Gradus Suivitatis
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Bild 0-1: Formula for gradus suivitatis after Leonhard Euler. 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.
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().
Bild 0-4: Modified version of gradus suivitatis "gradus tilde" according to the demands of AOG. 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.