The Giant Steps Progression
("Coltrane Changes"):

Here are the three key centers in Giant Steps;

B, Eb,G

If you make them major chords and put them in this order;

Bmaj7 Gmaj7 Ebmaj7 Bmaj7

and then precede each with a V chord from its key center (except for the first B chord) and add bar lines:

| Bmaj7   D7 | Gmaj7 Bb7 |

| Ebmaj7   F#7 | Bmaj7 |

This 4 bar progression could be used as an embellishment of this "progression" in order to add harmonic interest:

|Bmaj7 | | | |

If you look at the first 7 bars of Giant Steps you'll see that it's essentially the above progression, except in this case it stops after the Ebmaj7 and backs up to the D7 (adding Am7, the II as an embellishment) and then finishes out from there:

| Bmaj7 D7 | Gmaj7 Bb7 | Ebmaj7 |

| Am7 D7 | Gmaj7 Bb7 | Ebmaj7 F#7 |

| Bmaj7 |  

So there's where the "minor third - fourth" pattern comes from; major key centers in major thirds, with V chords added. It's basically a fancy way to get from a I chord back to a I chord. Coltrane also used this same concept for the tune "Countdown" (based on the tune "Tune Up") except here he was embellishing a II V I progression instead of just a I chord:

Original II V I used in "Tune Up":

| Em7 | A7 | Dmaj7 |       |

New version used in "Countdown":

| Em7 F7 | Bbmaj7 Db7 | Gbmaj7 A7 |

| Dmaj7 |

In the key of D, the "augmented triad" that the other keys are derived from would be

D, Gb/F#, A#/Bb

Really, the only difference between this progression and the "Giant Steps progression" is that this one begins with the II chord and the GS one begins with the I chord. Still, in the "Countdown" version you can see the II V I in there (it's just got V-I in Bb and V-I in Gb sandwiched between the II and the V).

The next 8 bars of the tune simply repeat the same process in descending whole steps:

| Dm7 Eb7 | Abmaj7 B7 | Emaj7 G7 | Cmaj7 |

(so here we have a II V I in C with the added "augmented substitution" keys of Ab and E)


| Cm7 Db7 | Gbmaj7 A7 | Dmaj7 F7 | Bbmaj7 |

(and here a II V I in Bb with the augmented sub keys of Gb and D)

Note that the third 4 bars uses the same 3 key centers as the 1st 4, just rearranged.

As for "Miss Jones", look at the bridge changes;

| Bbmaj7 | Abm7 Db7 | Gbmaj7 | Em7 A7 |

| Dmaj7 | Abm7 Db7 | Gbmaj7 | Gm7 C7 |

We'll ignore the last bar as it's just a II V to get us back to the home key of F, and let's take the II chords away:

| Bbmaj7 | Db7 | Gbmaj7 | A7 | | Dmaj7 |

Does this look familiar? If we add a V chord back to Bb:

| Bbmaj7 | Db7 | Gbmaj7 | A7 |

| Dmaj7 | F7 | Bbmaj7 |

... then we get the "Giant Steps progression". Miss Jones instead goes back to a II V I in Gb, then chromatically down to a II V I in F.

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