 Hi, and welcome to your instructional video for linear theory number 10. This lesson is on intervallic inversions. And up till now, we've worked really hard on getting all of your intervals correct and you can now identify intervals by their broad term, seconds, thirds, fourths, fifths, sevenths, and octaves. And they're more specific term, major or minor, perfect, augmented or diminished. And at this point, that should be pretty natural for you. You've had a lot of practice on that. And now we're going to take it one more step. There are, there's a term called inversions. And when you think of the term inversion, what are we doing when we invert something, but we're simply flipping it over. And that is the same idea with intervallic inversions as well. And there are some really good rules and sort of precepts that go along with intervallic inversions that make this really quite easy. So let's take a look at some of the specifics here. Now I'm going to give you a couple of rules, and I think it'll bring some ideas together for you. Let's take a look at a few intervals, and I'll show you what I'm talking about. If we have the interval of a perfect fifth, and we simply say we're going to take the bottom note, the C, and we're going to put it above the top note, the G. Here we had the interval of a perfect fifth from C to G. Now take a look from G to C, and you can quickly see that it's a fourth. And I'm going to tell you, you can count the half steps, but you're going to see that that's a perfect fourth. So rule number one, perfect fifths invert to perfect fourths all the time. So if you have an interval of a perfect fifth, it'll always invert to a perfect fourth. Let's show another example, and this will hopefully bring some of our other ideas together. I'm going to start on C again, because if we work in the key of C, it's easy. We just don't have to worry about any sharps or flats. Let's use the interval of a third from C to E is a major third. And we take that C, and we simply move it above the third. If you take a look at that, you can see very quickly from the distance that it inverts to a sixth. And I'm going to tell you really quickly that's a minor sixth, and you can certainly count the half steps and confirm that. So we now know that a minor third inverts, or excuse me, a major third inverts to a minor sixth. We're going to take a few rules from that in just a moment as well. We're going to do one other one. Let's use the concept. Let's use a how about a second? We'll start with a C. And let's make an augmented second from C to D sharp is an augmented second. And so we'll take that D sharp. And we'll move the C up here. And you're going to learn oops, I'm going to do this augmented second. And you're going to if you count those half steps from D sharp to C, you're going to see that that inverts to a diminished seventh, an augmented second inverts to a diminished seventh. So start to take a look at that. And I think you're going to begin to pull together a few really important precepts. Let's give them to you right now. In terms of the qualifiers, perfect intervals always invert to perfect intervals. Major or minor intervals always invert to major intervals and vice versa major intervals invert to minors and diminished intervals always invert to augmented intervals. These are hard and fast rules that you can take to the bank. Also, fourths always invert to fifths, thirds always invert to sixths, and seconds always invert to sevenths. And incidentally, unisons always invert to octaves, although you're not going to see that all that often. Okay, so makes things really easy. A major sixth, we can tell right away, we'll invert to a minor third. An augmented sixth would invert to a diminished third. And this is a rule it works all the time. So as we start doing inversions, if you can accurately identify an interval, a to c is a minor third, you can real quickly invert it and see that that's going to be a major sixth. And trust me, if you count the intervals, you will count the half steps, you will catch that and it always always works. We could do some examples, but I think at this point, you probably really get it. It always works. Incidentally, one other thing, this notion that perfect intervals invert to perfect intervals, kind of should start to clue you in on why they're called perfects. They're the only intervals that invert to another perfect majors, invert to minor, it's not the same, diminished invert to augmented, not the same. But these perfect intervals are special because they invert to other perfect intervals. So that ought to be a good clue for you as well. So go ahead and go to work, try to get these intervals taken care of. Once you've accurately identified the interval in front of you, then you will be able to very easily identify the inverted interval. If you take a look at your assignment, I just want to make sure that you read the instructions accurately on the assignment. If you go to the lesson 10 assignment, you're going to notice that the one section says to use the given note as the bottom pitch of the interval named and use it as the top note of the inversion. So you'll notice that you're in base clef. It gives you the interval perfect fourth, and then there's a line that give you a C. And so a perfect fourth above C would be would give you an F. And then you take that F and you use it now as the bottom note of the inversion. And P five perfect fifth is the inversion. And you could even count those half steps to make sure that you got the right answer. And that would be correct for the first one. The second one gives you diminished fifth, and then a line, and it starts on an E. So again, you're going to use the given note as the bottom pitch of the interval named. So E to B flat is a diminished fifth. And then we're going to take that B flat and move it to the bottom. And that should give you an augmented fourth. Okay. And that gets us where we want to go. This would be absolutely accurate for the second one as well. Go ahead and try the assignment. Good luck. And hopefully you get these intervallic inversions. I do want to say one last thing and that's that melodic inversions are a little bit of a different concept. So don't get confused between melodic inversions and intervallic inversions. We'll show you melodic inversions in a different video.