Hi everyone; welcome back! I'm still Seth Monahan, lifelong music theory geek, and this is the fourth in my series of videos about the basics of classical harmony and counterpoint. In this video we're going to master the topic of INTERVALS. Now what is an interval? An interval is simply the distance between two pitches. This whole lesson is going to be about measuring the distance between notes, as quickly and accurately as possible. But before we get into anything too specific, we want to make a few broad distinctions. The first has to do with how intervals unfold in time. Because on the one hand we have "melodic" intervals—that's between two notes that sound in succession (say, G going to D.) And on the other hand, we have "harmonic" intervals which are two notes sounded together. So here's the same notes played at the same time. These are sometimes called "linear" and "vertical" intervals, based on the way they look on the page: a linear interval unfolds from left to right, and with a harmonic one, we see them stacked on the page, on top of each other. Now the good news is that, regardless of whether an interval is melodic or harmonic, they're all measured the same way. One other important distinction to make is between "simple" intervals, which are an octave in size or smaller, and "compound" intervals, which are larger than an octave. For the most part, in this video we're going to deal with simple intervals—the logic being that we can often think of compound intervals as some simple interval *plus* one or more octaves. So to give you a concrete example, let's say I give you this large interval G up to a high D, clearly bigger than an octave, clearly a compound interva. We're gonna treat this as roughly equivalent to G to D in its simple form, falling within one octave. Which is to say, we're gonna think of this big G to D as a simple G to D whose top note was sort of "bumped up" an octave. And the reason this works is that most of the things we would say about the small G to D interval—how constant or dissonant it is, for instance—will also be true about the large one as well. And of course by talking about simple intervals, we save ourselves the trouble of talking about the many thousands of intervals that occur on the piano keyboard. Now we're just talking about the intervals that occur within the one octave. It's a much more manageable task. So let's get to measuring intervals. When we measure an interval, we're gonna address two factors: the GENERIC size and the SPECIFIC size. All intervals have both. Generic size is the easier one; this is the number of slots on the staff the interval spans. In other words, this is the number of lines and spaces the interval covers. Here in treble staff are instances of all the generic sizes between a unison and an octave and again. I want to stress that the ONLY factor here is the number of lines and spaces. So generic sizes are not affected by, say, a change of clef. I don't need to change my labels on the intervals here if I change from treble to alto clef, or from alto to bass clef. Thirds are still thirds, fourths are still fourths, and so forth. Even more importantly, it doesn't change even if we add all kinds of wacky accidentals. If you look at the third here even though we have this crazy interval of C# to Ebb, as long as those two notes are on adjacent lines or adjacent spaces it's going to be *some* kind of third. Now, specific size is trickier. Specific size involves applying one of five adjectives to the generic name. And these five adjectives are: diminished, minor, perfect, major, and augmented. And this gets tricky specifically because no one generic size takes all five names there is. In other words, no generic size that can be diminished, or minor, or perfect, or major or augmented. Rather, we have to think of these in terms of two broad families. What I call "Family 1" includes unisons, fourths, fifths, and octaves. And Family 2 includes seconds, thirds, sixths and sevenths. And the way this works is that generic intervals from Family 1 can be diminished, perfect, or augmented. While those from Family 2 can be diminished minor, major, or augmented. So in addition to telling us what interval sizes are available, this also tells us which ones we'll never see. If you look at Family 1, for instance, fifths fall into Family 1; you will never encounter a "minor fifth." That's simply not possible. Just like in Family 2, none of these can be perfect. There are no "perfect sixths"; there are no "perfect sevenths." So now that we know which families use which specific sizes, let's see how specific sizes change as we change the size of intervals. So here's the G and D we heard earlier in the lesson. The generic size here is some sort of fifth; that's because they're on lines separated by one blank line. (This