Perceived pitch can arise from harmonics alone even when no actual fundamental sounds

Evidence

The f0 value of the middle C of a 32β€² stop (C2) is 65.4 Hz and thus its bottom note is two octaves below this (C0) with an f0 of (654/4) or 16.35 Hz. The f0 for the bottom note of a 64β€² stop (C βˆ’ 1) is 8.175 Hz, which is below the human hearing range but within the frequency range of difference frequencies that are perceived as beats (see Figure 2.6). Harmonics that are within the human hearing range will contribute to a perception of pitch at these f0 values, which are themselves below the frequency range of the hearing system. … Organists will sometimes play fifths in the pedals to imitate this effect, particularly on the last note of a piece. However, the effect is not as satisfactory as that obtained with a properly voiced resultant bass stop, because the third harmonic (e.g., 102/3β€²) should be softer than the second harmonic (16β€²) for best effect. β€” David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1651

Categorization

  • XREF: This is the missing fundamental / residue pitch phenomenon β€” the same principle behind why small speakers can reproduce bass they cannot physically output. β€” connects to: Perceived musical pitch arises from regularly repeating acoustic pressure waves. β€” David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 774; The ear perceives a virtual pitch not physically present in a sound’s components β€” David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 859
  • QUESTION: Does the amplitude relationship (third harmonic softer than second) hold across other instruments and contexts as an optimal cue for residue pitch?