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The Craziest Tone In All Of Music

On The Shepard's Tone And Its Unlikely Origins

On January 26, 2017

Regina Spektor’s piano-work and lyricism are brilliant, especially on a song like “Laughing With.” She’s spare and morose with her piano chords, at times resolving the mood with a major chord but mainly relying on the minors, and her lyrics confront religion, devolving God into a temporal being. God is self-effacing, “at a cocktail party when listening to a good God-themed joke”; as well as cunning, “when told he'll give you money if you just pray the right way.” Spektor waters down the abstract into something a little more worldly -- an artistic maneuver that complimented the tropes of HBO’s The Leftovers, when “Laughing With” featured towards the end of a season two installment.

Her 2016 album Remember Us to Life is what brings us here today. There’s a tone buried in the song “Tornadoland,” I want to talk about. About a minute into “Tornadoland,” imbued by a formidable string section, she plays a piano scale that, tying back to the song title’s vortex imagery, seems to be eternally descending. With this scale she doesn’t, however, proceed to octaves deeper and deeper along the piano (if that were the case, eventually you wouldn’t be able to discern notes anymore); instead she seems to loop it in a manner where its point of restarting becomes indecipherable. While “Laughing With” was abstract lyrically, here she’s abstract musically. Known as the Shepard tone, Spektor is playing an esoteric device rooted in both cognitive and computer science.

Psychologist Roger Shepard fathered the Universal Law of Generalization, which postulates that an organism will conflate a stimulus with another depending on the level of similarity between the two. An online psychology glossary offers alongside its definition that “when a person learns that some species of snakes are dangerous,” for example, “that response generalizes to a fear of all snakes.” He expounded upon this law in a 1987 paper, but its basis was inchoate within his Shepard tone, programmed on a computer back in 1964.

By overlapping two ascending scales that are an octave apart, the higher abates its volume at a particular rate, while the lower rises in volume at that same rate. The lower scale, at its final note, segues into what was originally the higher scale; simultaneously a new lower scale begins. (A descending Shepard tone, as in “Tornadoland,” just reverses the placement of scales: a new higher scale begins once the original higher segues into becoming the lower.) Via a musical method, Professor Shepard compounded the jargon of his 1987 law -- two stimuli generalized into a single stimulus. You’re supposed to think it’s just one ineffably eternal scale/tone.

An oft-made visual analogy is the Penrose stairs -- created by mathematicians Lionel and Roger Penrose -- the infamous spiral staircase that, if you trace your finger along it, hasn’t an end. Super Mario 64 removed the cyclical design but maintained the Penroses’ impetus with its “endless stairs” level (, which you can actually reach the top of by exploiting a glitch and having Mario jump up the stairs backwards. If you ascend them while facing forward, then the stairwell is, as intended to be the level’s hinderance, endless. And to emphasize this jist, video game composer Koji Kondo chose to play a Shepard tone in the background.

Aside from visual forms, it’s also complementary to aesthetics specifically within the field of music -- like post-rock. Godspeed You! Black Emperor incorporate it into their track “Slow Moving Trains,” from their 1997 debut F#A#Infinity, when, following the rumble of a train chugging, strings play a creaking, descending Shepard tone that crescendos and eventually reaches a steady drone. Through subsuming reverb-guitar barrages and generally lengthy songs, Godspeed strive to embody the infinite (which can be inferred from their album title) as closely as possible within their post-rock -- so their playing a Shepard tone makes perfect sense, since it’s an element that captures and reflects that precise embodiment of infinity.

The Beatles used it towards the end of “I Am The Walrus”; Queen, in the fanfares that begin and end their album A Day At The Races; Pink Floyd too, during the penultimate minutes of their epic “Echoes.” Obviously the Shepard tone was a point of fascination for classic rock at the peak of the genre’s popularity (years before it was eligible for the “classic” epithet). And it can be conducive to the mechanics of today’s popular music as well. The Shepard tone endowed the mentioned artists’ respective works with ambient texture, something that seems to be a burgeoning affinity among many A-list electronica artists. The tone’s presence within the likes of Tycho or Flume may very well be imminent -- imagine all the Dionysian dissonance and apprehension it could incite, building anticipation ad infinitum for a drop.

As are the 4/4 time signature, the 1-6-4-5 chord progression, and the post-chorus, the Shepard tone isn’t bound to just one genre, loosely uniting post-rock, classic rock, and video game soundtracks (and soon maybe electronica, too). Unlike those other “genreless” elements, though, the tone is an auditory illusion. A song can be so magnificent that it leaves you jaw-dropped and speechless, but Roger Shepard discovered a way for a song to leave you jaw-dropped and speechless -- and stupefied, and then making you question your own aural capabilities. The Shepard tone turns the hyperbole, I can’t believe what I just heard, into a literal statement (although that statement can easily go both ways with Spektor, Godspeed, and others).

Profile Picture of Eli Zeger
Eli Zeger

Eli Zeger has written for Noisey, Van Magazine, Real Life, Hyperallergic, DownBeat, and others. He loves his guitar and cat!

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