Jazz piano lesson # 5: About scales—magic, hearing, and playing


There’s always more to say about experiential learning and improvisation, the subjects I addressed previously in Jazz piano lesson #4. So this post is a part 2 to the previous one.

Actually, we might just narrow things down and say jazz improvisation at the piano. But, really, improvisation is the large, overall topic we’re discussing.

But, first, about the image with which this post begins: It’s a few buildings on a lake in Reykjavík, Iceland. It’s easy to see—the two buildings mirror in the water. Maybe it’s obvious, but that’s what improvisation is:

Improvisation is a mirror image of the improviser.

Improvisation, for example?

It took Arnold Schoenberg a long time to get to the style he finally called a method for composing with twelve-tones related only to one another. About his learning path towards his twelve-tone method:

It wasn’t about improvisation but it must have been a serious path of experiential learning.

It wasn’t about improvisation because Schoenberg was a composer. It was a serious experiential learning path because Schoenberg was trying to work out an approach to composing without knowing explicitly what and where the goal was.

Schoenberg taught himself how to learn about something without first knowing what exactly he was learning.

That’s improvisation, yes?

The boiling water (of improvisation)?

Here, Arnold Schoenberg discusses what it means to him to make music. And here in his famous boiling water speech, he describes his difficulties crossing the line, so to speak, from tonality to atonality.

He talks in the boiling water speech about feeling like he was boiling. BOILING, which at that moment was his metaphor for what it felt like to look for something that wasn’t there to begin with.

If we look for something that’s not there and if we don’t know what we’re looking for, that has to be a process we characterise as improvisation, yes? From tonality to atonality, what a journey that must have been. How do you know where the line between tonality lies? How do you know, that is, if you don’t know you’re looking for atonality?

How exactly do you know when you’ve crossed the line?

Be the worst one on the bandstand!

Another of my teachers used to say when he was talking about improvisation, and I paraphrase:

Be the worst musician on the bandstand. That way you’ll always be learning from musicians with more skill and experience.

That was HIS way of saying we learn from experience and here’s a question:

What’s the experience we need to bridge the gaps—such as they might exist—if they exist?—what’s the experience we need to connect twelve-tone rows to jazz? What do we get when we make those connections?


To like or not to like? (that is the question)

My experience is

It’s literally impossible to discus or teach or learn about twelve-tone repertoire or technique, or improvisation for that matter, unless there’s something about it we like or interests us.

The key idea is liking something is akin to having fun with something. Liking and having fun go together. Is it even possible to like something but when doing it to not enjoy it? Maybe that wasn’t a question to which Arnold Schoenberg had to answer?

Essential for Arnold Schoenberg was: as regards twelve-tone technique, distinguish between a method and a system. Distinguishing between a method and a system was essential.

That’s because for Schoenberg, a method implied personal choice. But a system—that pointed to all-must-fall-within-certain-parameters.

So, to state the obvious, Schoenberg must have been interested first and foremost in the idea of personal choice. Yet, Schoenberg was well aware of and knowledgeable in the tradition in which he worked.

He understood so-called rules of the game, such as they were. He also knew when and how and why to break the rules. He discussed how that works, staying with or discarding rules, in his book The Theory of Harmony.

In any case, method or system:

What’s the last twelve-tone piece we played or introduced to anyone, a student, a teacher, or a friend? What’s the last twelve-tone piece we listened to raptly and with enjoyment? What’s the last twelve-tone piece with which we engaged?

Do we enjoy the process of improvisation?

The Arnold Schoenberg Centre

One way to to break on through to the other side, to the side of engagement with twelve-tone repertoire—the twelve-tone row side that Arnold Schoenberg inhabited is: Visit the Arnold Schoenberg Centre in Vienna. Of course, that’s easier said than done—obviously we can’t all pick up and go to Vienna right now. But, that said, the Schoenberg Centre does have a fairly extensive presence on the web.

