The harmonic content of a sound is a big component of how we hear it, but the articulation over time of the sound also plays a significant role. This is referred to as the ADSR (Attack Decay Sustain Release) envelope. I would also imagine that each harmonic of a sound has its own slightly different ADSR envelope, so that harmonic profile would change over the duration of the sound.

Not just that, but every note has a different spectrum, and the spectrum evolves in a different way.

Instruments with dynamics - not a pipe organ, unless you include the swell pedal or some of the dynamic effects, like tremulant - the spectrum also varies with dynamics.

So generally, no, you can't accurately reproduce a sound with a single plot of the harmonics.

I'm more curious about how the physicist worked out a spectral plot by hand before sampling and FFTs were invented and oscilloscopes were barely a thing.

I'd guess he sketched the waveform from a scope plot, broke it down into points by hand, and performed a manual DFT - which must have taken quite a while.

Frequency Analyzers have been around nearly as long as oscilloscopes. Basically they’ll sweep a band pass filter and plot amplitude vs frequency on the screen.

Also - you can reproduce a sound by the frequency domain IF you look at the time progression of it.

Some Hammond Organs intentionally had a percussion control where the 3nd or 3rd harmonic would decay over time, giving the instrument timbre a bit of a pop.

> I'm more curious about how the physicist worked out a spectral plot by hand before sampling and FFTs were invented and oscilloscopes were barely a thing.

Before there were digital FFTs, there were analog equivalents. A prism basically does an FFT on light. I don't know, but I'd bet there were many analog based frequency analysis tools available before digital frequency analysis.