Never-ending Scales

Put on your headphones or turn on your speakers and listen to this sound pattern by pushing the play button(>) . It's called a Shepard scale.

You may notice that the scale always seems to be going down, but not getting much lower. It's an auditory equivalent of an old-fashioned barber pole. But how is it possible in a sound pattern?

The Paradox of Shepard Scales
It's not easy to describe what's going on in Shepard scales, but if you're interested keep reading!

Most sounds that we think of as having a "pitch," like a singing voice or a note played on a musical instrument, are complex signals that are composed of energy at many different frequencies. For example, when you sing a middle "C," the sound you produce contains energy not only at the "middle C pitch" that you hear (about 260 Hz), but also at harmonic frequencies of 520, 780, 1040, and so forth—that is, multiples of 260 Hz. Our auditory system uses this spacing, and not just the fact that 260 Hz is the lowest frequency, to determine which note you are singing. In fact, if you erased all of the energy at 260 Hz, you would STILL hear the note as a middle C.

Shepard tones, like the ones you just heard, are a little different. They have energy only at harmonics that are related by OCTAVES, which means that each successive frequency is twice the last one. (In the case of a C, there might be 130, 260, 520, 1040 Hz, etc. instead of the constant spacing of 260 Hz). The presence of all of these frequencies tells you that it's a C of some kind, but you can't use that constant 260 Hz spacing to determine exactly WHICH C.

To make things really tricky, in Shepard tones volume is set higher at a constant frequency unrelated to the "pitch" of the note (for example, 368 Hz). It tapers off to near-silence at the higher and lower ends of the range. No matter what note you hear, it has the most energy at the harmonics that are closest to this constant frequency.

Ever-ascending Staircase Visual IllusionThese features make your brain hear a seemingly impossible scale: one that constantly descends, but doesn't get any lower.

The result is an "ever-ascending" scale, which is a sort of auditory analog to the ever-ascending staircase visual illusion.

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