Until you go there you might not know that when Arnold Schoenberg came up with a twelve-tone row for a composition he then made a physical contraption to help him see the row and it’s permutations. Or maybe it wasn’t that he needed to see the row.

Maybe, instead, he needed to feel the row, literally, to hold it in his hands. Feel it in his hands meaning that as regards the row he required a tactile, in addition to an aural, connection.

Gunther Schuller and the magic row (and improvisation)?

Here’s one way to look at a twelve-tone row. This particular passage and the row comes from a quote from Gunther Schuller in an interview with him conducted by Ethan Iverson, the jazz pianist:

Yeah, sure. … and there’s the prime form, the retrograde form, the inversion and the retrograde inversion. And when you have all that, bundled, it’s 48 row possibilities. So, if I sing one prime version, or say, it’d be C#—half a step up, D—a fourth up, to G—B-flat, minor third. Now, let’s say I’ll go down, a diminished fifth to E—half step up to F—then A, major third—then a major second to B natural—and then come G#, F#, E-flat, C. Now, I don’t know how much of that you remember, but you will see that there are huge tonal elements in it.

The row is:

{ C# D G Bb E F A B G# F# Eb C }.

This is now a good time to play through it. Experiment. Play the pitches backwards and upside down.

Make chords from the row. Use collections of any size from the row to make chords and then use the notes that remain to make melodies.

Play the notes as widely spaced up and down the keyboard as is possible. Compress them into the smallest possible space.

The catch, the rub, as it were

There’s only one catch, the rub so to speak. We may or may not find the things we’re improvising sound all that great.

That said and that out of the way, if we find what we’re playing doesn’t sound that great but, yet, if we stay with it and keep at it, then there will be a break-on-through-to-the-other-side moment. Break on through to the other side in the exact same way Jim Morrison sang those words in a song by the Doors. Break on through to the other side—we will eventually find something we like.

It’s just a function of time and hence experiential learning. Which is to say with just about anything, we can explore and see where it goes. That’s slightly different than seeing where we’d like it to go.

What it is and what we want it to be. Those are two different things entirely.

J.S. Bach and the magic scale

Here’s a collection of pitches from Bach’s 4th Invention in Dm. We build the collection like so:

Start on the note D above middle C:

{ D E F G A }

Now surround those notes, which we’ll call the THE LIST with THE HEAD and THE TAIL. THE HEAD is C#. THE TAIL be Bb.

So the scale is:


Here, from bottom note to top note are the pitches, or, as we’ve said: the HEAD, the LIST, and the TAIL:

{ C# D E F G A Bb }

Here are the pitches as notes on a staff. Again, C# is the head and Bb is the tail.

Improvisation and Mark PolishookPiano
From JS Bach's Fourth Invention in Dm

And why are we using terms like HEAD, LIST, AND TAIL? The answer is: we’re using those terms, borrowed as they are, from the LISP programming language because HEAD, LIST, and TAIL eloquently express the first item (in a list) which is the HEAD, the last item (in a list) which is the TAIL, and the list itself.

But, also, and maybe more importantly, those terms work because the HEAD of our list leads so clearly right to the list itself—the list of D, E, F, G, A. And d the tail points back so clearly to that same list.

In other words, when we say the HEAD and the TAIL lead, let’s ask, thinking about those seven pitches—C#, D, E, F, G, A, Bb—lined up in a scale-like fashion from bottom note to top note, as they are:

  1. Why does C#, the head, ascend to D?
  2. Why, when we reach Bb, the tail, does it want to descend to A?

It’s possible, the answers need to be stated. On the other hand, it’s possible our ears will tell us what we need to know.

Sing the scale to weight the equation to hearing and the ear. Meanwhile, we might as well call this scale, after Gunther Schuller’s row, a magic scale. That’s because those seven pitches happen to be the first seven pitches in Gunther Schueller’s magic row. They’re taken from J.S. Bach’s Fourth Invention in D minor—that’s a good reason all by itself. However, most importantly:

Play the seven pitches from the magic scale in any order, with any rhythm, with any repetitions, or any anythings. The only requirement is play only with those seven pitches.