would be the same thing if they were on spaces that were separated by one space.) Generic size is a fifth. Specific size is perfect for now. (I'm just telling you that it's perfect, and you'll understand why in a few moments.) Let's also note that a perfect fifth is seven semitones wide. That'll let us track variations in size very precisely. Suppose I add a sharp to the top note. That's gonna make the interval bigger. So it's not going to be perfect anymore; it's gonna be some other descriptor, some other specific size. Since we've made the interval bigger, it's going from 7 to 8 semitones in width. It's a bigger interval now. Looking up to the diagram on the top, we see that perfect, when it becomes bigger, becomes augmented. So taking this perfect fifth, making it bigger by one semitone, we've made an augmented fifth. And the same thing would be true if, instead of sharpening the top note, we had flattened the bottom one. Flattening the bottom note makes the interval bigger; it goes from seven to eight semitones. Perfect becomes augmented. However: if we had put the flat on the *top* note instead, we wouldn't be making the interval bigger. We'd be making it smaller. We're bringing the ceiling down; the room gets more cramped. So instead of expanding it, we're contracting it, from 7 to 6 semitones. And if we look on our continuum at the top, perfect becomes diminished when it's made smaller. So this is an instance of a diminished fifth, which is the same thing we would've had if we had sharpened the bottom note: bring the floor up, the room gets more cramped. Perfect fifth becomes diminished. Now this is all well and good, but it presupposes we know what specific size we're dealing with. And we actually haven't done that yet. So how do we know what the specific size is? Well, one way to figure that out will be to count semitones. And if you wanted to go along that route, here's a chart that would let you do it. This has generic sizes along the left, the specific sizes down the middle, and then the semitone count. So let's say you came across something that was clearly a sixth: you counted it up; it was 8 semitones in size. You'd know you were dealing with a minor sixth. I don't advise doing this. Counting semitones is tedious and impractical—at least with intervals bigger than a second. If you're dealing with a half step or a whole step, maybe counting semitones is fine. But you need a better way; you can't be counting eleven semitones every time you see a major seventh. Thankfully, SCALES can make our lives easier on this account. Now, in this case we're gonna have different procedures for Family 1 generic sizes and Family 2 generic sizes. So let's say I'd give you some kind of fourth. it's E up to A. You know it's a fourth from the distance of the lines and spaces. But you don't know what specific size it is. With Family 1 generic sizes, you have to ask: "does the top note of the interval appear in the major and minor scales of the lower one?" So in other words, with this one, "does A appear in E major and E minor?" Now we've learned about scales; hopefully you can call those to mind fairly quickly. Here they are on screen: E major and E minor. In this case, the answer is "yes": A-natural definitely appears in E major and E minor. So if the answer is "yes," then the interval is perfect. What if the answer's "no"? Here we've got E and an A#. Hopefully you know that A# is not in either E major or E minor. So the answer's "no." You have to reckon the interval as a *modification* of a perfect interval. So looking at E and A#, you might think "OK—A# is not in the key of E major or E minor; but A is. So I'm dealing with E to A, which is a perfect fourth, but I've expanded it by one semitone by sharpening the top note— so perfect becomes augmented. Thus I'm looking at an augmented fourth." And you'd be right. But since we're talking about Family 1 intervals, I have to give you this one speed: tip anytime you're looking at a fourth or a fifth, if the accidentals are *matched,* you're dealing with a perfect interval. That's to say, if you're looking at a fourth or a fifth and *both* notes are sharp, both notes are flat, or both notes are natural, the interval is perfect...EXCEPT if the two notes are B and F. Those are the only exception. B and F require mixed accidentals to be perfect. Any other combination of notes making a fourth or a fifth? Matched accidentals means it's perfect. That'll save you a lot of time. So let's look at Family 2 generic sizes. Now here I've given you some sort of sixth; the distance in the lines and spaces tells us this is a sixth. What kind of sixth is it? We ask: "does the top note in the interval appear in the major or minor scale of the lower one?" Now here it's major OR minor; it matters which one it is. And I also want to point out