But high frequency notes will have beats emerge even when there is no audible difference in pitch - a feature exploited in tuning instruments, by relying on beats to get more accurate tuning than could be accomplished by relying on perceived pitch differences alone. The beats are determined by the absolute difference in frequency, but, as is typical of much perception, pitch perception is logarithmic. The beats will emerge from the shifting tones in a different way for a normal hearer and for a pitch invert. More importantly, auditory experience has a kinesthetic aspect. High tones are associated with tightenings - of vocal cords, increased lung pressure, diaphragm tension, and so forth.
Low notes are low in the throat, produced by relaxings, larger air flow, and so forth.
These associations most likely permeate all experience of pitch, not just that of tones the perceiver is producing or contemplating producing. The vast richness of these myriad connections and associations is an important part of what gives experience its character. The conscious brain is an unbelievably vast network, with connections across multiple areas, sensory and motor. Part of the experience of a sound may be shaped by subliminal experience of what is required, what it is like, to produce similar sounds. While it might be possible to attempt to avoid this objection by supposing the kinesthetic qualia to be inverted as well, the point is that qualia are not raw and simple, they are embedded in a vast network of connections and associations.