Bit Width
When we talked about sampling, we made the point that the faster you sample, the better the quality. Fast is good, it gives us resolution (in time), just like in the old days when the faster your tape recorder (remember those? Maybe your great-great-grandmother had one?) moved, the more (horizontal) space it had to put the sound on the tape. But when you had fast tape recorders moving at 30 or 60 inches per second, you used up a lot of tape. The faster our moving storage, the more media it's gonna consume. While this may be bad ecologically, it's good sonically. Accuracy in recording demands space.
However, if we only have a limited amount of storage space, we need to do something about that space issue. One thing that eats up space, digitally (in the form of memory or disk space) is bits. The more bits you use, the more hard disk or CD ROM or memory size you need. That's also true with sampling rates. If we sample at high rates, we'll use up more space.
We could, in principle, use 64 bit numbers (capable of extraordinary detail) and sample at 100 kHz — big numbers, fast speeds. But our sounds, as digitally stored numbers, will be huge. Somehow we have to make some decisions balancing our need for accuracy and sonic quality against our space and storage limitations.
For example, suppose we only use the values 0, 1, 2, and 3 as sample values. This would mean that every sample measurement would be "rounded off" to one of these 4 values. On the one hand, this would probably be pretty inaccurate, but on the other hand, each sample would then be encoded using only a 2 bit number. Not too consumptive, and pretty simple technologically! Unfortunately, using only these 4 numbers would probably mean that sample values won't be distinguished all that much! I.e., most of our functions in the digital world will look pretty much alike! This is very low resolution data, and the audio ramification is that they would sound like... oh, we can't use that word in this book (it's a family webtext!). Think of the difference between, for example, 8 mm and 16 mm film — now pretend you were using 1 mm film! That's would a four bit sample size would be like.
So, while speed is important — the more "snapshots" we take of a continuous function, the more accurrately we can represent it in discrete form — there's another factor which seriously affects resolution, the resolution of the actual number system we use to store the data. In the example above, with only three numbers available (say, 0, 1, 2), every value we store has got to be one of those three numbers. That's bad. We'll basically be storing a bunch of simple square waves. We'll be turning highly differentiated, continous data into non-differentiated, overly discrete data.
An example of what a 3 bit sound file might look like (8 possible values). An example of what a 6 bit sound file might look like (64 possible values).
Figure.x
Figure.x
In computers, the way we describe numerical resolution is by the size, or number of bits, used for number storage and manipulation. The number of bits used to represent a number is referred to as its bit width. It's also called, just as often, bit depth. Bit width (or depth) and sample speed more or less completely describe the resolution and accuracy of our digital recording and synthesis system. Another way to think of it is as the word-length, in bits, of the binary data.
Common bit widths used for digital sound representation are 8, 16, 24 and 32 bits. As we said, more is better: 16 bits gives you much more accuracy than 8 bits, but at a cost of twice the storage space. (Note that they're all, except for 24, powers of 2. Of course you could think of 24 as halfway between 24 and 25, but we like to think of it as 24.584962500721156).
We’ll take a closer look at storage in a bit, but for now let's consider some standard number sizes.
4 bits
1 nibble
8 bits
1 byte (2 nibbles)
16 bits
1 word (2 bytes)
1024 bytes
1 kilobyte (K)
1000 K
1 megabyte (MB)
1000 MB
1 gigabyte (GB)
1000 GB
1 terabyte (TB)
TABLE .x Some convenient units for dealing with bits. If you just remember that 8 bits is a byte, you can pretty much figure out the rest.
You may notice that lower sampling rates make the sound "duller," or lacking in high frequencies. Lower bit widths make the sound, to use an imprecise word, "flatter" — small amplitude nuances (at the waveform level) cannot be heard as well, so its timbres tend to become more similar, and less defined.
sample rate (in Hz)
16 bits
8 bits
44100
22050
11025
5512.5
TABLE .x Some soundfiles at various bit-widths and sampling rates. Fast and wide are better (and more expensive in terms of technology, computer time, and computer storage). So the ideal format in the table above is 44100Hz at 16 bits (which is standard audio CD quality). Listen to the soundfiles and see if you can hear what effect sampling rate and bit width have on the sound.
Let's sum it up. What effect does bit-width have on the digital storage of sounds? Remember that the more bits we use, the more accurate our recording. But each time our accuracy increases, so do our storage requirements. Sometimes we don’t need to be that accurate — there are lots of options open to us when playing with digital sounds.