Why do some musical notes sound AWFUL together?

In The Murderous Maths of Everything we see how you can cut organ pipes to different lengths and so make different musical notes. For example if you take a C pipe and cut it to 2/3 rds of the length you get a G pipe. If you play these two notes together they'll blend nicely.

These pictures show the vibrations coming out of a C pipe and a G pipe that’s 2/3 of the length. There are two C vibrations in the same space as three G vibrations.

When you play the C and the G notes together, the vibrations get mixed up. The green line shows the vibration pattern that reaches your ear which sounds more interesting. If you take the first half and spin it round so it’s upside down you get the second half. The pattern then repeats itself which makes it sound tuneful.

The book explains how you can make a "B" pipe in two different ways. Unfortunately they don't produce exactly the same musical note. Here’s an idea of what we’d get if we played the two different B pipes at the same time!

We’ve only shown the first little bit because the pattern won’t repeat for ages. Instead of sounding interesting it’ll sound more like you’ve got a wasp in your ear. If it was loud it could even be quite painful!

You might also be interested to know: How do guitar strings make different notes?

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