As we explored last week, sound is pressure variations in the air and that's continually variable. It's not discrete steps, but constant. The computer can't understand that kind of information. Only thing the computer can deal with is strings of numbers. Things represented in 1 and 0s, what we call binary information. So, there's a process to go from the continually variable sound into the stream of ones and zeros. And that process is called a sampling process which we talked briefly about before. But I'd like to go into a little more depth here. And before we even get to sampling I want to talk about binary information. You're going to find that so much of what you deal with and so many of the numbers you see when dealing with music Production is really based on this kind of information. So, binary information is based primarily on the bit. And a bit is a single, kind of, memory location, and everything comes down to bits. In a single bit, is a 1 or a 0 and that's all you have. And every number is collections of those ones and zeros. So the number of bits, determines the maximum number of states, or the biggest number that you can represent. If we have a single bit, we can represent two things, on or off. Maybe heads or tails on a coin. or on or off of a switch or a number from 0 to 1. If we want to represent larger numbers, we have to start collecting bits into words. And a word is a, a collection of bits. And very often, in the computer, we make a standardized kind of collection. You'll have MIDI data, for instance, uses, commonly uses seven bit words. Or if we're dealing with digital audio, we use 16 bit words. So it's important to know kind of how many values you can represent with a specific number of bits. Or with a specific word length, how many bits using a, in a particular word. If I have a one bit word it's going to be two values. If I have a two bit word we can actually represent four values. And it's really just all the permutations of ones and zeroes with that many bits. So if I have a two bit word, we have values of zero, zero, zero, one, one zero or one one, so we can represent four things. So if I wanted to represent the seasons of the year, I could use a two bit word and get Spring, Summer, Fall, and Winter no problem out of that. But if I wanted to represent something larger, I would need a longer word length. Now, it's good to know how to kind of know with numbers how many bits, what's the largest number you can represent. And it's always two to the power of the word length is going to give you the number of, numbers, the value that you can represent. So take it on yourself, let's do a little quiz here. What can you get, how many values can you represent, if you have a 2 bit word? What about a four bit word? Seven bit? Eight bit? 16 bit and 24? You're going to see that every time you add a bit, you actually double the number of values. And it gets very large very quickly. Now when we're representing sound in digital audio. You're going to find that there's a couple standards, CD standard is a 16 bit word. And when we start measuring sound to create, to, to create digital audio, we're going to find that we make many, many measurements very fast. And each one of those measurements has a specific word length. it's also known as the bit depth, but I like the term word length better because words have length. bits don't really have depth, do they? So CD standard, is 16 bits. So that means every we measure sound, we're using a 16 bit word. And that really is a great number. We can represent, I mean everything you hear on a CD, is done in that quality but in the studio we tend to use a higher word length. And maybe 24 bit would be a great setting for when you're recording. And what that gives you is a wider dynamic range, so we're going to find that the two,two,two really important parameters in digital audio. What we're talking about right now is word length is related to amplitude and the one we're about to talk about is the sampling rate and that will be related to frequency. So, word length, the longer the word length, so if I have 24 bit word length I have a wider dynamic range. And that is going to really, it's not going to be that perceptible, but what it does allow you to do is not record at such a high value. And we noticed that when we're recording we had to set our input gain very carefully. And we wanted to get as loud as possible without clipping without ever distorting. Well if we're recording at 24bit, we can actually record a little bit quieter and still get a good recording. And that's the benefit because you're not going to be so close to distorting as you're recording. So I really recommend when you are recording, record at 24 bit and you might want to take a moment to go into you DAW or into your audio interface preferences. Or even look for the switch on the outside of your audio interface to see just how you can convert between or how you can set the interface with the DAW to work in 24 bit mode. It's an important characteristic, an important thing you want to decide before you start. whenever you're working with these digital audio principles, you want to make sure you set them once, and then use them throughout our project. There can be small issues if you do change these settings in the middle of a project. So you want to create kind of a standard for yourself. So, the word length is going to control your dynamic range, how you know, and we also call it the resolution of the recording that you're going to have in your DAW. And that's related to amplitude. The other digital audio property we're going to be dealing with is the sampling rate. So like we said before, when we're converting from analog to digital, we're making many, many measurements per second. And each one of those measurements has a specific word length, which we just talked about. But how often we do the measurements is known as the sampling rate. And that has to happen very fast and on a perfect clock, right, over and over very carefully. And the sampling rate has to happen actually, we, we have to measure over 40,000 times per second to be able to accurately represent the continuously variable signals in the air as a digital representation. So it has to happen very fast and very