on screen in red this doesn't work with seconds. This is only true of thirds, sixths, and sevenths. Sorry—it's just the way it is. So we're looking at some kind of sixth. Does the top note appear in the major or minor scales? The answer is yes, it does. In E minor we have the note C natural. So when you get a "yes": if it's in the major scale, it's a major interval; and if it's in the minor scale, it's a minor interval. So C is in the E natural minor scale—that means it's a minor sixth. And once again, if the answer is "no"—if for instance I gave you this E to Cb interval—hopefully you know fairly quickly Cb is not in E major and it's not an E minor. So once again we have to reckon the interval as a modification of some familiar minor or major interval. So in this case I'd give you E and Eb and you'd say "well E to C...I know C is in E minor, so Ee to C is a minor sixth. But by flattening the top note, we're making it smaller. Minor made smaller becomes diminished, so this is a diminished sixth." The last topic we want to deal with is inverting intervals. And what does it mean to "invert" an interva?l This simply means taking the bottom note and putting it on top, or vice versa. So here's Eb and G; it's a major third. (How do I know that? Because G is in the Eb major scale; it's a major third.) We can invert it by putting the Eb on top. So we've taken this...it inverts to this. And when we invert it, it becomes a minor sixth. And if we invert it again— put the G up on top or the Eb back beneath—we end up with the same interval we started with. How did I know that a major third inverts to a minor sixth? I didn't have to figure it out. There's actually a strict pattern. And there's a different set of rules for generic and specific sizes. So inverting an interval is a two-part process, following these patterns. On the left, specific size: any augmented interval becomes diminished when we invert it; any major interval becomes minor when it's inverted; and perfect intervals stay perfect. On the right-hand side: unisons will invert to become octaves; seconds invert to become sevenths; thirds invert to become sixths; and fifths invert to become fourths, and vice versa, of course. Now here, there's a very specific numerical pattern: all of the inversional pairs add to 9. So the arrows here all connect integers that add to 9: 1 + 8 is 9; 2 + 7 is 9; and so forth. And then you just let the chart do the work for you. Let's say I give you a minor 7th, G up to F. We want to invert it. I've marked "minor" and "7th" in our diagram, and we simply follow the paths. When we invert it, putting the F on the bottom, minor becomes majo,r seventh becomes second, and we have a major second. And we know we're right, because this always works! Let's try another one. I'll let you try this one on your own. Here is G to C#. It's an augmented 4th. I'm gonna invert it putting the G on top...what do we get? Pause the video and figure it out. Hopefully, using the diagram, you discovered that augmented fourths invert to become diminished fifths...and you'd be right. Now, there's a practical use for inverting intervals as well. If you get stuck with a big interval you can't identify—let's say you just don't know what this thing is...G up to F#...oh goodness— if you can't identify that, you can follow this process: you can invert it, so we're gonna put the G on top. Then you can ID it: it's a minor second. (Any big interval that you invert becomes a small interval, and small intervals are usually easy to recognize. There could be nothing easier to recognize an F# to G, because that's as close as notes can get together...it's a minor second I hope you see that at sight.) So then, once we've ID'd it, we RE invert it—we put that G back on the bottom—and we know using our chart that a minor second inverts to become a major seventh. So we figured out that the thing we started with is a major seventh. And you can do this any time you see an interval that's large—and which you can't figure out out—as long as it's a simple interval. This won't work with intervals bigger than an octave. You'll have to make them smaller than an octave and then do the same thing. So that concludes our study of intervals. With a little practice, you'll be able to spell, identify, and invert any interval you come across. Of course, here we've only dealt with two notes at once, which is a little artificial. Because in real music, you probably know that we often find three or more notes at once—often in groupings that form what we call chords. And that is indeed the next leg of our journey. Videos 5 through 7 are gonna introduce the basic features of the chords we find in classical harmony—starting with the most common chord type in western music, the TRIAD. So thanks for tuning in, and I hope to see you back for Video no. 5!