– Hi. In our first course on sight singing and sight reading, we tried to get the reading of pitch underway by simply almost singing and playing by numbers, thinking about which degree of the scale we might be dealing with, and getting an idea about moving in steps, in other words, just going from one note to one of its neighbouring notes, or by doing little skips, you know, going from one note, missing out the next note, and singing the next note, just so we could get some idea about reading the outline of the pitch and moving up and down in the right places, and getting some idea as to what these gaps between the notes might be about.
Whether you are going to be following this course with the intention of really learning to sight sing on its own, or whether you’re really interested in being able to sight read on an instrument, it’s really good if you can read accurately the intervals between notes. If you’re singing, if you can look at an interval between two notes and think, “I can hear what the next note is”, well, you’ll be a reliable sight singer. If you’re playing, if you can look at the interval and hear the next note in your head, then when you play that note you can feel confident about it, or if you play an incorrect note, you’ll immediately hear that something’s wrong and preferably, even be able to hear what’s wrong with it.
So I’m a great believer even if your sight reading on an instrument, that people should learn to sight sing so that you develop this ability to hear the next note. So we’re going to get into a little bit more detail now on how we read these intervals, the distance between one note and the next, and really begin to get to grips with what those intervals actually sound like. So we need to start with a little bit of theory so we can understand what’s going on here. So let’s just start with a stave. For the time being, we’ll work in the treble clef. And we might as well start with C as our lower note. So this is how intervals work. If I have a C followed by a D, then this is what we call a second, because we count C as number one, D as number two. If I have a C followed by an E, then this is a third, simply because we count C as number one, C, D, E, that’s a third. I’m sure you’re getting the idea very quickly here. If I go C up to F, that’s going to be a fourth, C, D, E, F, one, two, three, four. The thing to remember is whatever the lower note is, you must count the lower note as number one, otherwise you get the number wrong of the interval. Obviously going on from there, if I start with a C and this note, this is going to be a fifth, why is that? Because C, D, E, F, G, that’s my fifth. If I start with C and I go up to this note, this one’s going to be a sixth, C, D, E, F, G, A, there’s my sixth. If I start with C and I go up to a B, well, you can see that that will be a seventh. And if I start with C and go up to the next C, you might be tempted to call that an eighth. Technically speaking, it should be called an octave, because an octave is eight notes, oct, meaning eight. And we abbreviate that when we write it by simply writing 8ve. So, that’s how we determine the number of an interval, second, third, fourth, fifth, sixth, seventh, eighth, and between any pair of notes, you can calculate the interval. So what you do is you look at any pair of notes that you’ve got an interest in, and you take the lower note, you call the lower note number one, and you simply count up to the upper note to work out what the number of that interval is. You may also hear these terms, melodic and harmonic intervals, which all sounds terribly complicated. Actually it isn’t. If I play two notes together, then this is a harmonic interval, because it’s making harmony. But if I play this note followed by this note, or even the other way around, this note followed by this note, that is a melodic interval. I’ve got one note followed by the other note, so it’s making a melody. So if I look at this interval, I’ve got C at the bottom and E at the top, so it’s this one here isn’t it. So you can see it’s a third. If I play those two notes together, I call that a harmonic third. And if I play this note followed by this note, or this one followed by this one, I call that a melodic third. So that’s not as complicated as it sounds. If they sound together, it’s a harmonic interval. If they sound one after the other, it’s a melodic interval. So that’s dealt with that corner, and it’s dealt with the numbering of intervals, which is quite important to know about when it comes to actually singing these things. Okay, now let’s take this on a step because apart from knowing that something’s a third, or a fifth, or an octave, there’s also something else we need to know about, which is, well, what kind of third is it? What kind of sixth is it? What kind of octave is it? And that’s what I want to talk about next. We have basically two kinds of interval. One is called a perfect interval, and the other is called a major interval. Now, don’t worry too much if this doesn’t make sense at the moment, because it soon will. Now, take it from me, that the perfect intervals are the fourth, the fifth, and the octave. So when you’ve counted the distance between two notes in the way that we’ve just done, if you see that you’ve got an interval of a fourth, or a fifth, or an octave, you can start by thinking, well, this is basically a perfect interval. There are reasons why they’re called perfect intervals, but I’m not going to go into those at the moment because it’s just, to be honest, a bit of a distraction from what we’re trying to learn. Now, if intervals are not perfect, then they start life as major. So the major