accurately. And there are many settings we can have here and there are different settings for that sampling rate. But I'd like to just talk about why we would choose a specific sampling rate and the fact is, the higher the sampling rate the higher frequency that can be represented accurately in the digital domain. And this frequency that, that can be represented accurately is known as the Nyquist frequency, but really is just half your sampling rate. So if I look at a sampling rate of say 44,100 hertz we can accurately represent Half of that in the digital domain and that will be 22,050 hertz. If we think back to the human hearing range, we said that the highest thing a human can hear and that's even kind of an extreme is 20,000 hertz. So the CD standard sampling rate of 44,100 hertz can accurately represent everything we can hear as human beings. Which is why we chose it for this CD. Now there are some benefits to go to a little higher sampling rate. In working with video, and working with with videographers you find that they have a standard setting of 48,000 hertz. Now I don't think the, the difference in sound is very audible, I don't think you can really hear the difference very much, but it does make it easier to work with a wide variety of people. So I would suggest you actually use the higher settings than we have in a CD. And that I would say a 24 bit recording or 24 bit word length is a good idea, and I would switch over to 48000 hertz sample rate. I'd like to take a moment to demonstrate some of these digital audio principles. I have here an audio file that was recorded at 48,000 hertz. So the sampling frequency was 48,000 hertz. Its a 4 second WAV file, and what I have recorded in it is a sine wave playing a 500 hertz tone. Let's hear the wave form. [SOUND]. If I zoom way in, you'll see it has a sine wave shape, a very smooth kind of shape. In the sonogram display we have a single line at 500 hertz, and in the spectrum analyzer, we had a single peak at 500 hertz. A sine wave is a special type of wave form because it's energy at a single frequency. We said earlier that most musical sounds are energy at a fundamental frequency and then they have partials or harmonics above that. And we saw that with the sonogram and spectral analysis of my voice earlier. A sign wave is special because its energy at a single frequency; you can think of it as only a fundamental tone. Now, we said earlier, that this is recorded at a 48,000 hertz sampling rate. And if I zoom way in we'll actually see I have the sine wave. And if I zoom further in we can see the individual points that are those individual measurements of digital audio. So, when I play back this sine wave at 48,000 hertz, it's going to play each one of those at a 48,000th of a second. So we hear one sample and then a 48,000th of a second later, we hear the next sample. Then a 48,000th of a second later, we hear the next sample. What happens if I play this back at a different sampling rate? Well, let me try it. The, the sampling rate originally is forty-eight thousand hertz. I'll play it back at 96,000 Hertz. Now, let's hear it. [SOUND]. Do you notice what's different? Now we see a peek at 1k, 1,000 hertz. And we have our fundamental frequency line here at 1,000 hertz. We also see that the wave form is now half the length. It was four seconds before, and now it's at two seconds. So playing something back at a different sampling rate, is like speeding up or slowing down a, a record in a turn table. In that if I speed it up twice as fast, from 48,000 to 96,000. And if I speed it up twice as fast we're going to have half the length, and it's going to be double the frequency, or an octave higher. Now, I point this out because sometimes you get errors like this. So this is the original 500 hertz tone. [SOUND] . Playing back at a 48000 hertz sample rate. What if I was to change this a little bit to put it at 44100? [SOUND] . It's a little bit out of tune. And it is a little bit longer. So sometimes, when working with digital audio, you'll have a sample rate mismatch, where something's played back at the wrong sample rate. And it sounds as if a record was played a little faster or a little slower. Or a lot faster or a lot slower, depending how big the mismatch is. So, something to be aware of, and to watch out for. And also something that you might want to play with creatively at some point if you want to speed something up or slow something down drastically. Now the next thing I would like to point out is just how good we are at hearing individual samples. I'm going to zoom in around two seconds here. Quite a bit. To the point where we see the individual samples. Now rarely do you need to adjust the level of an individual sample but sometimes for corrrective purposes if there's a digitial glich. you do want to go and edit individual samples and this DAW has the ability to do that. So I will grab and just move one of these samples in both left and right, just a little bit. So you see, I'm just changing a single sample. Remember there are 48 thousand of these per second right, so it's a very very tiny slice of time actually a 40th thousandth of a second. And what I find amazing is how obvious it is when we hear that. That little mismatch, that tiny little moment, is clearly audible. Let's hear. [SOUND]. It's kind of hard to hear in this, see in this spectrum slate, but there's a, a thin blue line there. Right here's the thin blue line, that's that click. And I sure heard it. Let's hear it again. [SOUND]. That high frequency click, that was that one sample out. So, even a single sample can have a dramatic impact on your audio and the quality of your audio. It's really nice to know what these kind of digital glitches are so you can identify when you hear a problem. But it's also really important to know just how specific and how perfect that audio has to be. It has to come out exactly in time, 48,000 times per second, and those samples have to be perfect every time. If you think about it, that's actually a lot of computational power that needs to happen in the computer. To make sure each one of those samples goes out perfectly 48,000 times per second. Because even if just one of them is wrong, it's going to be an audible click for the listener.
