The concept is easy to learn, but hard to master. To get started, let’s say you’re soloing over an A7 or A7#9 groove. The first thing ’Trane’s formula reminds you is that you don’t have to stay in one scale or mode over a one-chord vamp such as this. Specifically, using the formula, you might start by playing a few notes of A Mixolydian—which suits A7 perfectly—and then ascend a minor third to C Mixolydian, another minor third to Eb Mixolydian, another minor third to Gb Mixolydian, and a final minor third back to the key of A, where the cycle begins again. The challenge is switching keys seamlessly, and one thing that helps in this regard is staying in the same general position for all four scales [Ex. 1]. Actually, I often just use pentatonic fragments from these scales, as in this line [Ex.2], which, using the formula, implies an A7-C7-Eb7-Gb7 progression over the static A7 background. With practice, you can move away from pattern-based licks and improvise less predictable phrases, like this [Ex. 3].
At first, I merely used this concept as an improvisational tool over static, one-chord jams. But then I thought, “What if I wrote a table that shows just about every possible chord each scale works over?” Using minor pentatonic scales (a minor third apart, of course) I did just that, and used the table to create a progression that changes tonalities to diatonically suit each new scale and key [Ex. 4]. This progression became “Spillway,” a song I recorded with Derek Trucks—who I don’t think was even old enough to drive at the time—on his album Out of the Madness. To practice soloing with the formula, start with A minor pentatonic and modulate up a minor third with each new chord, as suggested pentatonic scale key listed above each measure.