For the most part, I understand the application of simple ratios when determining consonance/dissonance, but I still don’t really know what makes one ratio more ‘simple’ than another. What really defines how ‘simple’ a ratio is? One thing I’ve noticed is that if you add the two numbers in the ratio together, the smaller the total, the more simple it is, but why? Does anyone have a good understanding of what a simple ratio really means?
The basic idea is that (supposedly) interval rations sound less dissonant if the largest number in either the numerator or denominator has smaller factors that other cases.
Octave: 2/1 big factor 2 Fifth: 3/2 big factor 3 Just Third: 5/4 big factor 5 Pythagorean Third: 81/64 (or something close, I'm not sure) big factor 81
A few quick computations will show that one can't have all intervals in a scale close to good if major and minor chords should have their "ideal" ratios, 4:5:6 and 10:12:15.