puredata-doc 0.48.1-3 / usr / share / puredata / doc / 3.audio.examples / E05.chebychev.pd

#N canvas 224 60 657 571 12;
#X obj 23 269 output~;
#X obj 45 74 / 100;
#X floatatom 45 54 5 0 100 0 - - -;
#X obj 23 144 *~;
#X text 403 539 updated for Pd version 0.37;
#X obj 22 29 osc~ 220;
#X obj 45 97 pack 0 50;
#X obj 45 121 line~;
#X text 97 54 <-- index in;
#X text 117 68 hundredths;
#X obj 23 169 *~ 128;
#X obj 23 217 tabread4~ E05-tab;
#N canvas 0 0 450 300 graph1 0;
#X array E05-tab 259 float 1;
#A 0 -1.20148 -1 -0.810724 -0.63326 -0.467216 -0.31221 -0.167866 -0.0338144
0.0903053 0.204849 0.310166 0.406597 0.494477 0.574137 0.645895 0.71007
0.766969 0.816895 0.860145 0.897008 0.927771 0.952708 0.972093 0.98619
0.995261 0.999557 0.999329 0.994816 0.986257 0.97388 0.957912 0.938572
0.916074 0.890625 0.86243 0.831684 0.798582 0.76331 0.726049 0.686977
0.646266 0.60408 0.560583 0.515931 0.470276 0.423765 0.37654 0.328738
0.280493 0.231934 0.183183 0.13436 0.0855808 0.0369554 -0.01141 -0.0594134
-0.106956 -0.153946 -0.200292 -0.245909 -0.290715 -0.334633 -0.377589
-0.419512 -0.460337 -0.5 -0.538443 -0.57561 -0.611449 -0.645912 -0.678953
-0.710532 -0.740609 -0.76915 -0.796122 -0.821497 -0.845248 -0.867354
-0.887794 -0.906551 -0.923612 -0.938965 -0.952601 -0.964516 -0.974704
-0.983167 -0.989906 -0.994925 -0.99823 -0.999832 -0.999741 -0.997972
-0.994539 -0.98946 -0.982757 -0.97445 -0.964564 -0.953125 -0.94016
-0.925699 -0.909772 -0.892414 -0.873658 -0.85354 -0.832098 -0.809372
-0.785401 -0.760228 -0.733895 -0.706446 -0.677928 -0.648387 -0.61787
-0.586426 -0.554105 -0.520957 -0.487033 -0.452386 -0.417069 -0.381135
-0.344638 -0.307632 -0.270174 -0.232319 -0.194122 -0.15564 -0.11693
-0.0780487 -0.039053 0 0.039053 0.0780487 0.11693 0.15564 0.194122
0.232319 0.270174 0.307632 0.344638 0.381135 0.417069 0.452386 0.487033
0.520957 0.554105 0.586426 0.61787 0.648387 0.677928 0.706446 0.733895
0.760228 0.785401 0.809372 0.832098 0.85354 0.873658 0.892414 0.909772
0.925699 0.94016 0.953125 0.964564 0.97445 0.982757 0.98946 0.994539
0.997972 0.999741 0.999832 0.99823 0.994925 0.989906 0.983167 0.974704
0.964516 0.952601 0.938965 0.923612 0.906551 0.887794 0.867354 0.845248
0.821497 0.796122 0.76915 0.740609 0.710532 0.678953 0.645912 0.611449
0.57561 0.538443 0.5 0.460337 0.419512 0.377589 0.334633 0.290715 0.245909
0.200292 0.153946 0.106956 0.0594134 0.01141 -0.0369554 -0.0855808
-0.13436 -0.183183 -0.231934 -0.280493 -0.328738 -0.37654 -0.423765
-0.470276 -0.515931 -0.560583 -0.60408 -0.646266 -0.686977 -0.726049
-0.76331 -0.798582 -0.831684 -0.86243 -0.890625 -0.916074 -0.938572
-0.957912 -0.97388 -0.986257 -0.994816 -0.999329 -0.999557 -0.995261
-0.98619 -0.972093 -0.952708 -0.927771 -0.897008 -0.860145 -0.816895
-0.766969 -0.71007 -0.645895 -0.574137 -0.494477 -0.406597 -0.310166
-0.204849 -0.0903053 0.0338144 0.167866 0.31221 0.467216 0.63326 0.810724
1 1.20148;
