectrum
+\, so SR*16/4096 or SR/256.;
+#X text 145 216 "bang" into this inlet to graph it;
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+#X text 187 425 One bin is SR/4096:;
+#X text 72 540 <-just out of curiosity \, here's the fundamental pitch
+;
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+#X text 501 198 ---- 0.02 seconds ----;
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+#X text 501 720 updated for Pd version 0.37;
+#X text 486 384 1;
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+#X text 490 403 -- partial number --;
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+#X text 282 118 <-- On/Off;
+#X text 565 46 WAVEFORM;
+#X text 548 229 SPECTRUM;
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+#X text 226 177 modulation;
+#X text 222 192 frequency in;
+#X text 185 209 <-- "steps" of f/16;
+#X text 97 -1 RING MODULATION: multiplying a complex tone by a sinusoid
+;
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+;
+#X text 107 343 <-- graph once;
+#X obj 84 321 metro 500;
+#X text 107 298 <-- graph repeatedly;
+#X text 35 463 Now we ring modulate the signal by multiplying it by
+another sinusoid. The modulation frequency is controlled in steps of
+f/16 where "f" is the fundamental frequency \, giving roughly 11 Hz.
+per step. Note that if the modulation frequency is set to zero we can't
+predict the overall amplitude because it depends on what phase the
+modulation oscillator happened to have at that moment.;
+#X text 32 579 If you choose a multiple of the fundamental as a modulation
+frequency (16 \, 32 \, 48 \, 64 \, ... "steps") the result is again
+periodic at the original frequency. If you select a half-integer times
+the fundamental (8 \, 24 \, 40 \, ... steps) the pitch drops by an
+octave and you get only odd partials. For most other settings you'll
+get an inharmonic complex of tones. These are sometimes heard as separate
+pitches and other times they seem to fuse into a single timbre with
+indeterminate pitch.;
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