Apple Logic Pro /LogicExpress Discussion

Okay, so here is the deal with bits.  A bit can be a 0 or a 1.  If you had a 1 bit audio interface, it could either be on or off at any given moment.  Now, you could still do something with that.  I mean, we all know such an interface as the square wave oscillator, right?  It's off or on.  The other factor, the sampling rate, gives you the ability to turn it on or off really fast, thus creating various frequencies and so on.  But you can't make a lot of sounds with a square wave.

So if you add a second bit, you get a 0 or a 1 followed by another 0 or 1.  You can make the numbers 00, 01, 10 and 11.  That's four settings.  With that you can capture a little more complex of a sound, you have a few more subtleties.  Your interface can be either full on, pretty high, pretty low, or off, and it can vary those at the sampling rate.  So instead of just being able to make square and pulse waves you can now make a whole bunch of different waves, including extremely crude sines, triangles, etc., as well as sampled or recorded sounds with some more veracity.  But try to imagine drawing a sine wave with only four levels -- it still won't be that accurate a reproduction.  

The number of possible values for each bit depth is easy to figure out -- it doubles each time:

1 bit: 2 values
2 bit: 4 values
3 bit: 8 values
4 bit: 16 values
5 bit: 32 values
6 bit: 64 values
7 bit: 128 values
8 bit: 256 values
9 bit: 512 values
10 bit: 1024 values
11 bit: 2048 values
12 bit: 4096 values
13 bit: 8192 values
12 bit: 16384 values
13 bit: 32768 values
14 bit: 65536 values
15 bit: 131072 values
16 bit: 262144 values

So once you get to 16 bits, you are effectively drawing your sound wave with 262,144 possible values for its height at any given point.  You can draw curves with extreme subtleties to them with that kind of accuracy, and at that point we can more or less not hear the difference anymore between the real thing and our stair-stepped approximation, for most people. 

So why ever use more than 16 bits, especially if you master to CD, which is a 16 bit medium? The answer is that you sometimes process sounds in ways that make the teeny tiny bumps more apparent.

Suppose you've recorded a wave in 3 bits, so it has 8 possible values.  And let's suppose that wave is a straight diagonal line.  Your values look something like this:

1,2,3,4,5,6,7,8

That makes an okay line, right?  Right.  (Well, assume it is for the purposes of our discussion.) I mean, you have a "stair height" of at most 1 unit, and we'll suppose that looks pretty good.

However, suppose the line you were recording were half as loud.  Your values would look like this:

1,1,2,2,3,3,4,4

Still the stair stepping is about the same, one unit at a time.

Now you normalize it.  Do you wind up with our original line above?  No.  The computer says that the maximum value was half as loud as the maximum possible loudness, so it will double every value.  Now your line looks like this:

2,2,4,4,6,6,8,8

The stair steps are twice as apparent now. The volume jumps by 2 each time it changes. Also, we're only using 4 of our 8 possible values.  It's as if our recording was made with 2 bits instead of 3.

Now think how many times you cleanse, fold and manipulate your audio in a given project.  If you're like me, you run it through the wringer and back.  Every manipulation stretches and mutates the resolution of your recording.  The more possible values, the more resolution your data had, at the outset of the process, the more data you're likely to be left with at the end.

This is exactly why many good instruments will have 16 bit outputs but perform their internal processing at 24 or 48 bits.  And that's why, if you do a lot of processing, you can benefit from recording or processing at a higher rate and then dithering down to the target format at the final mastering stage. 

-- 
Irfon-Kim Ahmad
http://www.ramp-music.net

On 2010-09-16, at 11:48 PM, brianmc7@... wrote:

> From what I've been told more bits equals more dynamic range???????????
> 
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