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Gradus Suivitatis

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Formula for gradus suivitatis after Leonhard Euler. See also CMJ 44/1.

Bild 0-1: Formula for gradus suivitatis after Leonhard Euler. See also CMJ 44/1.

Example calculating the degree of dissonancy inbetween two numbers according to gradus suivitatis. Hint: Skip prime factors which have both numbers in common. See also CMJ 44/1.

Bild 0-2: Example calculating the degree of dissonancy inbetween two numbers according to gradus suivitatis. Hint: Skip prime factors which have both numbers in common. See also CMJ 44/1.

Second example.

Bild 0-3: Second example.

public static int gradusSuivitatis(int a, int b)
{
           int bcd = biggestCommonDivisor(a,b);
           
           int c = (a/bcd)*(b/bcd); //rest primafactors which both a and b do not have in common.
           int cc = c;
           int result = 1;
           for(int p=0;p<prim.length;p++)
           {
               if(prim[p]>c)
                   break;
               int qq=0;    
               while(cc>=prim[p] && cc%prim[p]==0) {cc/=prim[p]; qq++;}    
               
               result+=(prim[p]-1)*qq;
           }
                      
           return result; 
}

Code 0-1: Method to calculate gradus suivitatis in Utilities.

public static int biggestCommonDivisor(int a, int b)
{
           if(a==0 || b==0) return 1;
           a=iabs(a);
           b=iabs(b);
           int x = min(a,b);
              
           for(int i=x;i>=1;i--)
               if(a%i==0 && b%i==0)
                   return i;
           return 1;        
}

Code 0-2: Helper method biggestCommonDivisor().

Modified version of gradus suivitatis

Bild 0-4: Modified version of gradus suivitatis "gradus tilde" according to the demands of AOG. See also CMJ 44/1.

Mean g~ for each number of an excerpt of N according to 20 neighbours of each specific number. See also CMJ 44/1.

Bild 0-5: Mean g~ for each number of an excerpt of N according to 20 neighbours of each specific number. See also CMJ 44/1.