When two patterns are overlayed there is a third pattern which is the interference of the two patterns, or a pattern of the sums and differences of the two patterns.
If the first two patterns have a simple fractional relationship you can visualize the resulting pattern in your head, and the brain when hearing perceives this as predictable and regular, and predictability is boring and sounds consonant.
If the fractions are more complicated we end up with a more complex combined pattern which is harder for the brain to predict and is perceived as richer or more dissonant.
If the patterns get very far from the fractional relationship (for example
If an instrument is out of tune) these patterns start to feel non deterministic or non repeating to the brain and we tend to hear this as unpleasant.
If the patterns have no particular mathematical relationship we end up with a completely non repeating pattern that is indistinguishable to the brain from randomness, and we call this unpitched or noise.
When two patterns are overlayed there is a third pattern which is the interference of the two patterns, or a pattern of the sums and differences of the two patterns.
If the first two patterns have a simple fractional relationship you can visualize the resulting pattern in your head, and the brain when hearing perceives this as predictable and regular, and predictability is boring and sounds consonant.
If the fractions are more complicated we end up with a more complex combined pattern which is harder for the brain to predict and is perceived as richer or more dissonant.
If the patterns get very far from the fractional relationship (for example If an instrument is out of tune) these patterns start to feel non deterministic or non repeating to the brain and we tend to hear this as unpleasant.
If the patterns have no particular mathematical relationship we end up with a completely non repeating pattern that is indistinguishable to the brain from randomness, and we call this unpitched or noise.