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#X obj 29 125 *~;
#X obj 60 125 *~;
#X obj 29 155 sqrt~;
#X obj 332 109 block~ 4096 1;
#X obj 29 181 biquad~ 0 0 0 0 1;
#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 obj 24 494 s fundamental;
#X obj 16 517 ftom;
#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 552 384 3;
#X text 584 384 4;
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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;
#X text 715 367 0;
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#X text 714 305 0.5;
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#X text 300 102 partials;
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#X obj 187 239 r freq-step;
#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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