GEN14 — Stores a polynomial whose coefficients derive from Chebyshevs of the second kind.
Uses Chebyshev coefficients to generate stored polynomial functions which, under waveshaping, can be used to split a sinusoid into harmonic partials having a predefinable spectrum.
size  number of points in the table. Must be a power of 2 or a powerof2 plus 1 (see f statement). The normal value is powerof2 plus 1.
xint  provides the left and right values [xint, +xint] of the x interval over which the polynomial is to be drawn. These subroutines both call GEN03 to draw their functions; the p5 value here is therefore expanded to a negativepositive p5, p6 pair before GEN03 is actually called. The normal value is 1.
xamp  amplitude scaling factor of the sinusoid input that is expected to produce the following spectrum.
h0, h1, h2, etc.  relative strength of partials 0 (DC), 1 (fundamental), 2 ... that will result when a sinusoid of amplitude
xamp * int(size/2)/xint
is waveshaped using this function table. These values thus describe a frequency spectrum associated with a particular factor xamp of the input signal.
Note  


Here is an example of the GEN14 generator. It uses the file gen14.csd.
Example 1141. Example of the GEN14 generator.
See the sections Realtime Audio and Command Line Flags for more information on using command line flags.
<CsoundSynthesizer> <CsOptions> ; Select audio/midi flags here according to platform odac ;;;realtime audio out ;iadc ;;;uncomment iadc if realtime audio input is needed too ; For Nonrealtime ouput leave only the line below: ; o gen14.wav W ;;; for file output any platform </CsOptions> <CsInstruments> sr = 44100 ksmps = 32 nchnls = 2 0dbfs = 1 ;after the example from The Csound Book, page 83 instr 1 ;compare results from GEN13 & GEN14 iwshpfn = p6 inrmfn = p7 aswp linseg 0.01, p3*.5, .49, p3*.5, 0.01 ;index sweep function aindex poscil aswp, p5, 2 ;sound to waveshape atable tablei aindex, iwshpfn, 1, .5 ;waveshape index anrm tablei aswp*2, inrmfn, 1 ;normalization aenv linen p4, .01, p3, .02 ;amplitude envelope asig = (atable*anrm)*aenv ;normalize and impose envelope asig dcblock2 asig ;get rid of DC outs asig, asig endin </CsInstruments> <CsScore> f 2 0 8192 10 1 ;sine wave f 28 0 4097 13 1 1 1 0 .8 0 .5 0 .2 ;waveshaping function: GEN13  odd harmonics f 280 0 2049 4 28 1 ;normalization function for f28 f 29 0 4097 14 1 1 1 0 .8 0 .5 0 .2 ;waveshaping function: GEN14  same harmonics f 290 0 2049 4 29 1 ;normalization function for f29 f 30 0 4097 13 1 1 0 1 0 .6 0 .4 0 .1 ;waveshaping function: GEN13  even harmonics f 301 0 2049 4 30 1 ;normalization function for f30 f 31 0 4097 14 1 1 0 1 0 .6 0 .4 0 .1 ;waveshaping function: GEN13  even harmonics f 310 0 2049 4 31 1 ;normalization function for 31 s i1 0 3 .7 440 28 280 i1 4 . .7 . 29 290 i1 8 . .7 . 30 301 i1 12 3 .7 . 31 310 e </CsScore> </CsoundSynthesizer>
These are the diagrams of the waveforms of the GEN14 routines, as used in the example:
Information about the Chebyshev polynomials on Wikipedia: http://en.wikipedia.org/wiki/Chebyshev_polynomials