[Theo Verelst]

When making sounds, the most fundamental way to create samples which represent pure and well defined waves is to use mathematically defined waves, for instance by explicit formulea as a function of time or sample number, assuming the samples are from a function of time with frequency spectrum limited to the Nyquist rate (half the sampling frequency). The latter is not completely true for the below example, but the spectrum is limited enough to give usefull results.

This is where Tcl comes in to make a usefull script which executes exactly the right commands to let us drive maxima and a dedicated C program to generate waveforms from powerfull formulea. Not a very big script (not counting [bwise] along, because strictly speaking the below works mostly also without bwise) but one which calls two major applications ([maxima] and [gcc]), and which does the essential packing of a [fortran] function in a suitable file, and finally automatically executes the compiles program, which writes a standard .wav file (see [snack]) to play with some media player.

Maxima can be integrated with tcl in two main ways, see [Calling Maxima from Tcl] and [Maxima through a pipe], and see also [Bwise combined with Maxima]. Here I use the easier programmable and memory friendly way to start up the executable from the tcl (bwise) script.

This is the main tcl script, which is combined with ([source]d) bwise:

 # Give some initialisation to maxima, run it, and peel out the result
 proc domaxima { {m} } {
    set t "display2d:false;\n$m;"
    return [string range [exec maxima << $t | tail -2  ] 6 end-7]
 } 

 # Similar as above but get a fortran converted result
 proc domaximafor { {m} } {
    set t "display2d:false;\nlinel:3000;\nfortran($m);\n"
    return [string range [exec maxima -q << $t ] 42 end-18]
 } 

 # Make the fortran source file and compile, and link it with the C main program, and run that.
 proc formake { {e} } {
   global f
   set t [subst -nocommand {
      subroutine sayhello(x,r)
        real x,r
        r = $e
        return
      end
   }]
   set f [open sub.f w]
   puts $f [string trim $t \n]
   close $f
   exec gcc -ffixed-line-length-none -o fm sub.f mw.c wav.o -lm
   #exec gfortran -ffixed-line-length-none -c sub.f
   #exec gcc -o fm sub.o main.c -lm
   return [exec ./fm]
 } 

Of course maxima must be present on the system and reachable according to the PATH shell variable (like [wish] and [tclsh]). I've done this setup on Linux, which when set up right gives excellent maxima and compile times, with complicated formulas (see below) a seconds long wav file is created in under a second (!). I guess this tcl/maxima/fortran/C setup is therefore usefull for general application, too.

You need to have these files in the current directory which contains the wav file and C loop part of the target program:

----
/***** wav.c *****/

 #include <stdio.h>
 #include <fcntl.h>
 #include <sys/stat.h>
 #include <string.h>

 #include <sys/types.h>
 #include <stdlib.h>

 /* #define CYGWIN */

 int fd;
 FILE *fp;
 
 #define MSEC(t) (int)(t*44.1)
 
 iwrite(fd,n,l)
 int fd,l;

 unsigned int n;
 {
    write(fd,&n,l);
 }
 
 int initwav(s,l)                 /* wav header, s=filename, l=#samples */
 char *s;
 int l;
 {
 #ifdef CYGWIN
    fd = open(s,O_WRONLY|O_CREAT|O_TRUNC|O_BINARY,S_IRUSR|S_IWUSR|S_IRGRP);
 #else
    fd = open(s,O_WRONLY|O_CREAT|O_TRUNC,S_IRWXU);
 #endif
    if (fd < 0) return(-1);
 
    write(fd,"RIFF",4);
    iwrite(fd,(2*l+36),4);
    write(fd,"WAVE",4);
 
    write(fd,"fmt ",4);
    iwrite(fd,(0x10),4);
    iwrite(fd,((short) 0x01),2);
    iwrite(fd,((short) 1),2);              /* Mono */
    iwrite(fd,(44100/1),4);                  /* Sample rate */
    iwrite(fd,(2*44100/1),4);
    iwrite(fd,((short) 2),2);
    iwrite(fd,((short) 16),2);
 
    write(fd,"data",4);
    iwrite(fd,(2*l),4);

    return(0);
 }

 void writewav(p,n)
 short *p;                      /* Sample values */
 int n;                         /* #samples      */
 {
    int i;
 
