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I'm not sure if this is the same thing as consonance/dissonance, but the graph of sin(x) + sin(2x), an octave, is regular and pretty and the graph of sin(x) + sin(sqrt(2)x), a tritone, is much less so.

https://www.wolframalpha.com/input/?i=sin%28x%29+%2B+sin%282...

https://www.wolframalpha.com/input/?i=sin%28x%29+%2B+sin%28s...

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If you plot them as XY it's even more obvious which one is perfect consonance and which one dissonance:

https://www.wolframalpha.com/input/?i=%7B+x+%3D+sin%28t%29%3...

Except that if you use a frequency ratio of sin(x)+sin(2.01 x), which is really very close to an octave and really sounds just as consonant as an octave to almost all people, you almost the same "dissonant" picture:

https://www.wolframalpha.com/input/?i=%7B+x+%3D+sin%28t%29%3...

The strange thing is, none of these "simple ratio" theories account for the fact that our brains allow a lot of "fuzziness" around these simple ratios, so much that you can't really call them simple ratios as they encompass a whole bunch of not-simple ratios as well.

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