Looking at a keyboard, we see a compromise. The notes in our Western scale are derived from Pythagoras's "pure" ratios, but these pure ratios do not fit neatly into a twelve-note system. D-sharp is not really the same note as E-flat, nor is E-sharp really the same as F, and so on. Thus, Western music has had to compromise, resulting in intervals that are almost pure, but not exactly. Modern equal temperament, for example, is based on the square root of 12, not a pretty number at all, but close enough for our ears. In this system, the only pure ratio is the octave. The result of these impure ratios is more dissonance.
Italian composers in the 17th Century were not happy with this compromise, however, and began composing music for instruments with more than 12 notes to the octave. One instrument is the cimbalo cromatico, a harpsichord that has 31 notes per octave.
Take a listen to this "uncompromising" music. I think I like music with more dissonance better. All those pure ratios, oddly, make me feel dizzy and uneasy.
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