Feynman is talking about "harmonics" in that sentence. "Harmonics" is used in the context of periodic signals. Concerning periodic signals, the human ear has a frequency resolutionrange that goes from 20Hz to 20.000Hz.
If you really wanted to disprove what Feynmann is saying, you should consider a periodic pulse signal of frequency that sits comfortably between 20Hz and 20.000Hz and compare it with a periodic white noise. And clearly you want the two signals to have the same volume, so you would have to run the periodic pulse on a device with a large voltage output so that the pulses are as close as possible to ideal ones.
If you did the above experiment and found a clear difference between the two sounds, maybe you would convince me.