Two coupled modes split above and below the test frequency, causing beat frequencies

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 (#exemplifies, via linked claim)

Categorization

• XREF: connects to: Coupled oscillators trade energy back and forth, creating audible beating; Beats arise when two close frequencies combine in unresolved filters; Two inaudible high tones can produce audible low phantom tones that interfere — Eric J. Heller, Why You Hear What You Hear- An…, 2303 (+5 more)

Related

• Two inaudible high tones can produce audible low phantom tones that interfere (similarity 0.91)
• Combination tones become audible only above roughly 70 dB primary level (similarity 0.87)
• Beating between two high-frequency tones can create a phantom low-frequency tone (similarity 0.83)
• Two simultaneous tones generate audible lower tones absent from the stimulus (similarity 0.83)
• The ear generates audible combination tones not present in the stimulus (similarity 0.82)
• Two frequencies can mechanically generate sum and difference frequencies in the ear (similarity 0.82)
• Phantom tones are heard despite being absent from the presented sound (similarity 0.81)
• Pitch can exist with no tone heard at that frequency, unlike phantom tones (similarity 0.81)
• Combination tones beat against other near-pitched instruments unless masked (similarity 0.81)
• Two close sine tones produce amplitude beats at their frequency difference (similarity 0.81)
• Combination tones exist below both source tones and vary in audibility (similarity 0.81)
• Coupled oscillators trade energy back and forth, creating audible beating (similarity 0.80)
• A true difference tone is audible even from inharmonic partials separated by 200 Hz (similarity 0.80)
• Difference noise generated by ear nonlinearities can be heard before the test tone itself (similarity 0.80)
• Coupled oscillators barely interact when their natural frequencies differ greatly (similarity 0.80)

Broader Connections

• Beats arise when two close frequencies combine in unresolved filters #corroborates (0.95)
• Perceived beat rate equals the frequency difference, not true waveform periodicity. #expands (0.90)
• Two inaudible high tones can produce audible low phantom tones that interfere #exemplifies (0.85) — Eric J. Heller, Why You Hear What You Hear- An…, 2303
• Combination tones exist below both source tones and vary in audibility #exemplifies (0.80)
• Difference noise generated by ear nonlinearities can be heard before the test tone itself #exemplifies (0.75)