RE: Is there a real chance that there is a multiverse?
September 9, 2016 at 1:32 am
(This post was last modified: September 9, 2016 at 3:11 am by bennyboy.)
(September 9, 2016 at 1:12 am)Alex K Wrote: Looks deeper before you realize that you don't end up in the same place after going round once if you use pure intervals due to the pythagorean comma. A pity, really
Yep, and the math should be almost painfully obvious. How many iterations of (3/2)^n (a circle of perfect fifths) are ever going to arrive at an even multiple of 2? When you then start taking each of those notes and their overtones (f/2, f/3, f/4 etc.), you quickly realize that any amount of modulation among keys will almost instantly lead to chaos.
Tuning systems require two things: (1) fudge frequencies to make the math work; (2) have people's tolerances built to accept the impure sounds.