    for (i=0; i<n; i++)
       write(fd,&p[i],2);
 }
 
 void closewav()
 {
    close(fd);
 }

----
 /****** mw.c ******/
 
 /* This is file: main.c */
 #include<stdio.h>
 #include<math.h>

 extern void sayhello_(float *, float *);
 extern int initwav(char *,int);
 extern int writewav(short *, int);
 extern void closewav();

 int main(argc, argv)
 int argc;
 char *argv[];
 {
   float in, out;
   float x, start, stop, incr;
   short s;

   if (argc == 1) {
      start = 0.0;
      stop = 3.0;
      incr = 1.0/44100.0;
    if (initwav("math.wav",3*44100) != 0) return((int) -1);
    for (x=start; x<(stop-incr/2); x+=incr) {
      in = x;
      sayhello_(&in,&out);
      /* printf("%f %f\n", x, (float) out); */
      s = (short) (32000*out);
      writewav(&s,1);
    }
    closewav();
   }
   return((int) 0);
 }

----

Running the tcl script with a complicated formula (using commands, not BWise blocks):

 formake [domaximafor {(sin(6.2831*110*x)*exp(-2*x)+(1/2)*sin(2*6.2831*110*x)*exp(-4*x)+(1/3)*sin(3*6.2831*110*x)*exp(-6*x)+(1/4)*sin(4*6.2831*110*x)*exp(-8*x)+(1/5)*sin(5*6.2831*110*x)*exp(-10*x)+(1/6)*sin(6*6.2831*110*x)*exp(-12*x)+(1/7)*sin(7*6.2831*110*x)*exp(-14*x)+(1/8)*sin(8*6.2831*110*x)*exp(-16*x)+(1/9)*sin(9*6.2831*110*x)*exp(-18*x))/(1+(1/2)+(1/3)+(1/4)+(1/5)+(1/6)+(1/7)+(1/8)+(1/9))}]

generates this fortran file:

      subroutine sayhello(x,r)
        real x,r
        r =        2.52E+3*(exp(-18*x)*sin(6.2202690000000002E+3*x)/9.0E+0+exp(-16*x)
     1   *sin(5.5291279999999997E+3*x)/8.0E+0+exp(-14*x)*sin(4.837987000
     2   0000001E+3*x)/7.0E+0+exp(-12*x)*sin(4.1468459999999995E+3*x)/6.
     3   0E+0+exp(-10*x)*sin(3.4557050000000004E+3*x)/5.0E+0+exp(-8*x)*s
     4   in(2.7645639999999999E+3*x)/4.0E+0+exp(-6*x)*sin(2.073422999999
     5   9998E+3*x)/3.0E+0+exp(-4*x)*sin(1.3822819999999999E+3*x)/2.0E+0
     6   +exp(-2*x)*sin(6.9114099999999996E+2*x))/7.129E+3
        return
      end


And this [http://82.170.247.158/Wiki/math.wav] is the resulting wav file, its a 260 kilobyte 16 bit wav file.

Part of he formula in neater form:
[http://82.170.247.158/Wiki/form1.jpg] ...

Finally, it is also possible to read the resulting wav file in a sampler or sample software and 'play' it with different keys on a (usb or midi) keyboard, which is great fun.

I've used the open source swami program to make a soundcanvas from the sample, in principle a multi sample can also be created this way:
[http://82.170.247.158/Wiki/swami.jpg]

I'd like a tcl script or package, or integrable command line utility to make soundcanvasses under tcl control..

Versions of the software used are: Tcl version 8.4 on Linux Redhat Fedora core 5, gcc 4.1.0, Maxima 5.12.0-3.fc5, Bwise 0.343 with console for Unix (,swami 0.9.4, fluidsynth 1.0.7). ''See also'' [a tcl script for function value listing based on a fortran expression]. I recently alo used FC6/64 with tcl 8.4 Maxima 5.12.0 , gcc 4.1.1 .

As a side remark: in Electrical Engineering and various other disciplines the above type of combined exponential / sine terms are very important and fundamental types of formulas which arise as the solution to important network theoretical linear but reactive circuits or systems differential equations.

Needless to say, because of the block facilities or bwise and general tcl/tk possibilities, a powerfull environment can be made.

Maybe I'll put an example here of a block based formula rendering.