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#N canvas 53 63 581 571 12;
#X obj 31 212 output~;
#X obj 32 178 +~;
#X text 320 537 updated for Pd version 0.40.;
#X obj 32 110 +~;
#X obj 187 105 +~;
#X obj 187 52 osc~ 440;
#X obj 32 57 osc~ 330;
#X obj 53 81 osc~ 330.2;
#X obj 208 75 osc~ 440.33;
#X obj 342 102 +~;
#X obj 343 52 osc~ 587;
#X obj 364 75 osc~ 587.25;
#X obj 33 147 +~;
#X text 133 7 Beating between closely tuned sinusoids;
#X text 33 280 In each of the three pairs of oscillators above \, the
two frequencies are within 1/3 Hz or closer (for example \, the leftmost
ones are close to 330 Hz but separated by 1/5 Hz.) The result is a
gradual change in amplitude as the phases of the two slip against each
other. This is called beating. More complex beating pattenrs may be
made by using three or more oscillators. Also their amplitudes need
not be equal (as they are here).;
#X text 31 407 They are all summed using "+~" boxes. They could have
been summed in any order ("+~" is commutative for practical purposes)
but here they are added in pairs to emphasize the relationships between
them.;
#X text 30 474 In contrast to the previous example \, the oscillators
are not tuned to the overtone series (ratios 1:2:3:4...) and so the
frequencies 330 \, 440 \, and 587 are heard separately.;
#X connect 1 0 0 0;
#X connect 1 0 0 1;
#X connect 3 0 12 0;
#X connect 4 0 12 1;
#X connect 5 0 4 0;
#X connect 6 0 3 0;
#X connect 7 0 3 1;
#X connect 8 0 4 1;
#X connect 9 0 1 1;
#X connect 10 0 9 0;
#X connect 11 0 9 1;
#X connect 12 0 1 0;
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