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Zero Crossing

The A-Zed of Audio

Set of allen keysStep 1: Attach metal bracket to wooden frame using provided screws.

Step 2: Fasten screws and bracket.

Step 3: Attach lower support to table legs using "C" brackets.

Step 6: Fasten all screws from Step 5 using included Allen Key.

Step 5? Where's Step 5?? What happened to Step 4?!

You find yourself building a piece of furniture and halfway through you realize that your instruction booklet is missing a page. You’re left hanging; there’s no obvious next step and you’re at a loss of what to do. Your cursing starts picking up speed and hopefully – for the sake of your new furniture and for the people walking on the sidewalk below – your half-assembled table is too heavy for you to pick up and throw out the window.

The scene probably hits close to home because we all know how infuriating this is. In a strange way there’s a lot of similarity with digital audio that has been edited without looking for a zero crossing.

Let’s back up here. 

Physical sound is the back-and-forth movement of air molecules, electrical “sound” is composed of positive-and-negative charges, and digital “sound” is a series of 0s and 1s. Sound sounds pretty simple. All that your sound system (or headphones, or bluetooth speaker) receives is a set of instructions from this code saying, “Move forward now! Move backward! Move 1/3 of the way forward and then the full way back!”

John Coltrane playing saxophoneIf all is going well, when you sit in front of your speakers you can’t distinguish between what you’re hearing and say, John Coltrane’s saxophone. But when things start going awry is when it becomes most obvious that Mr. Coltrane hasn’t been cryogenically frozen, shrunk, and stored inside your iPhone only to be thawed and woken every time you hit play. When the instructions come to a sudden end strange things happen, even by jazz standards.

If we have audio with a sample rate of 48 kHz, your speakers are being given 48000 instructions every second commanding them where to be. What we pay for in quality headphones or loudspeakers is the ability to carry out these instructions with extremely high precision (or, we pay for coloured plastic and and endorsement by a semi-retired rapper). Now what happens if those speaker instructions abruptly end?

When we’re editing audio this happens, and it happens a lot. Maybe it’s a voiceover and the actor stumbled over a word which you want to remove. You go in and cut out the awkward word, and paste the two good pieces back together. Brilliant.

You’ve likely just created the audio equivalent of a burr, and it’ll drive you mad. At least the little clicking sound at your edit point should drive you mad. What happened is that the speaker may have been given instructions to be at its maximum forward position and then once the instructions suddenly cut off the speaker needs to jump to its resting position 1/48000th of a second later, but this is impossible.

Standing audio speaker setFortunately, there’s a way around this whole problem and it lies at the zero crossing. The zero crossing is the point at which silence exists, or to put it differently, it’s the instant when the speaker diaphragm passes through its resting point as its pushing motion turns into pulling motion. In the physical world we could say it’s like the apex of a ball thrown up in the air – yet in the physical world that exact apex can forever be sliced smaller and smaller and if you really look for it you end up in some sort of situation like Zeno’s paradox where the slice can always be cut in half and then you conclude it doesn’t actually exist.

In the digital realm the slice actually does exist because the infinite number of points on which Zeno made his fortune have been rounded off to 1/44100th- or 1/48000th-, or 1/96000th of a second depending what sample rate we’re using. If we make our edit right at the point when the signal is at zero, it’s like losing that page of our furniture instructions that had all those useless cautions about flammability and suffocation and warranty registration. In other words, your instructions are missing at a perfect place and you don’t curse at all. Likewise, audio cut at a zero crossing should be clean and click-free.

The interesting thing about the click is that it ties back to what we discussed earlier on when we considered the glitch. If all of our John Coltrane or Teletubbies theme song recordings exist within the digital system, the click is outside the content – depending on your perspective it’s either a failure or a charm of the code that stores that content. As tiny as these clicks are, they’re incredibly bothersome. 

Marshall stackFifty years ago when Jimi Hendrix et al. were experimenting with distortion on their electric guitars, there were lots of folks who were turned off, even offended. The guitar was meant to play melodies and chords and this gritty awful sound was something outside the guitar. It was a noise from the container, much like code contains the content of our recordings. Part of Hendrix’s genius was expanding his scope of what music was, and instead of rejecting this sound he explored how he could manipulate it.

Living in 2015, it’s impossible to understand how a distorted electric guitar could ever have this power when bands like Green Day put together Broadway musicals about rock. All these years later, Jimi Hendrix and his distorted guitar have been nearly neutered of their power.

As with all power, it never dies; it moves. The click has some of that power and you can experience it in that moment of hearing one and feeling that feeling it comes with. That feeling is the spirit of experimenting in sound; it takes us by surprise and offers more than just a pleasant walk down memory lane.

As with distorted guitars, not everyone is so excited by clicks and fortunately there’s a simple method to eliminate them: the fade. Remember that the zero crossing is the same point at which silence occurs. That means that if we create silence, we’re strong-arming the speaker diaphragm back to the zero point regardless of where it was supposed to be. Once the audio is at the zero crossing we can slice and dice our audio until we’re blue in the face and live in a clean and click-free world.

Sanding the edge of a piece of woodThe fades we use as sandpaper on our cut edges can be absolutely tiny. If our samples are 1/48000th of a second, we really only need this fade to be a few samples long and it’ll accomplish the task of getting us back to zero so we can make our cut cleanly.

Stereo recordings are a very good candidate for fades because they have two separate channels which probably have few zero crossings in exactly the same place. Using a fade overcomes this issue because it forces everything to go back to zero even if the left and right signals aren’t lined up.

As much as some of us like to live in experimental worlds they can only work if we know how to do things the ordinary way and we’re looking for alternatives. When it comes to furniture, we’re usually looking for the ordinary way and if some avant-garde IKEA popped up who sold items with randomly missing pieces it’d be hard to imagine it had lineups on Saturday mornings for its undercooked/overcooked/rightly-cooked cinnamon-or-something-else buns. 

With audio there’s a world of interest we can find in clicks and glitches but the assumption is that you know how to do it cleanly and now you’re exploring the farther reaches of what might be possible. Making clumsy audio recordings and calling them experimental would fly about as much as if you buy a cabinet from IKEA that turns out to be half-couch-half-table and when you try to return it the clerk tells you it’s a piece of experimental furniture. In that case, it’s important to get back to basics and just like with counting, zero is a great place to begin.


Jordan Mandel is a Creative Media Instructor at the UW Stratford Campus and writes for this blog regularly. His hobbies include Braille typography, cable management, and glass blowing. More of his work can be found at jordanmandel.com/blog, which is home to the award-winning satire rag, The Outa Times.

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