If you’ve ever listened to Coltrane’s “Giant Steps,” you may wonder how he did it…or even further still, why he chose the chords that he did and how they somehow work together. Rumor has it that when Coltrane presented “Giant Steps” to his band, his pianist struggled to keep up and solo, because the chords were not all in one key.
Well today we’re going to check out jazz matrix cycles, also known as Coltrane changes. We’re going to look at how you can play them and how you can improvise over them. These matrix cycles use harmony that moves either up or down in major thirds.
Originally, these chord changes were used in jazz standards like “Have You Met Miss Jones."
John Coltrane later popularized these changes through tunes like “Giant Steps” and “Countdown.” The matrix cycle that he used in “Countdown” is particularly useful when applying the matrix cycle to a jazz ii-V progression.
To analyze some ways we can approach these matrix cycle chord changes, we’re going to check out some content from Andrew Gould’s PDF package on jazzlessonvideos.com, entitled 27 Exercises on Matrix Cycles.
Contents
How “Have You Met Miss Jones” works as a matrix cycle
The tune “Have You Met Miss Jones” was written in 1937, and the bridge moves into a few different key centers that are all related to one another by a major third.
We start on a concert Bb, then we move up to F#, D, and back to F# again. Coltrane used a very similar movement when he wrote his matrix cycles—like we said, they are all related by major thirds.
That said, we can assume that Coltrane likely took inspiration from this tune as he pushed forward into his own compositions.
Taking apart “Giant Steps”
“Giant Steps” is such an iconic tune for Coltrane, we’ve actually written an entire blog about it.
So let’s check out how this tune works. To start off—you guessed it—these key centers are all related by a major third.
So if we relate it back to our circle of fourths, we can see that this basically splits up our octave into three equal parts.
Starting on C, we move up to E. From E, we move up to Ab, and from there we come right back to C.
But one interesting thing about “Giant Steps” is that instead of moving up in major thirds, it actually moves down for the first eight bars—starting on the key of Ab, down to E, and down again to the key of C.
Taking apart “Countdown”
Our next progression is the tune “Countdown,” which we’ve mentioned now a few times.
This tune functions because we’re basically inserting a matrix cycle over what would be a normal ii-V-I progression. We’ll start on the standard ii chord, then we’ll go up a half step to the V chord, which then resolves to our first key in the matrix cycle. From there, it’s just basically Giant Steps until we get to our tonic chord, and we see that we even have the original V chord right before we resolve to our I chord in the last bar.
Getting the sound first
We’re going to check out some exercises that you can use to get yourself comfortable with the Coltrane changes. But before we do that, let’s start by getting comfortable with the chords in the progression.
Basically what we’re going to do is arpeggiate each chord from the root—1, 3, 5, 7 and hearing how each of these chords sounds going into the next is going to help us identify ways to create strong voice leading.
Don’t skip out on this part—it is important, now matter how much you think you already know it. You can also try starting the arpeggios from the third, fifth, or seventh, if you want to give it more challenge.
Giant Steps Diatonic Exercise
For our first exercise, we’re going to use the “Giant Steps” matrix cycle, and we’re going to mix up the arpeggios.
On the first chord, we’ll do 3, 1, 5, 7. Then we’ll move down a half step using smooth voice leading to get to the next chord, where we’ll play 5, 3, 1, b7. Moving from the b7 down to the third of the next chord, we have a half step motion. We’ll do a 3, 5, 1, 7 here, too, followed by a 5, 3, 1, b7 on the following chord, just a half step below the 7th. Then we’ll move down one more half step to the third of our final chord, where we’ll do 3, 5, 7, 9, 9, 1. Now noticed on this exercise, we’ve used nothing but the arpeggio notes for each chord, and we’re ending our phrase again with an arpeggio that reaches up to the ninth of the chord.
If you want to check out how this sounds slow and up to speed, be sure to check out how Andrew plays it in our accompanying YouTube video, How to Play Coltrane Changes.
Countdown Diatonic Passing Tone Exercise
In that last exercise, you can really see how we took the arpeggio notes to create some smooth voice leading for a slightly uncommon, weird chord progression. For this next exercise, we’ll use some diatonic passing tones in combination with everything to help smooth things even more.
Starting again on our ii chord, we’re going to play 1, 2, 3, 5, which is a common sequence to use on matrix cycles. The 2 in this case is what’s functioning as a passing tone, but it’s diatonic because it’s still part of our scale and relates to the chord while connecting our first degree to our third. Now this technique is one thing that really strengthens our use of just being able to play ideas fluently through the chord changes. Connected ideas have stronger voice leading in the middle of the measure, not just going from bar to bar and chord to chord.
As we get into our next chord, we have 6, 5, 3, 1, then 1, 2, 3, 5—the same pattern we had in bar 1. Then going down, 9, b7, 5, 1, then 3, 5, 9, 1, and b7, 5, 3, 1. That straight descending arpeggio then resolves to 9,7, 1, 9, 3, 5 in that last bar. You’ll notice a number of 9s, 11s, and 13s in those exercises.
Again, you’ll want to check out how Andrew plays it in our videos How to Play Coltrane Changes on YouTube so you can see how he does it slow and fast.
Giant Steps Chromatic Passing Tone Exercise
For this last exercise, we’re going to jump back to “Giant Steps.” This time we’re going to try using some chromatic passing tones to further increase our voice leading and find even more melodic ways to connect our lines.
In the first measure, we’ll start on the 5 of the chord, followed by a chromatic passing tone leading down to the fourth, then the third, before resolving to the root of the next chord, where we then have a chromatic passing tone leading down to the b7, then back up to the root again, and we have the 3, 1, and chromatic passing tone to the 9.
Then, we’ll resolve up a half step into the root of the next chord, down a chromatic passing tone, down another half step to the b7, back up to the root, landing on the 3 again. We do 3, 5, 9, then a chromatic passing tone leading down to the root, with a chromatic passing tone leading down to the fifth, then the fourth. Finally, our last chromatic passing tone is the b3 leading up into the major third to resolve.
This one you’ll definitely want to hear how Andrew plays it fast and slow. So check out our video How To Play Coltrane Changes on YouTube so that you can get up to speed.
That’s all for today, but if you liked this and want to dive in deeper, make sure to check out Andrew’s PDF package with JLV, 27 Exercises on Matrix Cycles. If you practice this stuff, you’ll notice a difference in your playing in no time.
We’ll see you next time!