If I understand your question correctly, Big Man, the Do-Re-Mi stuff corresponds to the notes in the scale of any particular key. In the key of C, then Do = C; Re = D; Mi = E; Fa = F; So = G; La = A; Ti = B..."and that will bring you back to 'Do'." In the key of G, Do = G; Re = A; Mi = B...and so on. How the originator came up with these particular sounds for the notes of the scale is for more musicological-ly minded minds than mine to explain.

Regards, Neil