Using just those seven pitches is it possible to play something that doesn’t sound good? Well, the answer could be an imperative: DEFINE GOOD.

But putting the imperative of DEFINE GOOD to the side, is it possible to make something that doesn’t sound good with those seven pitches? Assuming the answer to that question is NO, then have we connected J.S. Bach, Gunther Schuller, seven pitches, and thus the magic?

Does the magic scale possess magic because every combination of notes that come from it sound minimally, well, at least, pleasant? Given that we’re talking about combining seven notes in any order and rhythm, an outcome of pleasant isn’t all bad? Yes?

Another way

Another way to explore and answer to those two questions above, which, again, are:

  1. Why does C# ascend to D?
  2. Why, when we reach Bb does it want to descend to A?

is just and simply:

Make up melodies from the notes in some particular scale.

We can listen to how the pitches in a scale work when we make up melodies. For example, how do the pitches interact with each other. Because we will likely hear that some pitches want to move aheadmore strongly than others.

Therefore, as we make up melodies consider it’s the experience of doing that that counts. That experience counts because it’s process through which we can understand and contextualise why and how one pitch wants to move to another or why one pitch is less than thrilled to continue on to another.

As we learn about the tendencies pitches possess relative to how much they want to move to and from each other, it’s far less important whether or not the melodies we make up are good, bad, or indifferent. That’s because over time, as we make up more and more melodies, they will get better. And better.

In terms of the magic scale, we may find, for example, that the more melodies we make, and the more of them to which we listen, the more we’ll hear—or at least begin to hear—the different ways how the HEAD and the TAIL of that scale function. In other words, returning to those two previous questions:

  1. Why does C# ascend to D?
  2. Why, when we reach Bb does it want to descend to A?

Or, we might just as well ask:

  1. What is it about the leading tone such that it generally wants to ascend to the tonic?
  2. Why, if we’re in the key of D minor and when we reach Bb, does the flatted sixth in a natural or melodic minor scale, does it want to descend to A?

Now, let’s think about this for a second. We could very easily just practice the natural minor and the melodic minor scales. We could just learn the fingerings for them and play them up and down the piano.

Better yet, we could learn the fingerings for them in all twelve keys and play them up and down the piano in every key. But, there’s a disadvantage to that which is:

Learn fingerings and play scales up and down, ascending and descending, and we’ll probably focus more on the mechanics of running scales across and around the keyboard instead of, and more importantly, listening to HOW THE NOTES IN A SCALE WORK TOGETHER AS A WHOLE.

In other words, at some simplistic level, do we privilege ears over fingers or vice versa? Or, in exactly the same vein, we could ask, what’s more essential, the mechanical skills that go into playing the piano or the listening skills that go towards hearing music?

Do, should, or can we play firstly and hear secondly? Or do, should, or can we hear firstly and play secondly?

Assuming that we want to consider one thing as more essential than the other—AND WE MIGHT NOT WANT TO DO THAT!—what’s more fundamental when learning how to play an instrument? And what’s more important when learning the art of improvisation?

  1. The physical, mechanical side of playing an instrument.
  2. The mental, auditory side of playing an instrument.

Experienced musicians usually say the ear is the weakest link in the chain. Well, experienced musicians may well say that, but, we might as well ask ourselves: What do WE think?

Maybe that question simply shows no one thing stands above the other? Maybe that questions suggests that the arts of playing an instrument and improvising consist of many smaller skills that, together, produce a whole that’s greater than the sum of the parts?


Order and twelve-tone rows (and improvisation)?

And about the different order of those same pitches in Gunther Schuller’s row? The fact that they don’t appear either in the order Bach used them or in the order we presented them?

