Two inaudible high tones can produce audible low phantom tones that interfere

Evidence

Another interval, f2 = 2048 and f1 = 3072 Hz (and analogous intervals), is remarkable in that, first, the difference tone f = f1 – f2 = 1024 and the combination tone f = 2f2 – f1 = 1024 are the same; thus what Koenig termed the lower beat tone (the difference tone) and the upper beat tone (the combination tone) coincide. This combination has loudness beats at 1024 Hz. If the higher frequency f1 is raised by A Hz, the difference tone should increase by A Hz, but the combination tone should decrease by A Hz. Indeed, as f1 = 3072 is lowered by hand, as is possible in the MAX patch Partials, one hears both rising and falling phantom tones (a rising combination tone and a falling difference tone) interfering with each other, causing beats when they are still relatively close in frequency. When f1 = 3073 Hz, there should be two beats per second, and that is what is heard. This is also the frequency of the waveform beats. If, on the other hand, the lower frequency is raised by A Hz, the difference tone should decrease by A Hz, but the combination tone should increase by 2 A Hz, implying a beating of between them of 3 A Hz. That is heard also. Quite an instructive example! We are feeding our ears only two pure tones, both above 2000 Hz, yet we are discussing the easily audible beating of two phantom tones, both around 1000 Hz! — Eric J. Heller, Why You Hear What You Hear- An…, 2303

Categorization

• QUESTION: The coincidence of difference and combination tones canceling one source of ambiguity is a lovely structural fact — worth chasing how Koenig characterized the lower vs upper beat tone distinction historically.
• SEED: An essay on how the auditory system manufactures ‘phantom’ structure that isn’t in the stimulus is a compelling angle on the deeper question of why we hear what we hear.
• corroborated: 2 independent passages support this claim — Eric J. Heller, Why You Hear What You Hear- An…, 2303
• XREF: connects to: Combination tones become audible only above roughly 70 dB primary level; Two coupled modes split above and below the test frequency, causing beat frequencies; Phantom tones are heard despite being absent from the presented sound (+5 more)

Broader Connections

• Two simultaneous tones generate audible lower tones absent from the stimulus #corroborates (0.95) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1571
• The ear generates phantom low tones absent from the actual signal #corroborates (0.92)
• Combination tones exist below both source tones and vary in audibility #corroborates (0.90)
• Upward masking makes intermodulation difference tones more audible than harmonics #expands (0.72) — Toole, Floyd E, Sound reproduction- the acoustics and…, 989