A couple of days ago I was watching a YouTube before going to bed, it was some folks playing a guitar and tweaking things through an amplifier.

Here’s the thing — when he played one note it was all super clean and pure. With no changes to anything he played two notes and it suddenly sounded all dirty and grungy.

It was at this point that what I had learned about IP3 suddenly clicked. IP3 refers to the third-order intercept point of an amplifier. Typically to measure it you take two tones, and normally this is well into the radio frequency (RF) side of the world — 10s of MHz well into the GHz — and see how an amplifier deals with them. If you have a clean amplifier the output will look simply like the two input tones, but bigger.

On any amplifier, regardless of how good it is, you’ll have not just the individual signals get amplified, but you’ll also have the sum and difference signals get amplified as well. This is known as intermodulation.

So, if you have two signals, let’s say 440 Hz (A above middle C in case you’re curious) and add in a 554 Hz (C# above it) you’ll not only get 440 and 554 Hz in the output, but you’ll also have the difference get added to them as well — 554-440 is 114 Hz. So you’ll have 440 – 114 and 554 + 114, 328 Hz and 668 Hz in the output as well. Both of those are awfully close to an E note above and below to complete the A major chord. For reference, E4 = 329 and E5 = 659, these are just a few cents off of what the correct. (This is also why the equal temperament scale sucks in a way — the differences arise from the averaging of notes to be “good enough.”)

And this is how I finally got a taste of how RF theory and music theory come together. Both are just ways of looking at frequencies and their interrelationships. And an added bonus in this case why a distorted guitar works as more than just a source of noise. (Bonus bonus: this is why “power chords” work.)

Somehow by making this connection I have a far deeper understanding of both fields. It doesn’t happen often at all, but I was just plain old giddy for an hour afterward.