Real musical instruments produce measurable distortion tones that fall near other scale notes

Evidence

If two descant recorders are playing the notes A5 and B5 simultaneously in equal tempered tuning, which notes on the equal tempered scale are closest to the most readily perceived combination tones? The most readily perceived combination tones are the difference tone and the combination tones for n = 1 and n = 2 in Equation 5.3. Equal tempered f0 values for notes are given in Figure 3.21. Thus A5 has an f0 of 880.0 Hz and, for B5, f0 = 987.8 Hz. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1587

Categorization

• SHARE: Perfect for a recorder player or anyone who has heard phantom tones in a duo — the two-instrument demo is oddly specific and delightful.
• XREF: connects to: Nonlinear distortion generates new frequencies that change timbre with volume; Pure-tone instruments readily produce audible combination tones — David Howard, Jamie Angus, coustics and Psychoacoustics, 1621; Harmonic distortion measurements poorly predict audible annoyance from real music. — Toole, Floyd E, Sound reproduction- the acoustics and…, 109 (+3 more)

Broader Connections

• Nonlinear distortion generates new frequencies that change timbre with volume #corroborates (1.00)
• Pure-tone instruments readily produce audible combination tones #corroborates (1.00) — David Howard, Jamie Angus, coustics and Psychoacoustics, 1621
• Harmonic distortion measurements poorly predict audible annoyance from real music. #contradicts (1.00) — Toole, Floyd E, Sound reproduction- the acoustics and…, 109
• The ear itself generates audible nonlinear distortion tones from two simple inputs #corroborates (1.00)
• Hearing’s own nonlinearity produces audible difference tones even in distortion-free equipment #corroborates (1.00) — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 1520
• Higher-order combination tones can be misheard as actual played notes #expands (1.00) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1589