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Shepard Tone (wikipedia.org)
99 points by tintinnabula on Aug 13, 2019 | hide | past | favorite | 34 comments

Similar in concept is the Risset rhythm (it's briefly alluded to in the article), where the tempo of the rhythm seems to constantly speed up or slow down.

The song "Fold4, Wrap5" by Autechre is a cool example. It's not hard to see how it works, but it's a delightful effect regardless. Each bar has a point at which the beat shifts to a double-time version of itself, while the tempo of the track constantly decreases so that the double-time rhythm transitions back to the original rhythm.

That song makes me really uncomfortable, like anxiety inducing. Neat! Always cool to see how different music makes different people vibe certain ways.

Here's a youtube link if anyone else is interested: https://www.youtube.com/watch?v=SLvFsP1izS4

I can't imagine listening to that style as a regular thing, but I could easily picture that as "alien music" for a movie or atmospheric background. Not 'musical' as I would think of it, but clearly recognizable as music for very different ears or mental structures.

Interesting! I'd like to see a version where the double-time track is fading in continuously, instead of arriving all at once at the beginning of a measure (which would be a closer analogue of the Shepard Tone). Can't quite tell if the other reply is an example of that.

Reminds me of the "getting short of breath" music in Sonic, although that doesn't use any fancy tricks.

I was going to say that this one (which sounds like a not that short loop) and the "fold4, wrap5" (which just sounds like a horrible short loop to me) didn't give me the same illusion, but then I listed to the one in the Wikipedia article again and it didn't work for me this time either (short loop). I think the Bach linked above broke the illusion for me or else it only works for a very limited time.

That was really cool. Tried to tap along and noted how my rythm increased, but changed how many taps per beat I did over time.

Here's a way to figure out how they work:

Listen to Bach's Fantasia from Fantasia and Fugue in G minor, BWV 542:


At about 3:54 you'll hear a famous section where Bach starts "circling" around fifths. The general pattern is that the notes of the chords in the hands "rise" while the feet descend.

Listen to the bass line. It seems to descend by step for thirty notes in a row. But try singing any note and singing down a scale for thirty notes in a row. You probably can't do it. And if Bach did that in the bassline the final note would be really low and flabby.

So how does the bassline seem to continue descending by step while remaining in the same general range?

The answer is a two-word phrase that is usually met by profound boredom in first-year music theory classes. But that concept is what Bach uses in the pitch domain here to achieve his aim. And its analogous to what happens in the frequency domain to produce a Shepard tone.

Reminds me of the accordion (left hand)... it has only one octave of pitches, so can only descend an octave before returning to the highest pitch. Then it's up to first overtones to continue the illusion.

I'm used to hearing the terms time domain and frequency domain. But I've never heard pitch domain as a separate idea. Isn't pitch just the same as frequency?

In this context, the term is just used to tell you to think in terms of pitch classes — where all notes that are separated by an integer multiple of an octave belong to the same class — and not expect actual Shepard tone trickery related to absolute pitch.

However, the relationship between absolute pitch and frequency isn't always trivial. The latter is a physical phenomenon, but the former is psycho-acoustic. When you have sounds with a normal set of overtones that align with a harmonic series, the perceived pitch matches the fundamental frequency. But that frequency doesn't actually need to be audible. By weighting the amplitudes of the partials in a certain way, you can also construct a sound that will be perceived as different pitches by different listeners, or by the same listener under different circumstances.

With sounds whose frequencies aren't all harmonic, assigning a pitch can get more complicated.

> However, the relationship between absolute pitch and frequency isn't always trivial.

Not only is it not trivial, it is undefined. For example, "middle C" can map to different frequencies depending on your tuning system, for just one example.

Pitch is the higher level abstraction. Especially on the organ, "middle C" may get interpreted as "middle C plus a C an octave below, plus another octave below for good measure" depending on context. I assume that's what Carpenter is changing when he's putting his hand on those pads where the stops should be.

Thanks! Very informative.

In general I've found the world of music theory to be difficult to penetrate as an outsider, just gotta take small bites.

There's a great example of Shepard Tones in Dunkirk: https://www.youtube.com/watch?v=LVWTQcZbLgY

Can’t watch the video atm, but in case it’s not mentioned - Nolan says he based the structure of Dunkirk on the shepard tone. Always rising in intensity, never ending. Great film!