#X coords 0 1 258 -1 200 140 1;
#X restore 262 46 graph;
#X text 497 28 subpatch to;
#N canvas 113 0 849 700 make-table 0;
#X obj 141 304 t b b;
#X obj 213 329 f;
#X obj 251 329 + 1;
#X msg 235 306 0;
#X obj 141 327 until;
#X obj 213 359 t f f;
#X obj 114 436 tabwrite E05-tab;
#X obj 140 355 sel 258;
#X text 203 172 normalize from -1 to 1;
#X obj 141 285 bng 15 250 50 0 empty empty empty 0 -6 0 8 -262144 -1
-1;
#X obj 88 386 expr ($f1-129)/128;
#X obj 141 262 inlet;
#X obj 171 534 t b b;
#X obj 243 559 f;
#X obj 281 559 + 1;
#X msg 265 536 0;
#X obj 171 557 until;
#X obj 243 589 t f f;
#X obj 144 666 tabwrite E05-tab;
#X obj 170 585 sel 258;
#X obj 171 515 bng 15 250 50 0 empty empty empty 0 -6 0 8 -262144 -1
-1;
#X obj 118 616 expr ($f1-129)/128;
#X obj 171 492 inlet;
#X obj 444 228 t b b;
#X obj 516 253 f;
#X obj 554 253 + 1;
#X msg 538 230 0;
#X obj 444 251 until;
#X obj 516 283 t f f;
#X obj 417 360 tabwrite E05-tab;
#X obj 443 279 sel 258;
#X obj 391 334 expr 16*$f1*$f1*$f1*$f1*$f1-20*$f1*$f1*$f1+5*$f1;
#X obj 444 209 bng 15 250 50 0 empty empty empty 0 -6 0 8 -262144 -1
-1;
#X obj 391 310 expr ($f1-129)/128;
#X obj 444 186 inlet;
#X obj 504 476 t b b;
#X obj 576 501 f;
#X obj 614 501 + 1;
#X msg 598 478 0;
#X obj 504 499 until;
#X obj 576 531 t f f;
#X obj 477 624 tabwrite E05-tab;
#X obj 503 527 sel 258;
#X obj 504 457 bng 15 250 50 0 empty empty empty 0 -6 0 8 -262144 -1
-1;
#X obj 448 558 expr ($f1-129)/128;
#X obj 504 434 inlet;
#X obj 88 410 expr 4*$f1*$f1*$f1-3*$f1;
#X obj 118 640 expr 8*$f1*$f1*$f1*$f1-8*$f1*$f1+1;
#X obj 448 582 expr 32*$f1*$f1*$f1*$f1*$f1*$f1 -48*$f1*$f1*$f1*$f1+18*$f1*$f1-1
;
#X text 641 622 6th C.P. and basta.;
#X obj 83 92 t b b;
#X obj 155 117 f;
#X obj 193 117 + 1;
#X msg 177 94 0;
#X obj 83 115 until;
#X obj 155 147 t f f;
#X obj 56 224 tabwrite E05-tab;
#X obj 82 143 sel 258;
#X obj 83 73 bng 15 250 50 0 empty empty empty 0 -6 0 8 -262144 -1
-1;
#X obj 30 174 expr ($f1-129)/128;
#X obj 83 50 inlet;
#X obj 30 198 expr 2*$f1*$f1-1;
#X text 203 198 2nd C.P.;
#X text 309 410 3rd C.P.;
#X text 331 660 4th C.P.;
#X text 613 357 5th C.P.;
#X text 259 51 This patch computes Chebychev polynomials and stores
them in a wavetable for use later.;
#X connect 0 0 4 0;
#X connect 0 1 3 0;
#X connect 1 0 2 0;
#X connect 1 0 5 0;
#X connect 1 0 7 0;
#X connect 2 0 1 1;
#X connect 3 0 1 1;
#X connect 4 0 1 0;
#X connect 5 0 10 0;
#X connect 5 1 6 1;
#X connect 7 0 4 1;
#X connect 9 0 0 0;
#X connect 10 0 46 0;
#X connect 11 0 9 0;
#X connect 12 0 16 0;
#X connect 12 1 15 0;
#X connect 13 0 14 0;
#X connect 13 0 17 0;
#X connect 13 0 19 0;
#X connect 14 0 13 1;
#X connect 15 0 13 1;
#X connect 16 0 13 0;
#X connect 17 0 21 0;
#X connect 17 1 18 1;
#X connect 19 0 16 1;
#X connect 20 0 12 0;
#X connect 21 0 47 0;
#X connect 22 0 20 0;
#X connect 23 0 27 0;
#X connect 23 1 26 0;
#X connect 24 0 25 0;
#X connect 24 0 28 0;
