Shepard tones use only power-of-two partials plus amplitude shaping to create the illusion.

Evidence

It is not difficult to explain how Shepard tones actually work, yet this is seldom done. An equal-tempered scale climbs frequency as factors of 21/12 per semitone. Normally, each note would have all the partials above it as integer multiples of the base frequency. However, Shepard used only a subset of these, those that are powers of 2, i.e., 2n, n = 0, 1, 2,… above the first partial. The other partials are given no amplitude. — Eric J. Heller, Why You Hear What You Hear- An…, 2114

Categorization

• QUESTION: Worth chasing: why exactly does restricting to powers of two (octaves) make the octave-transposed tones perceptually identical?