Wanna see a cool visualization of the question you propose? Google "Lissajous Pattern" and the like. Youtubes and images and wikipedia articles. This is NOT

Wanna see a cool visualization of the question you propose? Google "Lissajous Pattern" and the like. Youtubes and images and wikipedia articles. This is NOT what your eardrum looks like when you hear notes in tune, but it does provide a certain visual simulation of why simple integer-ish ratios sound better than random ratios.