According to Fourier's theorem, we know that a sawtooth wave can be represented as a sum of sine waves. These sine waves we know as harmonics (in the context of sound). My understanding is that it is the same for electrical current.
Let us take a band-limited sawtooth wave in an electrical circuit. Say its frequency is 440hz. We know that its next harmonic after fundamental is $880$ Hz.
Do we actually have something oscillating in this circuit at frequency $880$ Hz in a sinusoidal waveform? What is it then? Or this is just a mathematical concept?
I am thinking from a perception point of view: when we produce a sawtooth wave by gradually increasing the voltage from $-1$V to $1$V and then dropping it from $1$V to $-1$V almost instantly. And that is what we see in the oscilloscope: spikes of $2V$ at $440$ Hz. But we don’t see its harmonics there. Do they actually happen or this is just an abstraction?
Please, help me with some guidance.