Why is singing/playing an instrument off-key a thing? Why are some frequencies of the acoustic wave okay and some not okay?
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Just playing a single note out of tune is not likely to be offensive to anyone, because there is no other reference sound to compare it to, to determine if it’s in tune or out of tune. However, if you play two (or more) notes that are out of tune with each other, it will often be immediately obvious to most observers. Here’s why:
A musical note is a vibration at a certain frequency. A 440Hz note means something that is vibrating back and forth 440 times per second, whether that’s a metal string, a column of air, a block of wood, etc.
When playing multiple musical notes together at the same time, they sound best when the frequencies of the notes are in simple ratios to one another. For instance, if you play an A at 440Hz and an E at 660Hz, they sound pleasing together. This is because their ratio is 3/2, which is a simple ratio. If instead you played an A at 440Hz and an off-key E at 668Hz, it would sound nasty, because their ratio is 57/110, which is not a simple ratio. This complex ratio creates strange chaotic non-periodic interactions between the 440Hz tone and 668Hz tone, which sound harsh to our ears.
Combinations of tones that are considered pleasing are called “consonant”, and non-pleasing combinations are called “dissonant”. Note that this isn’t a black and white distinction, consonance and dissonance exist on a spectrum, and this can be used as a tool by a skilled composer to achieve different effects.
Check out [https://en.wikipedia.org/wiki/Consonance_and_dissonance](https://en.wikipedia.org/wiki/Consonance_and_dissonance) for more info.
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