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When I listen to the three sinewaves, two of which are supposed to feel more similar because they a factor two apart, I don't actually get any such similarity effect. They all seem just about equally similar to each other, even when played together. Is everyone here picking this sameness up? I'm curious what kind of mechanic underlies those feelings of sameness and what it feels like.

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Its very hard to hear this with sine waves.

Sine waves work to visualize the concepts but real instrument notes almost always are better modeled as a large number of sine waves with a mathematical relationship that sound simultaneously and in varying amplitudes that combine to create the timbre of the note.

Then when those notes sound together we get combinations of all those sine waves together to create a very complex wave that sounds a certain way to our ear based on the interactions between all of these waves at once.

So to visualize it or reason about it, my comment here makes sense:

https://news.ycombinator.com/item?id=30363653

But to hear it you would be much better off with triangle or sawtooth waves or samples of actual musical instruments.

Right. Octaves sound consonant because the harmonics of one note line up with the harmonics of the other. Without the harmonics you expect to hear no effect.

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