Sound Illusions
A bass note your phone speaker can't play, yet you hear it; a scale that keeps rising but never gets higher. Build both illusions from overtones and octave layers: the missing fundamental, where your brain hears the spacing between overtones, and the Shepard tone, described by Roger Shepard in 1964 and used in the score of Dunkirk and the endless staircase of Super Mario 64. Then test your ears and look back at the whole Sound & Science module.
In this lesson you'll
- Explain the missing fundamental: a note at 100 Hz has overtones at 200, 300, 400 Hz; remove the 100 and the brain still hears it, which is why a bass line survives on a phone speaker and why producers add harmonics with saturation or distortion.
- Build a Shepard scale: one note in several octaves at once, loudest in the middle, stepping up a half step at a time while the top octave fades out and a new one fades in at the bottom.
- Test both illusions by ear: full tone versus fundamental removed (same pitch or not?), and Shepard scales rising or falling, on good headphones and on a phone speaker.
Music in this lesson
- Dunkirk (film score)Christopher Nolan · Hans Zimmer · 2017
- Super Mario 64 (the endless staircase)1996
Remember
Overtones are spaced by the frequency of their note, so the brain hears the fundamental even when it is missing; organs fake low notes the same way with two pipes at 2x and 3x (the resultant stop).
A Shepard tone stacks octaves under a bell-shaped loudness curve: the top layer fades out as a new bottom layer fades in, so it never actually gets higher.
Pitch has two sides, note name and height: the illusion keeps the note name walking around the circle while the overall height stays put, tension with no ceiling.