[MUSIC] In the last lecture, we learned how to identify and construct triads. We defined a triad as a collection of three notes stacked a third apart. The lowest note is called the root, the middle note is called the third, since it's a third above the bass, and the top note is the fifth. No matter what octave they occur in, or where in relationship to the other notes of the triad, these notes are always called root, third, and fifth. Here are some examples of triads. Notice that two of them have four notes. But in each of them, a note is repeated, which means that there are only three different notes. They're still triads. This triad has the root as the lowest note as expected. These triads have the third as the lowest note and this one has the fifth as the lowest note. The lowest note of a chord is the most important one. It's the one that the listener hears most distinctly. Although the triad's name doesn't change when the third or the fifth is on the bottom, all of these are C triads, we say that the inversion changes. So here's a definition. When a triad has the third or fifth as the bottom note, the triad is inverted, regardless of the order of the notes above it. When the root is the lowest note, the triad is in root position. When the third of the triad is the lowest note, the triad is in first inversion. We can understand the term inversion by seeing the root as having been moved up and octave, as when we were inverting intervals by moving the lower note up an octave. Notice that the order and doubling of the upper notes does not matter for inversion. Inversion is determined by the lowest or base note. So both of these are first inversion triads because E is the lowest note, which is the third of the C, E, G triad. Here's another definition. The lowest note of a sounding triad is the base not, regardless of which note of the triad it is. In root position, the base note is the root. In first inversion, the bass note is the third, the root is one of the upper notes. When the fifth of the triad is the bass note, the triad is in second inversion. Here are ten triads. Let's identify the roots and positions of each. Here's the first one. We see the B flat is the lowest note, and if we have memorized all the possible triads, we can quickly say, B, D, F, to see if in fact those are the notes. And we see, in fact, there's an F and there's a D, so, yes, this is in root position. B, D, F, B flat, D, F are the notes. So the root is B flat and the position is root position. Here's the second one. We look at the bottom note, we said ourselves A, C, E. A is the bottom note, and in fact we see a C and we see an E. So, in fact, the root is the bottom note for this one also, it's in root position. For this one when we look at it, the bottom note is a G sharp, so we say G, B, D. And if we look up, we say no, there is no D. There's an E, though. So, if we try E, G, B, that works. There's a G and a B and an E, E, G, B. So, this is an E triad, where E is the root and the third is the lowest note, so it's in first inversion. How about this one? We have D as the lowest note, D, F, A, that doesn't work. There's a B up there, let's try B. B, D, F, that works. There is an F, there's a D, there's a B. And D, the third of the triad, is the lowest note. So, the root is B and the position is 1st Inversion. Here's another one. You see, C is the bottom note, so we'll try C, E, G, note there's an F and an A up there. So let's try F. F, A, C. Those work. F, and an A, and a C. So it's some sort of an F triad, an F, A, C. C is the lowest note, the fifth of the chord, so therefore the root is F and the position is 2nd Inversion. Here's one more. See, E flat is the bottom note, so try E, G, B. Yep, that works, there's a G and there's a B flat. So E flat is the root, and this is in root position. How about this one? We see an A sharp, so let's try A, C, E. Yes, indeed, there's a C, there's an E. So this one has the root as the lowest note, and it's in root position. So the root is A sharp and it's in root position. Here's one. B flat, B, D, F. Nope, there's an E and a G, so that doesn't work. Let's try the E, E, G, B, those work, there's a G, there's a B. And the fifth is the lowest note, E, G, B, so therefore the root is E flat, the position is 2nd Inversion. Two more to go. How about this one? F, A, C, that doesn't work. So let's try the next one up, D, D, F, A. Yeah, there's a D, there's an F, there's an A. So the root is D and the position is 1st Inversion, because F sharp is the third of the chord. And finally, here's a low G. Let's try G, B, D. Those all work, there's the B there's the D. So this is in root position, the root is the lowest note and it's G. So the root is G, the position is root position. So, in this lecture, we learned about inversions of triads. I showed that the base note, that is the lowest sounding note of the triad, determines the position of the triad. If the root is the base note, the triad is in root position. If the third of the triad is the base note, the triad is in first inversion. And if the fifth of the triad is the lowest note, the triad is in second inversion. In the next lecture, I'll show you the three common types of triads, plus a fourth type, that is quite a bit rarer. [MUSIC]
