Thread: The Audio Programming Book Chapter 0 pg41 - 42 Visualising algorithms / array [-1] ?

The programming is meant to make A matrix for serial music using the 12 tone technique. I can't visualise whats happening in specfically this bit of code

Code:

/* create inversion in column 1 */
    for(m = 1; m < 12; m++)
        series[m][0] = mod12(series[m-1][0] + series[0][m-1]
                             - series[0][m]);

I'm expecting something like this
for (m = 1; m < 12; m ++)
series[m][0] = [0][-1]
series[m][0] = [1][-1]
series[m][0] = [2][-1]

and so on...

is it saying take the result of mod12(series[x][x]) and put it into series[x][x]?

is series[x][x] a single value or two?

Code:

/* The first row of the matrix will receive the original twelve notes, from left to right.
 The inversion of the series will fill the first column of the matrix, from top to bottom.
 To complete the matrix, the other rows will receive transposed versions of the original
 series, each one starting with the note in the first column. */




#include <stdio.h>
#include <stdlib.h>


int mod12(int note) {
    while(note >= 12) note -= 12;
    while(note < 0) note += 12;
    return note;
}


int main(int argc, char** argv)
{
    int series[12][12], offset;
    int n, m, i;
    char* table[12]={"C","Db","D","Eb",
                    "E","F","Gb","G",
                    "Ab","A","Bb","B"};
    if(argc != 13) {
        printf("usage: %s note1 note2 ... note12\n", argv[0]);
        return -1;
    }
    /* loop until all available notes are entered*/
    for(n = 0; n < 12; n++)
        series[0][n] = mod12(atoi(argv[n+1]));
    
    /* create inversion in column 1 */
    for(m = 1; m < 12; m++)
        series[m][0] = mod12(series[m-1][0] + series[0][m-1]
                             - series[0][m]);
    
    /*create all transposition */
    for(m = 1; m < 12; m++)
        for(n = 1; m < 12; m++)
            series[m][n] = mod12(series[0][n] + series[m][0]
                                 - series[0][0]);
    
    for(m = 0; m < 12; m++){
        /* print the pitch classes, row by row using the
             translation table */
        for(n = 0; n < 12; n++) printf(" %s ", table[series[m][n]]);
        printf("\n");
    }


    return 0;
}

There is a difference between the subscript n itself going negative, which it never does, and the note going negative. Sometimes the note will go negative, which is why you mod12 it. I don't think you completely understand which numbers are doing what in the program.

This should show you.

Code:

int note;
for (m = 1; m < 12; m++) {
   printf("m=%d, m-1=%d\n", m, m-1);
   note = series[m-1][0] + series[0][m-1] - series[0][m];
   printf("note before mod=%d\n", note);
   series[m][0] = mod12(note);
   printf("note after mod=%d\n", series[m][0]);
}

These are some results here:

m=1, m-1=0


note before mod=0


note after mod=0


m=2, m-1=1


note before mod=0


note after mod=0


m=3, m-1=2


note before mod=0


note after mod=0


m=4, m-1=3


note before mod=0


note after mod=0


m=5, m-1=4


note before mod=0


note after mod=0


m=6, m-1=5


note before mod=0


note after mod=0


m=7, m-1=6


note before mod=0


note after mod=0


m=8, m-1=7


note before mod=0


note after mod=0


m=9, m-1=8


note before mod=0


note after mod=0


m=10, m-1=9


note before mod=0


note after mod=0


m=11, m-1=10


note before mod=0


note after mod=0

These are the results when :


for(n = 0; n < 12; n++)
series[0][n] = mod12(n);

Joels-MacBook-Pro:APB joel$ ./chap0 Db C D Eb E F Gb G Ab A Bb B
m=1, m-1=0
note before mod=-1
note after mod=11
m=2, m-1=1
note before mod=10
note after mod=10
m=3, m-1=2
note before mod=9
note after mod=9
m=4, m-1=3
note before mod=8
note after mod=8
m=5, m-1=4
note before mod=7
note after mod=7
m=6, m-1=5
note before mod=6
note after mod=6
m=7, m-1=6
note before mod=5
note after mod=5
m=8, m-1=7
note before mod=4
note after mod=4
m=9, m-1=8
note before mod=3
note after mod=3
m=10, m-1=9
note before mod=2
note after mod=2
m=11, m-1=10
note before mod=1
note after mod=1

I'm confused it looks like it does go into minuses, im not sure where its getting that value from. I would've presumed it is a bit a memory that isnt there?

the programme works with now the correct arg inputs. under /*create inversion in column 1*/ I just don't understand why series[0][-1] = -1 before using mod12() = 11.
but series[0][-1] is invalid ? surely this should be garbage values. A value is never put there because the element [-1] doesnt exist?

ah...arithmetic isn't moving through the array elements it's pointing to the actual values.

However, its seems that on the left side of the "=" with series[m][0], only the elements are adjusted wheres on the right side of the "=" the values are influenced is that right? What makes for this change in behaviour ?