I was just watching a Veritasium video about audio illusions. In the first segment they explain the trick of using the harmonic structure of a note to trick the brain into hearing a fundimental that is not there. Well as a lot of people in the comments pointed out. Not everybody hears that phantom fundimental but just distortion added to the true fundimental of the tone that's played. I only hear a distortion and no phantom fundimental and I do not care for tube amps. I like a cleaner signal. This must be the same meganism why people say tube amps sound "warm". Those people hear that phantom fundimental shifitng the tone of the amp down making it more mellow of a sound.
It is absolutely true that humans will perceive a sound as having a certain pitch when the low order harmonics, say up through about the 5th harmonic, of that pitch are present in the signal but not the fundamental, particularly with audio information that is below 5kHz.
There's decades of scientific research in psychoacoustics and hearing on this and many other aspects of pitch perception (and pitch is a perception related to but not the same as the periodicity of the signal the person is responding to). It's science, not voodoo.
Although the mechanisms for this are not comprehensively understood, it seems to related to the fact that in our cochleas basically do a little kind of Fourier transforms on incoming waveforms, with different locations on the cochlea's basalar membrane responding to different frequency parts of an incoming complex wave, then, the nerves that fire as a result of membrane movement and deflection of the tip end of the inner hair cells at each of those points, are phase locked to that particular frequency within the complex waveform.
It seems that we they have a brain comparison mechanism to kind of decide what the pitch of this complex sound is based on the timing and location information of its component parts taken in at the cochlea -- so, if the harmonics associated with a natural sound that would have had the fundamental of 200 Hz, are present and the nerve firing pattern of is present -- we will perceive a pitch of 200 Hz even if the 200 Hz fundamental is not present. Experiments show that if the row of tones are not mathematically appropriate integers related to a particular phantom harmonic, our perception of the sound's pitch will be ambiguous and varied.
When the harmonic series of the phantom fundamental represents what would only be the high order harmonics -- like 10th, 11th, etc -- pitch perception also becomes ambiguous. And, because our inner ear nerve firing is fast, but not THAT fast, for frequencies over about 5kHz, the phase locking of our inner ear nerve firing breaks down (it takes too long for the nerve firing mechanism to come to rest and then first again to stay lock on the same phase point in the cycle), and also our ability to form a perception of pitch breaks down -- if you play "Mary Had a Little Lamb" with sounds only above 5kHz, it will be hard for humans to discern the melody.
Also worth noting, our pitch perception for sinusoid tones and for complex tones is not the same (stimulus level intensity can also impact our perception of pitch).
Certainly it seems like harmonic distortion has something to do with why some people like and prefer the sound of tube amps. But I'm not sure it has to do specifically with pitch perception -- don't forget the harmonic distortion present in the amp is derived from the signal -- there IS the fundamental AND its recorded harmonic present in addition to whatever other harmonic information is being generated by distortion. More likely it has to do with timbre perception.
Timbre is, like pitch, not a physical attribute of a sound but a perception, in this case related too but not the same as the presence, spectrum, amplitude, and changing envelope of the harmonic content of a complex sound as well to characteristic aspects of the attack of the sound. We put information about these things -- and perhaps other things, certainly including memory of the timbres of instruments we've heard -- together in our minds to form a perception of timbre. Anything in the audio chain that impacts the harmonic content of a complex sound -- and certainly harmonic distortion does -- and the attack characteristics of a sound, can have an impact on a listener's perception of timbre. And certainly tube amps with certainly degrees and spectrums of harmonic distortion can be perceived as having a timbral richness and texture that is more pleasurable to a given listener than other kinds of sounds, and also can be more closely associated with that listener's perceptual model of what "real" music sounds like.
There are probably other things as well that people may be responding too in tube amps that make them sound more pleasurable -- like frequency response alteration under load -- and more real to a listener, and other things that high levels of lower order harmonic distortion might be doing to mask higher order harmonic distortion. But I do think it's how the harmonic distortion effects the timbre that is the primary element, not so much how the harmonic content impacts the perception of phantom pitches.
The thing about audio is that our hearing and our perception is a really complicated process -- more complicated than our visual system -- and one that involves not only the brain assigning meaning the sounds we take in to form a perception, but also an active connection and feedback loop from the brain to the inner ear through the descending auditory pathway that literally allows our brains to actively shape our hearing at input; and, furthermore, there's plasticity in the descending auditory pathway, like, it appears to have slightly different performance characteristics in professional musicians than others, so what we hear is very much shaped by what we've learned.
(As a side note, the best guess for why we fill in fundamentals that aren't present to form a perception of pitch when a particular series of tones that correspond to the harmonic series of that fundamental are present, is because from birth we're immediately exposed to sounds in the world around us that have these characteristics so we learn pitch.)
On top of that, our hearing and our perception behave differently with complex tones than they do with sinusoidal tones -- which is one of the reasons why the kind of testing we do on audio equipment, while they're very good at telling us what the equipment is doing and what differences there are between equipment, doesn't always tightly correspond to how people hear music played with the equipment. A recorded music waveform going into the ear is a crazy complex single complex wave that our inner ear breaks down into multiple component frequencies from which we can form a perception, and somehow in that process our ears and brains can take this signal full of overlapping information at all kinds of frequencies, and, say with an orchestral recording -- still recognize and assign the timbral characteristics of a clarinet to the clarinet that's playing the same note at the same time as the entire violin section. That's a hell of a complicated -- and fast -- hearing and perceptual process.
