 Hi, we're now on Theory Lesson 7 for linear theories, and today's theory is going to take our last discussion on intervals a step further. Last week we discussed the general description of an interval, a second, a third, a fifth, that type of a general name of an interval, and now we're going to more accurately qualify those names of intervals. And today we're going to focus in on three particular intervals. We're going to focus in on the fourth, the fifth, and the octave. Okay, so let's go ahead and get started with this assignment. First of all, last week we said that we had the following intervals. We have one interval that I didn't really mention last week, and that's a unison. That's when we have the same note, like an A and the same A, that would be called a unison. But then we also have the others that we discussed last week. Seconds, thirds, fourths, fifths, sixths, sevenths, and octaves. Now I told you that this week we're going to focus in on three particularly. We're going to focus in on the fourth, the fifth, and the octave. Now the reason we're focusing in on these is these are known as perfect intervals. Now you might be curious why those are perfects and the others are not. And that's sort of a long description, but it's worth understanding that fourths, fifths, and octaves are known as perfect. The others are known as major or minor, and we'll get to that next week's lesson. And incidentally, the unison is a perfect as well. We just don't use it as much because it's theoretical. We're not going to use it all that much, but we will use fourths, fifths, and octaves a lot. So let's take a look at these and see if we can determine how they're designed. Let's start with an interval of an octave. This is kind of an easy one to get. An octave, and let me start by saying that all of these intervals grow from our good old major scale. So if we take this major scale, and remember that a major scale is whole, whole, half, whole, whole, whole, half. It seems like everything goes back to this. If we take this major scale, all of our perfect intervals grow from the major scale. So a perfect octave is the distance from the first to the eighth note in a major scale. Well, how do we measure distance? Well, we take a look at the half steps. So here we have two half steps, two, one, two, two, two, and one. And if we count those half steps and add them all up, two and two is four, five, six, seven, eight, nine, ten, eleven, twelve. A perfect octave is twelve half steps or twelve semitones. A half step is a semitone. So a perfect octave is twelve semitones. Let's do a perfect fourth. A perfect fourth is the distance from the first to the fourth note of the major scale. So two plus two plus one half step. So a perfect fourth is five semitones. And of course a perfect fifth is from the first to the fifth note of the major scale. Two plus two plus one plus two half steps, which gives us seven half steps or seven semitones. Now, that allows us to know exactly what the perfect fourth, the perfect fifth, and the perfect octave are. Now, I do want to go back now and take a look at these a little more specifically. So if I gave you two notes, let's do this. We'll give you the notes C to the note F. Now, the first thing that we would want to do in identifying this is take a look and say, okay, what's the interval from C to F? That's the first step of the process. So number one, we want to determine the interval. That is the general name, okay? So C, D, E, F, second, third, fourth. So from C to F we know is a fourth, but now we have to count the half steps from C to F to determine what kind of fourth it's going to be. So if we have our good old piano keyboard and we have a C here, C, D, E, and an F, and now we can count those half steps one, two, three, four, five. So the distance from C to F is five semitones and that tells me that it's going to be a perfect fourth, okay? A perfect fourth is five semitones. Now, let's take that a couple of steps further because, okay, if we have a perfect fourth, what other kinds of fourths do we have? Well, let me give you a couple of things here. A perfect fourth is five semitones. There are two other kinds of fourths. There's a diminished fourth that's spelled D-I-M-I-N-I-S-H-E-D. A diminished fourth is four semitones and there's an augmented fourth and it is six semitones. So let's take a look. We said that C to F is a perfect fourth and it was five semitones. How would we find a diminished fourth, some fourth that might not be five semitones? Well, if we had C sharp to F and we count those half steps, we would learn that C sharp to F is a diminished fourth. Similarly, if we had C to F sharp, we would learn that that's six semitones and it is an augmented fourth. So the first step is to determine the general name. Is it a fourth? Is it a fifth? And then we count the half steps after that. Okay? Let's take a look at the descriptions of fifths here. A perfect fifth we already said is seven semitones. So if a perfect fifth is seven semitones, what do you think a diminished fifth is? If you said six semitones, you're absolutely right. And an augmented fifth would be eight semitones. Okay? And we have a perfect octave which is twelve semitones or half steps. A diminished octave is eleven semitones and an augmented octave is thirteen semitones. Now, if you're really thinking here, you might realize that a diminished fifth is six semitones and we also said that an augmented fourth is six semitones. Well, how do we know which is which? Well, let me just show you here. If we have C to F sharp from a C to an F, C, D, E, F, we know that's a second, third, fourth. We know that's got to be some kind of a fourth. But if we had C to G flat, C, D, E, F, G, that has to be some kind of a fifth, that's a diminished fifth. That's an augmented fourth. C to F sharp is an augmented fourth. C to G flat is a diminished fifth. They are, they would sound exactly the same if we heard them, but they in theory are very, very different. One's a C to F interval and one's a C to G flat interval. Okay? Would sound exactly the same, however. Okay? Your assignment this week is to really dive into perfect intervals that is fourths, fifths and octaves. Now remember, when you're working with these intervals, you first determine the general name. Is it a fourth? Is it a fifth? Is it an octave? And then you start counting half steps. If I were to show you a fourth or a fifth or an octave on the staff, let's just do this. We've got a note A here and we've got another note here, an E. Now we know we've got an A to an E. Now what's the interval and what is the more specific qualifier? Well, we can look at that visually and go, okay, that's a fifth. So from A to E is a fifth, but now we have to take a look at that keyboard and say, okay, we have, make a quick keyboard here just so we can refer back to this. There's our A and there's our E. Now we have to count half steps from A to E. One, two, three, four, five, six, seven. A to E is seven half steps. That tells us that it's a perfect fifth. And that gets you going in the right direction. Now I want you to think about one more thing if you could. I want you to consider that those words augmented and diminished. If we augment something, we make it bigger. So if you take your perfect interval and make it bigger, then it's augmented. If we diminish something, we make it smaller. So we're actually closing in on it. We're making it smaller. So if we take a perfect interval and make it smaller, it will be diminished. Now, how does that come into play here? Well, think about this. If we have an interval, again, let's use our good old interval of A to E. And we said that that is a perfect fifth. Okay? Now how would we augment that interval or make it bigger? Well, there's two ways. We could either make the top note sharp. That makes the interval bigger. Or we could make the bottom note flat. That also makes it bigger. Okay? So watch out. You can't always think sharps create augmented intervals and flats create diminished intervals. So we're really expanding the interval when we're augmenting it. Similarly, if we have that same A to E and we want to diminish it or make it smaller, we could make the top note flat. That brings it in, makes that interval smaller from the top. Or we might make the bottom note sharp. And that makes the interval smaller. So be careful as you're determining that difference between perfect diminished and augmented intervals.