intervals are all the other things that are not perfect, so in other words, a second, a third, a sixth, and a seventh. So when you’re calculating what an interval is, the first job is to determine the number of the interval. So if I’ve got this one, for example, I’ve got C at the bottom and G at the top. I’m just going to count from C, one, two, three, four, five. So I know that C up to G is a fifth. Now, because it’s a fifth, I’m starting to think perfect. On the other hand, say I had C up to A, I would again count the number of the interval. One, two, three, four, five, six. And I would know then that that’s a sixth, and I would immediately be thinking, well, if it’s a sixth, I’m starting to think major. Okay, bear with me for a moment, because we’re now going to construct a little table that will make sense in the fullness of time. These signs that I’m doing now are not musical signs but mathematical signs. So that doesn’t mean crescendo, getting louder, as it would in piece of music, it means lesser than, greater than. So what this means is, if I take a perfect interval and I make it a semitone bigger, we’ll explain all this in due course, so don’t worry. If I take a perfect interval and I make it a semitone bigger, it becomes something called augmented. Now, that word is sort of quite handy, because if you augment something, you make it bigger. I was recently working with a choir and we needed to augment the choir in order to perform a particular piece. We made the choir bigger, we invited more singers. So when you make something bigger, it’s augmented. If you make a perfect interval a semitone smaller, it becomes diminished. And again, the clue’s in the word. If something diminishes, then it means it’s getting smaller. So perfect intervals are the fourth, the fifth, and the octave, and if you end up with one interval that’s a semitone bigger than a perfect interval, you call it an augmented interval. So it could be an augmented fourth, or an augmented fifth, or an augmented octave. If you have an interval that’s one semitone smaller than a perfect interval, then it could be a diminished fourth, a diminished fifth, or a diminished octave. Okay, now what about the major intervals? Well, it goes the same way over here. If I make a major interval a semitone bigger, it becomes augmented. So that’s just the same as it is for the perfect interval, so that’s useful isn’t it? However, if I make a major interval a semitone smaller, it becomes minor. So that’s the one to remember isn’t it? Perfect intervals never become minor, they’re either perfect, or they’re augmented, or they’re diminished. Major intervals could be major, they could be augmented, but if they get a semitone smaller than major intervals, they’re minor, and if they get a semitone smaller than minor, then they are diminished. Slightly squeezing that on the board, but you get the drift of what I’m talking about. Now, let’s see if we can put that to some practical use, because so far that may not be entirely clear. Let’s take an example of a perfect interval. If I give you this interval which is C, up to F, the first thing we do, remember, is to count the number from the bottom note to the top note, counting the bottom note as number one. So one, two, three, four. C, D, E, F. One, two, three, four. So I know that this interval is a fourth. If I play the notes together, it’s a harmonic fourth. If I play one note after the other, or this, I know it’s a melodic fourth. Now, because it’s a fourth, I’m thinking perfect. Now then, how do we use this table? This is where you have to know a little bit about keys because to work out exactly what an interval is called, the answer is to work in the major scale of the lower note. Now, it doesn’t matter which key the piece of music is in, don’t worry about that. Just think whatever the key of the piece of music is in this interval, C is the bottom note. Because C is my lower note, I’m going to work in C major. Now I’m working with this interval, C up to F, and I’ve already said that that’s a perfect fourth, so hopefully everybody’s happy about that. Now what we’re got to do next is to say, well, if I’m working in C major, because C is the lower note, and I know that this interval is a fourth, this is the question: What is the fourth note in the scale of C major? Well, here’s the scale of C major, no sharps, no flats. So, this means that F is the fourth note in the scale of C major. Because F is the fourth note in the scale of C major, this interval C up to F is a perfect fourth, okay? It’s perfect because F is in the major scale of C, the lower note. So C to F is a perfect fourth. Now, what about instead of it being C to F, what would happen if it were C to F-sharp? Now then, the number hasn’t changed has it, because it’s still some kind of C to some kind of F. So always work out the number first before you start thinking about all this stuff. And C, D, E, F we know to be a fourth. Doesn’t matter if it’s F-sharp or F anything else, it’s F something so it’s a fourth. But now I’m looking at this interval and I’m realising that it’s a semitone bigger than the perfect fourth. So C to F was the perfect fourth because F is the fourth note in the scale of C major. But now I’ve got C to F-sharp. You can see and hear that those two notes are now one semitone further apart than the perfect fourth. So one semitone bigger than a perfect fourth is going to be an augmented fourth. So hopefully you can see how this is starting to work. Let me take another example of this. Say I gave you these two notes, C up to A. First of all, let’s see if we can work out the number of the interval. So, starting with C as number