#X connect 24 0 30 0;
#X connect 25 0 24 1;
#X connect 26 0 24 1;
#X connect 27 0 24 0;
#X connect 28 0 33 0;
#X connect 28 1 29 1;
#X connect 30 0 27 1;
#X connect 31 0 29 0;
#X connect 32 0 23 0;
#X connect 33 0 31 0;
#X connect 34 0 32 0;
#X connect 35 0 39 0;
#X connect 35 1 38 0;
#X connect 36 0 37 0;
#X connect 36 0 40 0;
#X connect 36 0 42 0;
#X connect 37 0 36 1;
#X connect 38 0 36 1;
#X connect 39 0 36 0;
#X connect 40 0 44 0;
#X connect 40 1 41 1;
#X connect 42 0 39 1;
#X connect 43 0 35 0;
#X connect 44 0 48 0;
#X connect 45 0 43 0;
#X connect 46 0 6 0;
#X connect 47 0 18 0;
#X connect 48 0 41 0;
#X connect 50 0 54 0;
#X connect 50 1 53 0;
#X connect 51 0 52 0;
#X connect 51 0 55 0;
#X connect 51 0 57 0;
#X connect 52 0 51 1;
#X connect 53 0 51 1;
#X connect 54 0 51 0;
#X connect 55 0 59 0;
#X connect 55 1 56 1;
#X connect 57 0 54 1;
#X connect 58 0 50 0;
#X connect 59 0 61 0;
#X connect 60 0 58 0;
#X connect 61 0 56 0;
#X restore 489 146 pd make-table;
#X obj 489 126 bng 15 250 50 0 empty empty empty 0 -6 0 8 -262144 -1
-1;
#X obj 517 126 bng 15 250 50 0 empty empty empty 0 -6 0 8 -262144 -1
-1;
#X obj 545 126 bng 15 250 50 0 empty empty empty 0 -6 0 8 -262144 -1
-1;
#X obj 573 126 bng 15 250 50 0 empty empty empty 0 -6 0 8 -262144 -1
-1;
#X obj 600 126 bng 15 250 50 0 empty empty empty 0 -6 0 8 -262144 -1
-1;
#X text 497 45 calculate;
#X text 495 64 Chebychev;
#X text 496 83 polynomials;
#X text 490 107 2;
#X text 517 107 3;
#X text 546 107 4;
#X text 572 108 5;
#X text 601 107 6;
#X text 134 2 waveshaping with Chebychev polynomials;
#X obj 23 193 +~ 129;
#X obj 23 242 hip~ 5;
#X text 107 256 This patch demonstrates using Chebychev polynomials
(of the first kind) to generate pure harmonics using waveshaping. The
pure harmonic only comes out when the index is one (top of the scale).
Smaller indices will give various mixes of harmonics. The table initially
holds the fifth Chebychev polynomial \, so you can get the fifth harmonic.
;
#X text 106 355 There is an audible "rolling" sound as the index changes
for the higher degree polynomials \, because the amplitudes of the
lower partials can rise and fall several times apiece as the index
rises from zero to one.;
#X text 105 422 Indices greater than one will try to read values outside
the table (which would be clipped appropriately). Anyway \, the polynomials
increase rapidly in value outside the interval from -1 to 1 that we
are using here.;
#X text 106 491 When you get tired of Chebychev polynomials you can
draw your own functions by hand and/or try other formulas.;
#X connect 1 0 6 0;
#X connect 2 0 1 0;
#X connect 3 0 10 0;
#X connect 5 0 3 0;
#X connect 6 0 7 0;
#X connect 7 0 3 1;
#X connect 10 0 29 0;
#X connect 11 0 30 0;
#X connect 15 0 14 0;
#X connect 16 0 14 1;
#X connect 17 0 14 2;
#X connect 18 0 14 3;
#X connect 19 0 14 4;
#X connect 29 0 11 0;
#X connect 30 0 0 0;
#X connect 30 0 0 1;