Tuning systems determine whether auditory combination tones align with harmonic series

Evidence

When the two notes played are themselves both exact and adjacent members of the harmonic series formed on their difference tone, the combination tones will be consecutive members of the harmonic series adjacent and below the lower played note (i.e., the f0 values of both notes and their combination tones would be exact integer multiples of the difference frequency between the notes themselves). The musical relationship of combination tones to notes played therefore depends on the tuning system in use. Two notes played using a tuning system that results in the interval between the notes never being pure, such as the equal tempered system, will produce combination tones that are close but not exact harmonics of the series formed on the difference tone. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1581

Categorization

• XREF: Connects to equal temperament vs. just intonation debates in music theory, and to missing-fundamental and virtual pitch phenomena from earlier chapters.