one, One, two, three, four, five, six. So that’s a sixth. So I’m thinking major, because it’s a sixth. So I’m now working in the major scale of the lower note, and the lower note is C, so I’m thinking C major. Because I know that this is a sixth from C to A, I need to know what is the sixth note in C major? One, two, three, four, five, six. Well the sixth note is A. So in other words, C to A, this interval here, is a major sixth. Now then, what about if this interval changed and instead of being C to A, it was C to A-sharp? Now, don’t look at that and think, well, that could be B-flat. Don’t worry about that for now. For the time being, let’s call it A-sharp. So, C to A-sharp is still a sixth. C, D, E, F, G, A, it’s still six notes. Doesn’t matter if they’re sharps, or flats, or anything else. And we know that C to A is a major sixth, because A is the sixth note in the scale of C major. So of I’ve now got C to A-sharp, actually this major sixth has got one semitone bigger. The distance between those two notes has grown one semitone. Therefore, C to A-sharp is an augmented sixth. Okay, let’s go back to major sixth for a moment, the C to A. What would happen if instead of it being C to A, actually my interval was C to A-flat? Well, it’s still a sixth because it’s some kind of C to some kind of A, but can you see what’s happened now? There was my major sixth. Now, instead of C to A, I’m going C to A-flat. So this interval is now a semitone smaller. So if it’s a semitone smaller than a major sixth, it must be a minor sixth. Okay, now let’s take this a step further. This may seem a bit strange what I’m going to say now, but if I did this interval, which looks like C to G, but we’re not going to call it G. We’re going to call it A-double-flat, which may seem very strange, but sometimes you get double flats and double sharps in music. So if I’ve got C to A, then I know that that’s a major sixth now. I know that C to A-flat is a minor sixth. So C to A-double-flat must be a diminished sixth, okay? And the same will be, we haven’t done this one up here, but say this was a perfect fifth, I’ll start on a different bottom note this time. I’m starting on D and I’m going up to A. So let’s count that. D, E, F, G, A, so fifth, so we’re thinking perfect. So if I go D to A and D is my bottom note, I’ve now got to work in the scale of D major because D is the bottom note. Now, the scale of D major goes like this. I now know that A is the fifth note of the scale of D major. So D up to A must a perfect fifth, however, if it was D to A-flat, those two notes have got one step closer together, so it’s a smaller interval, it’s a diminished fifth. So, D to A-flat is a diminished fifth. In the same way that if D to A is a perfect fifth, D to A-sharp must be an augmented fifth. Okay? Now I said a moment ago, you might decide that, you know, one note looks a bit like another note. Well, you know you could say, well, we’ve talked about D to A being a perfect fifth, and now we talked about D to A-flat being a diminished fifth, perfectly true. But the same notes might be written differently, for example, you might have D to G-sharp instead of A-flat, we’re calling it G-sharp in a different piece of music. Well, it sounds exactly the same as this diminished fifth we’ve just been talking about. But this time because it’s some kind of D to some kind of G, it’s no longer a fifth it’s a fourth. D, E, F, G, okay? So, D, E, F, G is a fourth. Now, D to G would be a perfect fourth because G is the fourth note of the scale of D major. Here’s D major. So you can see that D to G is a perfect fourth. But if I call it D to G-sharp, it’s actually one step bigger than this, isn’t it? So it must be an augmented fourth. So if it’s D to A-flat, it’s a diminished fifth. If it’s D to G-sharp, it’s an augmented fourth. Same sound but theoretically called by a different name. And this sort of stuff causes great confusion to people, trying to get to grips with reading intervals. But I hope you’re beginning to see that there’s some sense in what I’m saying here. By the way, just in passing, we just talked a moment ago about double sharps and double flats. Hopefully you’ve met these before, but just in case you haven’t. A flat lowers a note by one semitone, by one step on the keyboard, so, that is a semitone. This is also a semitone. So the shortest distance between two notes on a keyboard, is a semitone. If you have a flat, you lower the note by a semitone. If you have a double flat, two flat signs, you lower it by two semitones. So this note B, this note is B-flat, and this note is B-double-flat. If you have a sharp sign, one of these naughts and crosses things, that raises a note by a semitone. So if this note’s F, and I put a sharp sign in front of it, then it’s going to be F-sharp. If I had F-double-sharp, it would be this note. Some of you will be saying, “Well, that’s the same as G.” Yes, you’re absolutely right, because notes have more than one name. This could be a G but it could also be an F-double-sharp. Now, don’t worry too much about why that is, it’s just in different keys we might give notes different names. But the sign for a double sharp isn’t two sharp signs, it’s X. So if you see X, that’s a double sharp sign. So this is how the theory of intervals works. And the next thing we really need to do is to kind of convert that into something that we can understand aurally. And I think that you could spend an awful lot of time just getting familiar with intervals. Instead of just thinking, “I’m going up one, “I’m going down one,” or “I’m missing out a note,” can we begin to read these intervals. That’s what we’re going to do in the next film.