My favourite Shepard Tone example is Stephin Merritt's 'Project Song' video for NPR [1]. It's also way more playful than most.


I feel like we're in a moment of cultural shepard tone - there is the sense that we are barreling towards something and yet also the sense that nothing can or is changing.

What I'd like to see is the opposite effect: A keyboard where every note is generated using only combinations of Cs, but with the weightings chosen so that its average pitch is the one that that key usually has. This would have the strange consequence that nothing you played would sound dissonant and any piece you played would have the same affect as any other.

It would probably be boring to listen to all the time, but interesting to hear it playing a piece which usually makes use of lots of dissonance.

This is not quite that, but does have a piece that had a lot of chord motion converted to all C major:

(Coltrane's) Giant Steps in C. https://www.youtube.com/watch?v=qTYzYpb1MY0

For jazz musicians it's very funny, in a horrifying kind of way, maybe listen to the 1959 original first if you don't know it. https://www.youtube.com/watch?v=Lu0Lhysn_X8

And thank you! While getting the links I found this wonderful animation of a shortened version of the original: https://www.youtube.com/watch?v=rh6WTAHKYTc

p.s. Woohoo! Coltrane on HN! :-)


Sigh, I'd delete your comment if I could. I really wish you hadn't done that. Almost every sentence is cliché-ridden, crass and/or wrong, like the worst kind of journalism. Sorry.

Multiple pitches don't get averaged, it would sound like just a set of Cs. Could still be an interesting experiment, though.

You may not perceive the average for such large intervals, but there are cases in music where you typically will, for example during vibrato.

> This would have the strange consequence that nothing you played would sound dissonant

Pentatonic scales have that property, mostly how even beginner guitarists can achieve picking solos (as long as you know what the root note is and keep rhythm)


Same for some harmonicas.

> A keyboard where every note is generated using only combinations of Cs, but with the weightings chosen so that its average pitch is the one that that key usually has.

Sounds like you're describing a vocoder or auto-harmonizer but I can't be sure.

Suppose I play an F-sharp above middle C on your "averager" keyboard. What is heard? Is it only various C pitches? C pitches and a single F-sharp? Something else?

Do the C pitches have harmonics or is it only the fundamental?

Only various C pitches, and only the fundamental. I believe that this is also how most Shepard tones are made, except that when you play a different Shepard tone you vary the note (i.e. A, B, C, etc.) but keep the average pitch the same, whereas I want the opposite, where you keep the note the same but vary the average pitch.

I get the concept, but the aural result is going to be quite boring because the timbral content is so limited. It can be achieved through simple additive synthesis with a handful of sine waves.

What you are doing is playing a single note but with variations in timbre.

I imagine the best you can get will sound like playing the horn. By that I mean a simple horn, without pistons nor slide. Because horns have a fixed length, they can only play one note, but skilled players can control harmonics to create a melody.

> variations in timbre

Good insight, but these variations are correlated with variations in pitch. It's a single note in the sense that it's always a C; not necessarily always the same octave.

> horns [...] can only play one note

A piece in bugle scale doesn't sound like one note to an average listener, nor does playing such an instrument feel like staying on one note. I'd rather compare this to a didgeridoo than a horn.

But if I concede that we don't need to adhere to lower grade music theory and that the performer will not use advanced techniques that can alter pitch without the use of a slide or valve, what argument could be made to support the "one note" claim?

To clarify what I'm looking for, here's an example of such an argument (but I don't know how much, if at all, it applies to actual fixed-length horn instruments): If the exact frequencies of a note's overtones deviate from a pure harmonic series, one could make a distinction between pitch-shifting a note and varying the timbre. I.e. playing the next note above the instrument's fundamental pitch doesn't multiply the individual frequencies by a constant factor, but repeats the exact frequencies of the fundamental's overtones, thus reordering the frequency ratios between adjacent overtones.

No (nontrivial) additive combination of Cs is also an additive combination of Ds (or C#s or Bs or ...). You'd need something nonlinear like multiplicative combinations, effectively a C amplitude-modulated by another C, in order to get non-C results.

Here's another one, built with Scratch. https://www.youtube.com/watch?v=Cx96CbjUZbA

My favorite demonstration of this has to be the engine sound of the Batpod:


The first example of this I can remember was the endless stairs music from Super Mario 64.

i think it is worth to mention glenn branca, he used this technique a lot. good example is "The Tone Row That Ruled the World"

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