Scale Theory I: Half Diminished

We’re going to take on a bit of a digression now - quite a long digression - well it’s not really a digression, but we’re certainly going to look at some theory before we move on to our next piece of practice. First of all let me tell you the motivation for doing this. We’ve been looking at hot licks on a minor scale and I want to play my favourite tune on a minor scale, the standard “Autumn Leaves”. What you’ll find in it is it’s a minor tune and it uses II-V-I, but when it uses II there’s what’s called an altered chord - the fifth is flattened and on the V the ninth is flattened.

It’s quite a frequent occurrence in jazz that we alter the fifths and the ninths.

Unfortunately what also happens is we need - or we ought to - alter the scale that goes with the chord so that it matches the altered fifth and the altered ninth and that’s going to take us on a bit of a digression.

You might find this a bit hard going. If you do then make as much of it as you can and then perhaps come back and look at it at a later stage. You’re not going to get all this theory in one go or, at least, I’d be very surprised if you did. I can tell you the good news is that I’m a self-taught jazz pianist. I just got there by doing it really. The final discriminator about, you know, what works and what doesn’t is my ear. If I want to know if a note fits a particular chord or not then I play it and I make the decision as to whether it does or it doesn’t.

But there is a theory that underpins it and I kind of got to the theory later on. I’m going to give it to you now in the hope that it will help you to sort out what are the good notes and what are the bad notes when you are playing a particular chord. I actually have had a handful of lessons. I had them from the British jazz pianist Gareth Williams. If you haven’t come across Gareth’s work then I urge you to do so - he’s a wonderful, wonderful pianist. Gareth is known in some quarters as the “professor” because he’s so good on the theory of the music. He didn’t get there overnight.

He said to me that when he needed to learn all the various modes and so on that there are then, you know, he’d go through them if he was in the bath or on a train journey, or something. It’s something you will need to work at in order to get on top of but, as I say, take some encouragement from the fact that, in the end, your ear is the discriminator. So if you can’t get your head round all this theory then your ear can come to the rescue. What I want to do is to talk about some scale theory.

My approach to playing piano jazz is to start off with scales, because scales tell you the notes that are available to you. In the end, it’s motivic improvisation which is the key - playing musical phrases - but you have to know which notes are available to you to play those musical phrases on. That’s the point of scale theory. Well we’re going to have a look at our first scale - the half diminished scale. A half diminished chord is simply a minor seventh with a flattened fifth. Let’s work in the key of C. We know that in the key of C we have the root, the minor third, the fifth and the minor seventh. That’s our basic chord.

What we’re saying is now that we want to flatten the fifth - to there. First of all the notation. We write C minor 7 and in brackets flat 5 - or not necessarily in brackets - or perhaps even a more common notation than that is C with this circle with a line through it - the phi sign - and a 7. It means exactly the same thing - a half diminished chord. It’s called half diminished because it starts off being a diminished chord - minor third, minor third (minor third) - but then it doesn’t go minor third, it then includes the seventh.

The question is: what’s the scale that goes with this? If I keep the chord there and I put the scale on, well first of all the notes in the chord are clearly in the scale. So they’re in it. Then what about here at the fourth level - we have a choice between those two notes. Well we’re not going to put in the E natural because that’s going to counteract the minor chord. So we put in the fourth - that’s OK. What about between the G flat and the B flat?

Well there’s three possibilities: that note, that note, that note. The first note is no good because you get a minor third inside the scale and scales - most of the scales we’re going to be talking about - are scales where you go in half steps or whole steps. You go in semitones or tones to the next note. We can’t use the G because that would involve a minor third. Similarly we can’t use the A because that also would use a minor third.

So we choose the A flat. Those are all the notes so far that we insist must be in the scale. That leaves us with one note between C and E flat. What do we choose?

The answer is there are 2 choices: there’s the D and the D flat and it leads to 2 different scales. This scale … and this scale … I am going to do it in that order even though the second scale is probably the one that’s most used in the music and it’s easier because it’s just a mode of the major scale. The first one is a mode of the melodic minor ascending. First of all, let’s do a little bit of revision. A mode is just a scale that’s rooted elsewhere.

If we take the Ioanian scale - do, re, me fa, so, la, ti, do scale - then if we root it, for example, all the white notes on D - we get a different scale because the intervals, the semitones and the tones, are in different relationship to each other than they were if you start off with C major.

That’s called the Dorian mode, as you know. We come to the minor scale and you remember this ambiguity there, because there’s 4 possibilities. It starts of with (the second), the minor third, then the fourth, then the fifth and now there

are 2 possibilities for the sixth and the seventh level: they can either be naturalised or flattened. If we naturalise the fifth and flatten the seventh then we get our friend the Dorian scale. That’s one choice. If we flatten both of them - that’s known as the melodic minor descending because when we learn our scales we go … up and … down for the melodic minor - the melodic minor descending. In fact, when you talk about modes you’re not going to get anything new from the melodic minor descending because it’s just E flat major. So all the modes are going to be the modes of, in the end, a major scale. So nothing new will crop up.

