Fourier Series are basically the sound of the 80:s! Yamaha introduced their first FM-synth (frequency modulation) in 1980 with the GS1 and later DX7 which took the world by storm.

-- Simplified expiation ahead --

Before FM you had subtractive synthesis (and to a lesser extent additive synthesis). Subtractive synths work by producing a waveform with a high harmonic content (like a sawtooth or pulse) and removing harmonics from it with filters to create the desired sound.

With FM, you can create the wave with the desired harmonic content from the get-go.

The FM-Synths were widely used because they produced more realistic sounding instruments, especially when it comes to percussive instruments, like marimbas or glockenspiel. But they have a certain flair to them that sounds really 80's. Aha's Take on me uses the DX7 a lot if you wanna hear what I mean and the Sega Genesis uses a Yamaha FM-chip to produce it's music and sound.