Here, again is our order, the so-called magic scale.


C#—D E F C S—Bb

The huge misconception

One of the huge misconceptions about twelve-tone style is that pitches repeat exactly over and over again in the same exact order as they appear in the row. In fact, that’s exactly how composers didn’t work with their rows!

That last statement means there are many ways, a lot of them, to re-organise Gunther Schuller’s row. There are many ways to play with it. There are many ways to explore it.

And that’s the point of experiential learning. It’s about exploring something of interest, going in and around and behind and above and beneath it. That, rather than going immediately to some core knowledge about something. The thing is, if we go immediately to core knowledge, we’ not exploring—we’re just going to what we know.

Now, that doesn’t mean that exploration is always the preferred path. It’s just that the point is we have to try someone new, anything at all, if we’re going to learn.

What’s else?

Right now is a good time to mention something I think I read in Paul Bley’s autobiography, which is

a chord is simply a melody that’s standing stacked and upright and a melody is a

chord that’s played one note at a time.

Actually, Paul Bley’s autobiography is called Stopping Time. It’s available, right now, on Amazon. I got a copy there not long ago for Kindle. Whatever format it’s in, the first half is a great book with many revelations. I’m less excited about the second half because then the book turns into a listing of sessions and dates and such. But, regardless, it’s worth reading and reading if that’s how you see it because the first half of the book is indeed wonderful.

Also, you may have noticed: this is the fifth post in an ongoing series about learning to play jazz at the piano. But yet we’ve spoken very little about jazz, the piano, or what exactly to practice in order to learn to play jazz at the piano.

As we continue on, we’ll introduce more and more specifics. But before specifics come generalities. So that’s why these posts are preceding as they are. Which is to say that stuff specific to jazz and the piano will appear more and more and increasingly so.

What did we discuss?

We talked about a scale we found in a Bach Invention and a twelve-tone row by Gunther Schuller. Here’s a video that explains some of the basic ways in which composers have used twelve-tone rows. It’s an introduction, only, but it’s a very good intro at that.

These things—the scale we pulled from a Bach Invention and from Gunther Schuller’s twelve tone row are resources with which we can explore and invent. As such, they’re just groups of notes we can use as creatively as possible. In so doing, we acquire experience.

And that’s what we want:

We want experience because it leads to, or maybe it’s the same thing, experiential learning.

What’s next?

In upcoming posts, we’ll look more at scales and chords and how we can use them to improvise. We’ll keep in mind, always, that

a chord is simply a melody that’s standing stacked and upright and a melody is a chord that’s played one note at a time.

Actually, we can abstract just a little bit more upon that idea. Our new abstraction is a chord is just some series of intervals stacked up upon each other. To be sure, that’s not a new idea.

We see that abstraction centuries ago, for example, in figured bass notation. For example, we might have a root note upon which are stacked a fourth, another fourth, and a major third. … Although that’s not a combination we’re likely to find in a figured bass.

Or we might have a melody with starting note followed by a note a fourth higher and then another note a fourth higher and then a melody note a major third lower—the same intervals we listed for the previous chord.

Just to make that all concrete, the chord might spell out to C, F, Bb, and D. The melody might be C, F, Bb, and Gb. Notice with these examples that whether or not an interval goes up or down makes no difference. That’s why in the chord Bb is followed by D. That’s because Bb to D is an ascending major third. And it’s why in the melody Bb is followed by Gb. That’s because Bb down to Gb is a descending third.

This idea, that an interval up and an interval down are the same thing, isn’t really all that new. We can look to so-called pitch-class theory from the mid-20th century to see that it’s been here, there, and about and described as such. We can go back to J.S. Bach and then back some more to find examples.

In any event, as Paul Bley observed, so we ask:

Is a chord a melody where the notes are stacked up one over the other? Is a melody a chord where notes previously stacked up one over the over are now in succession side-by-side and one by one?

Yes, we can ask. We should ask? Yes?