but why, oh why, does 12 but not 12*1 nor 6+6, not even 5+7 but precisely as 2+2+1+2+2+2+1=12 is so important for music !?
how can we make a general object that describes such a "folded" structure?
this strtucture arises naturally from repeating 3^1 all the way to 3^12 and inserting the appropriate 2^n (where n is negative integer) to keep all between 1 and 2 (or 2 and 4)
is 2212221 a group?
if we stop at 3^7 instead of going all the way to 12 we have a diatonic major, if we stop after 5 iterations of multiplying 3*3 it's a pentatonic.
but why, oh why, does 12 but not 12*1 nor 6+6, not even 5+7 but precisely as 2+2+1+2+2+2+1=12 is so important for music !?
how can we make a general object that describes such a "folded" structure?
this strtucture arises naturally from repeating 3^1 all the way to 3^12 and inserting the appropriate 2^n (where n is negative integer) to keep all between 1 and 2 (or 2 and 4)
is 2212221 a group?
if we stop at 3^7 instead of going all the way to 12 we have a diatonic major, if we stop after 5 iterations of multiplying 3*3 it's a pentatonic.