Say you've written (or a bandmate as written) a tune that features a sustained Maj7b5 chord. What do you play over it? Probably you don't have standard vocabulary for this type of chord, and since it's unusual it's not likely you'll find many ideas by transcribing. So how could you quickly build coherent vocabulary?

Start with what's easy

Clearly you need to know the chord tones, so let's start there. The Maj7b5 arpeggio contains, of course, the notes 1, 3, b5 and 7; here are the CAGED fingerings (all diagrams come from by free ebook Arpeggio and Scale Resources):

This covers 4 out of the possible 12 notes available to us. To start with, we should internalise the sound of these and try to develop some musical ideas out of them. Four notes is a bit limiting melodically, and since they're all chord tones there's not much scope for building tension and release, but still you can apply techniques like enclosures, approach notes and side-slipping to make things more interesting.

What is vocabulary?

If we're going to extend this it would be good to have an idea of what our goal is. What does it mean to "build vocabulary" for this chord? For me "vocabulary" isn't about pre-learned phrases or "licks", at least in the traditional sense; I think these are hard to use when improvising and often come off as stilted. And what do you play in between these canned phrases? Other canned phrases? The danger is that you'll sound like someone playing through a book of licks one by one rather than making a coherent musical statement, which is what improvisation ought to be about.

However, just learning scales and running them up and down doesn't create good results either. We can learn a lot about how to deal with this from the raga system of North Indian music. A raga isn't just a scale, though it does include a pitch collection. It isn't a melody either, though it has certain melodic gestures encoded in it. For me a piece of "vocabulary" is like this: a set of notes, yes, but also characteristic ways those notes move together and "talk to each other".

You can pick this up by transcribing, of course, because there you're tapping into a tradition of players using fixed sets of notes in particular ways. But even when trying to develop something from scratch it helps to think about this aspect of it as well as just collections of notes.

Consonant vs Dissonant

Let's try an exercise with our Maj7b5 arpeggio. We want to add some notes to it that will have a consonant ("inside") sound against the chord. These will be notes we can move to to create mild tension that we can resolve by returning to the chord tones. The notes we don't pick will be dissonant ("outside") and will create a lot of tension. This doesn't mean we can't play them, but it starts to give us some structure to the non-chord-tones.

The notes that aren't in the arpeggio are b2, 2, #2, 4, 5, b6, 6 and b7; this set of notes is sometimes called the "complement" of the arpeggio. Our task is to break them up into two sets, one reasonably consonant and the other reasonably dissonant. In this case it seems to me it's easier to start with the dissonant notes.

Based on our knowledge of how things work in other harmonic situations we can expect that any note that creates a 3-note cluster, where the notes are separated by semitones, will be pretty crunchy. So the following will be dissonant sounds:

• b2 (creates a 3-note cluster with the 1 and 7)
• 4 (creates a 3-note cluster with the 3 and b3)
• b7 (creates a 3-note cluster with the 1 and 7)

As I said, you can do this on paper but of course you should check with the instrument to make sure there are no surprises. I would also avoid the 5 on any chord with a b5, as it will tend to make the b5 sound like a #4, which isn't what's intended.

So that gives us 4 notes we've chosen to define as "dissonant". The remaining notes are 2, #2, b6 and 6 -- let's call these the "inside" sounds and see what we can do with them. So the idea is to play these four notes for mild tension and resolve to chord tones when we want to. Here are the CAGED fingerings for this set of notes, with the "root" note (circled) being the 2:

(Notice that this is a symmetrical note-group with a nice "staircase" pattern that's very easy to learn).

It's now time to start trying to combine each of these two ideas with the chord tones and see if we can find things that work. Notice that this is much more than just choosing an 8-note scale; we have four note-groups that relate to each other in musical ways. For example, the #2 in the "inside" collection can clearly resolve to the 3 in the chord; but what about playing the sequence #2-7-3-1, which has a kind of symmetry to it? Ideas like this start to add some musical content to the abstract skeleton we started with. They arise naturally when you spend some time improvising with these patterns.

Of course, you can choose to play the "outside" notes, too. These are b2, 4, 5, b7, which make a m7b5 ("half-diminished") arpeggio built on the 5 of the underlying chord. Clearly we already know these notes are going to be more dissonant, but hopefully you already know your m7b5 arpeggios so experimenting with them should be a breeze.

What we now have is the 12 notes of the total chromatic divided into three equal parts: four chord tones, four inside extensions and four outside extensions. Since each set is only four notes, it's easy to work with. Spending time on each set individually, and then moving between them, will build individual vocabulary for the Maj7b5 chord.

Of course, it may not produce results you like all that much. On the other hand, you may want more options. So it's time to take this strategy and see what else we can do with it.

Working with the Results

A strategy like this doesn't necessarily produce anything instantly usable; it's designed to provide a framework for exploration, which usually means putting some time in with the instrument, where we discover things that would be hard to figure out merely on paper.

For example, we discover that each individual note from the "inside" set does indeed sound fairly consonant against the Maj7b5 harmony, but as a group they're highly dissonant. This isn't too surprising as they've just a pair of semitones separated by a tritone. So what can we do with them? We can split them into two pairs that we treat separately: for example, 2 and 6 versus #2 and b6.

Or we can look for suggestive patterns: for example, the 2 and b6 together with the 7 and 3 (which are in the chord) make a dom7 arpeggio built at the major third (III7); this is a very nice "inside" sound on this harmony. The #2 and 6, on the other hand, can be combined with the 1 and b5 (again, in the original harmony) to give a fully-diminished seventh chord built on the root. So these two arpeggios cover all the "inside" sounds in a very practical way.

The III7 choice, incidentally, might lead you to think about playing its Mixolydian scale, which would be spelled like this:

which is a hypermode. It's not completely successful, to my ears, partly because of that b2, but it's interesting and the b2 can of course be avoided.

As for our "dissonant" note-set, Vm7b5, one thing to notice is that if we slip it down a semitone to bVm7b5 we get a very consonant set of notes against the IMaj7b5. This is a nice way to introduce the sound, by slipping up from that more inside version and playing a parallel phrase in the dissonant note-set, then either slipping back down again or simply resolving to a chord tone.

These are the kinds of strategies that really, for me, constitute "building vocablary" -- everything else is preliminary tinkering about on paper.

Generalising the strategy

First, we noticed that when playing on a chord we have two choices: play chord-tones or non-chord-tones. Chord tones are always safe but rarely exciting, so our difficulty is in organising the rest in a useful way. Of course if there are n chord-tones there are 12-n others; in our case 4 chord tones and 8 others. So we're interested in giving those 8 notes some structure, and one way is to split them into two sets as we did above. Since there are 8 notes, and each can go in either of two sets, there are 2⁸=256 possibilities.

Not all these are equally interesting. Our list includes putting all 8 notes in one set and none in the other, which is hardly helpful. The split we went for was an equal one: 4 notes in each set. There are ⁸C₄/2=35 possible ways to do this. The one we came up with above was just one of these and any of the others might be musically interesting. This is a huge amount of raw material with which to start building vocabulary.

In this exercise we faced an uncommon chord that more or less forced us to build vocabulary from scratch. The same approach, though, can be used on any chord. Any four-note chord will leave us with 35 ways to divide the remaining notes into two sets, which seems to me to be a huge wealth of material to work with.

All the possibilities

Here are the 35 ways we can divide the complement of the Maj7b5 arpeggio into two equal sets. The one we discussed above is in bold. Which others might be interesting?