However, it turns out that something new does crop up if we use … the modes of the melodic minor ascending and we’re going to have a look at those modes in a later session, but we want to use one of them for the moment and it turns out that - oh just for completeness of course the other thing we forgot to mention is the harmonic minor … actually does have a minor third in it - but that is where you flatten the sixth and you naturalise the seventh. Meanwhile, back at the melodic minor ascending … this plays a big role in jazz in terms of the modes of it. We will come to that.

I want to use one of them for the moment. What I want to use is E flat minor - melodic minor ascending. So it’s … Let me press down all the notes with 2 hands … There’s all the notes. What I want to do now is base that on C, so I take the D down and the C down and I get that scale … Do you remember we had - when we were talking about the half

diminished chord - we had 2 possibilities: one where we naturalised the D, one where we flattened the D. Let’s do the first - first. Now officially it has a complicated name because it’s a mode - it’s the sixth mode of E flat melodic minor ascending. Gosh, I’m finding this hard.

It’s known as the “Locrian sharp 2”. The Locrian sharp 2 is a mode which consists of … those notes. It might be a little bit easier if we put the chord that goes with it. Well first of all, just in terms of a rooted chord, we take C minor7 and we flatten the fifth. That’s the basic chord. In terms of voicing, remember what we did with the minor seventh, we took it’s first inversion using the ninth - or the second, depending on how you want to look at it. That is indeed a note that belongs to our scale, but we flatten the fifth.

The very first chord that we use for C minor 7 flat 5, the half diminished is that chord … Then the other chord we had was the third inversion … again it’s got a D in it, so we don’t need to do anything about that, but the G we need to flatten to give us that. So that’s our other shape.

Now I’ve said to you that when we play our voicings we don’t play the root because that, after all, is the role of the bass player to either play or imply the root. So we don’t have rooted chords. We don’t play that for C minor7 and we don’t play that for C major7 - a chord in root position. Having said that, there is one exception that I make use of a lot, anyway, and that’s when it comes to the half diminished chord. I actually play a rooted chord. The rooted chord consists of the root C, the fourth F, the flattened fifth G flat and the flattened seventh.

So that’s the chord … I have to confess it doesn’t sound very good that low. I tend to use it from D upwards - E, F, G particularly. That’s probably too low … it’s a bit too muddy, but if I move it up to D then that’s quite nice. If I move it up to E - so E half diminished - I like that sound. I do use a rooted voicing - it’s exceptional - but I do use it and I do like the sound of this voicing in the middle of the piano. There we have it. We take our 2 standard chords for the minor and we flatten the fifth.

Then the scale that goes with it is … So that’s the first and, as I said, probably less used in jazz that the next one we going to talk about. I actually prefer it but then that’s just a question of taste. The one that’s usually used is where you use the other choice of D, namely D flat where we flatten it. So that, strangely enough, when we talked about the name of that scale where we naturalised D is known as Locrian sharp 2, because you sharpen, or you naturalise the second note. Now we’re going to talk about the scale where this is flattened and it isn’t called flat 2. We’re talking about this being the flattened ninth.

If that’s our root and this is the flattened ninth. Now C minor7 flat 5 will also imply C minor7 flat 5 flat 9. You see that there is as well as the previous indications by chords of C minor7 flat 5, of C half diminished, of C with a circle with a slash through it and a 7, you can also have it as C minor7 flat 5 flat 9 because the ninth is flattened. The good news is this is no new scale … because it’s a mode.

It’s the seventh mode of D flat major … If we take D flat major and we root it on C we get this mode which is why it’s called the Locrian mode of D flat major. So it’s D flat major scale - do re mi fa so la ti do scale - rooted on C. So the scale is easy. What about the chords? Well now we have to be a little bit more careful because we are going to flatten the ninth - or the second if you like. Our kind of basic rooted chord doesn’t change. We could include the flattened ninth but it doesn’t sound very good because it’s go that sound in it. What about voicings?

Well our first voicing, if you remember, is to take C minor, flatten the fifth and now we flatten the ninth as well. That is the chord that goes with our mode of D flat major … Similarly the third inversion - we flatten the fifth, we flatten the ninth (or the second if you wish) and then we get that.

In terms of our rooted chord we don’t have to do anything to it because there is no second or ninth in it. That rooted chord works for both versions of the half diminished scale. That’s a lot to take in, but that is the theory - or the first part of the theory anyway.