I have been thinking very much this for over a decade now. Down to even using the times and the division signs the same way (or + and - given they are more easi

I have been thinking very much this for over a decade now. Down to even using the times and the division signs the same way (or + and - given they are more easily typed). An interesting thing is that 2 is very special musically, but not mathematically, because it makes all notes musically the same (establishes pitch classes). A very funky thing (kinda annoying really) is as follows: Given a note, any note, as a tonal center or starting point (I call it O for origin) you 'make' a new note from this one by multiplying by 3 (O+3) [note 1]. Similarly we can make O+5. O+5 is in traditional western music closest to the major third AND O+3 corresponds to a 12-tet perfect fifth (flat 2 cents). In short +3 is the fifth and +5 is the third...weirdly annoying. note 1: Here's were 2 (which defines octaves) comes into play because it allows to say that O+3 defines a pitch-class no matter the octave.