12 tone matrix

Hey, this is a pretty obscure topic and of very limited use.

BUT

you're a bunch of smart people so you might find it interesting and I'm sure you can give me some ideas.

A 12 tone matrix is something used in atonal music, and it bears a striking resemblance to a Sudoku puzzle except the digits run 0 - 11 rather than 0 - 9.

I'm hoping for some input on the following:

//Future improvements will include 1] completing the matrix,
//2] playing the initial row via MIDI, and
//3] saving to disk as a text file. [I can figure this one out easily enough.]

Here's what I've got so far:

Code:

---

//The latest incarnation of my ongoing tonerow programming efforts (12/17/06)
//Currently generates P0 and I0 and prints them as the top and left side
//of an incomplete matrix. Also plays P0 and I0 with the cheesey 'Beep' command.

//Future improvements will include 1] completing the matrix,
//2] playing the initial row via MIDI, and
//3] saving to disk as a text file.

#include <iostream>
#include<cstdlib>
#include<ctime>
#include<iomanip>
#include <cmath>
#include <windows.h>

using namespace std;

int main()
{
  //Set constants
  double Semitone = pow(2.0, (1.0/12.0));
  double C = 261.626 * 2;
  double pitch;
  int delay = 500;
 
 
  //Initialize chromatic scale
  int row[12]={0,1,2,3,4,5,6,7,8,9,10,11};
 
  //Shuffle into a tone row
  srand(time(0));
  for (int i = 0; i<12; ++i)
    {
            int index1 = (rand()%12);
            int index2 = (rand()%12);
            int temp = row[index1];
            row[index1] = row[index2];
            row[index2] = temp;
    }
   
    //Print the row
    for (int x = 0; x<12; x++)
    cout<<setw(4)<<row[x];
    cout<<endl;
   
    //Play P0
    for (int tone = 0; tone<12; tone++)
    { pitch = C*(pow(Semitone,row[tone]));
        Beep(pitch, delay);}
   
   
    //Initialize I0
    int I0[12]={row[0]};
   
    //Generate IO !!YES IT WORKS!!
    for (int i = 1; i<12; i++)
    {int temp =row[0]+(row[0]-row[i]);
    if (temp<0)
    temp = temp + 12;
    I0[i]=temp%12;}
 
   
    //Display I0
    for (int x = 1; x<12; x++)
    cout<<setw(4)<<endl<<I0[x]<<endl;
   
    //Play I0
        for (int tone = 0; tone<12; tone++)
    { pitch = C*(pow(Semitone,I0[tone]));
        Beep(pitch, delay);} 
   
  cin.get();
 
  return 0;
}

---

Any input appreciated, thanks!

- JM

"double C = 261.626 * 2;" is not the best programming style. "261.626" is a completely arbitrary number. Better is:

Code:

---

double A1 = 440.0;                                            // standard tuning anchored to A1 = 440 Hz.
double C0 = A1 * pow( Semitone, -17 );            // 17 is number of semitones between C0 and A1

---

This defines C0 as 17 semitones (do I have that number right?) below A440.

Yeah, you're right, good call...

I changed it to

Code:

---

  double A = 440.0;
  double C = A * pow(Semitone, -9);

---

and it works fine - (C is nine half steps below A).


I still haven't completed the 12 x 12 matrix (confused by the 'clock math') or figured out any musical applications.

Lord knows if I laid any of this stuff on my high school band they'd run away screaming!

Thanks for the input

-JM