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What Atomic Clocks Can Teach You About Bit Depth

What if I told you that you had exactly 24 hours to make build a clock more accurate than a caseium timepiece?  Well, you’d probably reach into your drawer and pull out your laser-suspended strontium clock right out!

Right?

Well, if you don’t know (as I didn’t) – our modern “atomic” clocks are measured in their precision by the rate at which a given atom resonates.  This “sampling period” idea goes back all the way to sundials, which repeated it’s period once per day.  Most clocks that you know would either use quartz (10,000 oscillations a second) or caseium (9 billion oscillations a second).

But, the most precise timepiece in the world was built around 2005 by Hidetoshi Katori and his colleages at the University of Tokyo using an atom of strontium – which had previously been impossible to utilize despite it’s 429,228,004,229,952 per second oscillation rate.  Katori and crew solved the problem by building a multi-laser contraption by which the lasers create standing waves such that a few strontium atoms can be held gently like an egg inside of an egg carton – and then measured.

Now, while you might not be about the insane precision of a laser-suspended strontium clock, being an audio professional you certainly do care about mathematical precision. Without it, you wouldn’t have your glorius 24-bit sounds that you have today!  So let’s look into what bit depth actually means for digital audio more today, and explain a smidge more about why you are indeed a precise mathematician.

What is bit depth, anyway?

Previously, we talked about how all audio inside of a computer is just sets of numbers with a value between 1 and -1.  You probably know also know that computers store information in “bits” or, binary digits (either a 0 or a 1).

In binary math, every number that we use in Decimal math or “Base-10” (ie: the regular number counting system you use every day) has to get represented by a series of 0’s and 1’s.  So the number 4 in binary is 100 and the number 10 is 1010.  Eventually, the more accurate the number, the more 0’s or 1’s are required (and therefore more computer memory, too).

You may remember from grade school that between the numbers 1 and -1 are actually an infinite possibility of numbers.  This allows us for plenty of gradation in audio samples betwen these few numbers alone.  But what happens when we try and represent .3 in binary?  Well, .3 in binary is .01001100110011001101 – that’s a number that takes 20 bits to represent accurately!

Holy smokes, see?  You do care about precision after all!

Why does bit depth matter?

From that last example, I hope you’re freaking out a little bit.  If the number .3 can be represented in your audio, but you’re only using 16-bit sound, you must not be getting accurate sound – right?!

Well, yes and no.

As you already know, the sampling rate of a signal means that the signal is more accurate the more often it’s sampled.  96k recordings simply store more information than 48k recordings and therefore are more accurate.  A similar thing can be said with bit depth.  The greater the bit depth (like sample rate) the more information can be stored and the more dynamic range you can get in your recordings.

But what’s actually happening when we reduce bit depth?

Well, you may be familiar with the term “quantization” if you’ve ever programmed a beat before.  When some beats are off the grid, you can quantize them onto the grid – effectively taking somewhat imprecise beats and locking them into a precision timeframe.

The exact same process occurs when we’re talking about bit depth and representing number values.  If you’re representing a number like .3 inside of a 16-bit or 8-bit environment, the number will be “quantized” or perhaps “rounded” to the closest, most accurate number that can be represented by said bit depth.

Imagine you took your drum grid, turned it 90 degress, and only gave yourself 8 beats to work with.  Now try and draw a sine wave using only those 8 positions.  Congratulations, you just drew an 8-bit bitcrushed sine wave!

“But Adaaam!” you say, “I hate math!  I can’t possibly be a mathematician!”

Ah yes, but all great sound designers are also super closeted incredible mathemeticians and programmers.  It may take years, but I promise to prove this to you over time.  And now you really understand how bit depth is integral to your process and you just created your first bitcrusher.

How cool is that?!

So what did you just learn?

  • Bit depth actually means the amount of 0’s and 1’s it takes to represent a Decimal or “Base-10” number
  • The more 0’s and 1’s, the more precise your audio signal (and the greater dynamics
  • When the bit dept isn’t large enough, a signal is effectively quanitized (like drums – and this is okay!)
  • You do indeed care about precision and you are a mathematician

So next time you think “eh, close enough”

Remember that while you may not be suspending strontium atoms with a multi-laser array of standing waves, you’re pretty close.  Your math skills can bitcrush the crap out of some sick drum samples, after all!

I visualize these articles, by the way

If you have trouble wrapping your mind around the digital audio concepts I’m sharing, I visualize these articles on Instagram in carousels every week.  So, if you find yourself cross-eyed and not really understanding that sweet bitcrusher metaphor from earlier, hop on over to my Instagram and see it visualized!

I want to make these concepts easier for you to understand and really demystify the concepts of audio-inside-computers for you – so I’m going to take every opportunity I can get.  As always, I’d love your feedback – so I’d love it reply to this or leave a comment.

 


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