Equal temperament makes combination tones slightly out of tune

Evidence

When two pure tones are heard together, other tones with frequencies lower than the frequencies of either of the two pure tones themselves may be heard also. These lower tones are not acoustically present in the stimulating signal, and they occur as a result of the stimulus consisting of a “combination” of at least two pure tones; they are known as “combination tones.” … The frequency of one such combination tone that is usually quite easily perceived is the difference (higher minus the lower) between the frequencies of the two tones; this is known as the “difference tone”: where fd = frequency of the difference tone fh = frequency of the higher-frequency pure tone and fl = frequency of the lower-frequency pure tone Notice that this is the beat frequency when the frequency difference is less than approximately 12. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1571 (#corroborates, via linked claim)

Categorization

• XREF: connects to: Only the octave stays perfectly in-tune in equal temperament; Equal temperament allows all keys but in-tunes no interval; Twelve stacked perfect fifths fail to close the octave exactly (+5 more)

Broader Connections

• The ear generates audible combination tones not present in the stimulus #corroborates (0.85) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1571
• Whether combination tones are musical depends on the tuning system #expands (0.80)
• Combination tones exist below both source tones and vary in audibility #expands (0.75)
• Equal temperament’s beats caused mutation stops to fall out of use #expands (0.75)