Not really. C to E is a major third (4 semitones), E to G is a minor third (3 semitones), and C to G is a fifth (7 semitones).

4 + 3 = 7

it's just 12 notes, ignore the letters. I wrote this program to help me understand scales and modes better.

  #define TRUE 1
  #define FALSE !TRUE

  void print_key();
  void show_scale();
  double power();

  char notes[13][3]={"A ","A#","B ","C ","C#","D ","D#","E ","F ","F#","G ","G#","A "};
  char scale_name[8][12]={"Ion(M)","Dor","Phryg","Lyd","Mixolyd","Aeol(m)","Locr"};
  int scale[16]={2,2,1,2,2,2,1,2,2,1,2,2,2,1};

  int main()
  {
  int key=3,i,its;

  printf("\nWelcome to Scale Printer.\n\n");

  do
  {
          print_key(key); printf("\n");
          for(i=0;i<=6;i++)
          {
                  show_scale(key,i,scale_name[i]);
                  printf("\n");
          }
          key = (key + 7) % 12;
          its++;
          printf("\n");
  } while(its<12);
  return 0;
  }

  void print_key(int key)
  {
  int i;
          printf("Key of %s\t:",notes[key]);
          for (i=0;i<13;i++) printf("%s ",notes[(key+i) % 12]);
  }

  void show_scale(int key,int mode,char \*modename)
  {
  int i,j,scale_note;

  scale_note=key;

  printf("%s of %s\t:",modename,notes[key]);
  for(i=0;i<8;i++)
    {
                printf("%s",notes[scale_note]);
                scale_note = (scale_note + scale[i+mode]) % 12;
                printf(" ");
                for(j=1;j < scale[i+mode];j++) printf("   ");
        }
}

You’re loose with your definition of a third. If you play C to E and E to G you will notice they are not the same distance.

Nothing like some good ol' off by one errors.

Or where 2^7 = 1.5^12.

Not really as most professional musicians understand the problem, but it shows that no instrument can be “perfectly” tuned.

Scale degrees are 1-indexed. Unison is the "first" when it should be zeroth if you want to add indices like that.

(3-1) + (3-1) = (5-1)