Polyphony is a sweet phenomenon, even if in physics it just means that two sound waves overlap each other. The first few frequency ratios in the harmonic series sound consonant (stable), and the ratios further along sound more dissonant (unstable).
harmonic series: (n)/(n+1)
Here I have the ratios graphed out next to its counterpart notation in music theory (I flipped the fractions just because it is easier for me to visualize). The dashed line is the resultant wave of superpositioning the two waves. Not be confused with the musical term, the physics term for that gross fluctuating amplitude is beat (and that, my fellow string ensemble mates, is how you can tell whether your strings are slightly out of tune).
Recall that amplitude corresponds to volume, and period corresponds to frequency.
And what about superpositioning the same pitch? If you think about it, the resultant wave is just double the amplitude while maintaining the same shape. When sound waves overlap in a way that amplifies itself nicely, it makes resonance. Consonances are more resonant than dissonances.
These things are indeed taught at school, but no teacher strings them together this way. You may have heard that music and maths are related (now you know it means more than counting beats). This is only one of the examples.
And no, my point does not end here.
Playing in an orchestra or singing in a choir is a humbling experience. According to how resonance works, playing off pitch can cause interferences, decrease the amplitude where waves cancel out each other, and make beats (the physics term). In order to achieve resonance, everyone has to listen to each other and blend in.
Harmony, literally.
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