Just from experimenting with synthesizers, I’ve noticed that the perceived pitch of a tone is defined more by the relative frequencies of the harmonics, rather than their absolute frequencies. So, you can take a harmonic series like 100Hz, 200Hz, 300Hz... and add a constant to each of them and get something like 123Hz, 223Hz, 323Hz... and it will still sound more like 100Hz than 123Hz.
EDIT: Actually adding 23hz is probably way too much for the result not to just sound dissonant.
I think that is different – that’s simply the case where all the harmonics are integer multiples of the fundamental, but the fundamental itself is missing. Every cycle of the waveform will be identical, so the period will unambiguously be the frequency of the missing fundamental.
In my case none of the harmonics are an integer multiple of the perceived overall pitch. And while the waveform will be aperiodic, it shows clear signs (on visual inspection) of similarity at the perceived frequency.
There's a double bass player trick for when you don't have a low C extension to play the low note up an octave plus the note a fourth below. This creates an illusion of the low note being present. It works best with a bow since it's hard to get the simultaneous sounding of the notes perfect pizzicato.
EDIT: Actually adding 23hz is probably way too much for the result not to just sound dissonant.