Perceived beat rate equals the frequency difference, not true waveform periodicity.

Evidence

The case of adding 27 Hz and 25 Hz sinusoids is shown in figure 24.4. The GCD of these two frequencies is 1 Hz, and this is indeed the true periodicity of the tone. However, we expect to hear a 2 Hz beating, since the partials differ by 2 Hz, and we do. In fact, there are two loudness maxima per second, but as close inspection of figure 24.4 reveals, adjacent maxima are very slightly different. We can’t hear that slight difference; rather, we hear the maxima. Mathematically, this happens because the cosine oscillates at half the difference in frequency, or 1 Hz. However, there are loudness maxima at 2 Hz, because they happen whether cosine is near 1 or -1. — Eric J. Heller, Why You Hear What You Hear- An…, 2221

Categorization

Category: Causal Relationships

• SHARE: The GCD-vs-heard-difference subtlety is a wonderful nerdy fact for anyone into acoustics or synthesis.

Related

• Beat rate is set by frequency difference, not by the true tone periodicity. (similarity 0.92)
• Waveform beat rate depends on the lower partial’s frequency, not just the mistuning amount (similarity 0.82)
• Two coupled modes split above and below the test frequency, causing beat frequencies (similarity 0.80)
• Presented together, tones reveal far finer pitch differences via beats than sequential comparison (similarity 0.80)
• Beat perception occurs even when partials go to separate ears, ruling out physical nonlinearity (similarity 0.79)
• A combined waveform can produce a perceived pitch absent from its actual frequency components (similarity 0.79)
• Two close sine tones produce amplitude beats at their frequency difference (similarity 0.79)
• Hearing waveform beats disproves strict place theory of perception (similarity 0.78)
• A true difference tone is audible even from inharmonic partials separated by 200 Hz (similarity 0.78)
• Perceptual thresholds vary by listener but share common ordering (similarity 0.78)
• Simultaneously presented tones sharpen pitch discrimination down to beat disappearance (similarity 0.78)
• Mistuned musical partials produce slow timbre or quality beats distinct from loudness beats (similarity 0.78)

Broader Connections

• Presented together, tones reveal far finer pitch differences via beats than sequential comparison #expands (0.82) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 866