Recognizing modulation style / pattern in Steely Dan's "West of Hollywood"

Question

I'm a fan of Steely Dan's music, but I find analysis of their music to be difficult from a tone-, modal-, and chord-theory point of view. But perhaps the complex jazz-influenced M7/M9/M11 chords that SD is famous for is precisely the point of their style. (My personal study of music theory was based on [mostly 1980's] rock and pop music; both Becker and Fagen were trained in Jazz.)

Which brings me to "West of Hollywood"--the final track of SD's Grammy-winning album Two Against Nature (released in 2000). Stylistically, this song is similar to many other SD songs, with complex jazz-influenced chords, intervals, melodies, etc...

...At least for the verse/chorus/bridge sections of the song. But afterwards, the song has a nearly four-minute outtro featuring a saxophone solo by Chris Potter.

But, the two things I find intriguing about the outtro are

1. The chords played by the accompaniment (keyboards, bass/rhythm guitars, etc.) sound distinct and well-formed (in contrast to the complex, jazzy chords in the first half of the song), and
2. Many, many modulations--this song must surely have set some kind of record with the sheer number of tonal-center changes during the outtro. Often, the tonal center is established only for a few measures (see my chart below), and the transitions happen so quickly that the listener barely notices.

Because of (1) above, there's no denying what tonal center the song is in at any point in time, despite the vast number of modulations, and how often they occur, in (2).

I have "reverse engineered" the outtro to try to determine the modulation style/technique, and also to see what other patterns can be determined. The chart below shows what I've noticed:

4:29    b minor (one 6/4 bar)

=========== BEGINNING OF OUTTRO ========================================

4:31    e-flat minor (eight bars) ----------+
                                            |
                                      -1 semitone
4:44    g minor (two bars) -----------------|-----------------+
                                            |                 |
4:47    d minor (one 6/4 bar) --------------+           -1 semitone
                                            |                 |
4:50    f-sharp minor (ten bars) -----------|-----------------+
                                      -1 semitone             |
                                            |           -1 semitone
5:06    c-sharp minor (one 6/4 bar) --------+                 |
5:08    f minor (eight bars) ---------------------------------+
                                                              |
                                                              |
5:21    a minor (two bars) -----------------+           -1 semitone
                                            |                 |
                                      -1 semitone             |
5:24    e minor (one 6/4 bar) --------------|-----------------+
5:27    g-sharp minor (ten bars) -----------+                 |
                                            |           -1 semitone
                                      -1 semitone             |
5:42    d-sharp minor (one 6/4 bar) --------|-----------------+
5:45    g minor (nine bars) ----------------+

6:00    e minor (two bars) -----------------+
6:03    b minor (one 6/4 bar)               |
                                      -1 semitone
================ REPEAT #1 =================|===========================
                                            |
6:05    e-flat minor (eight bars) ----------+

6:18    g minor (two bars)
6:21    d minor (one 6/4 bar)
6:24    f-sharp minor (ten bars)

6:40    c-sharp minor (one 6/4 bar)
6:42    f minor (eight bars)

6:55    a minor (two bars)
6:58    e minor (one 6/4 bar)
7:01    g-sharp minor (ten bars)

7:17    d-sharp minor (one 6/4 bar)
7:19    g minor (nine bars)

7:33    e minor (two bars)
7:36    b minor (one 6/4 bar)

================ REPEAT #2 =============================================

7:39    e-flat minor (eight bars)

7:52    g minor (two bars)
7:55    d minor (one 6/4 bar)
7:58    f-sharp minor

8:04    N.C.
8:10    f-sharp minor (synth arpeggios)
8:16    f minor (synth arpeggios)
8:21    End of song

Track timings are on the left, and I've also shown some of the relationships I've noticed between tonal centers.

Now, I've read other pages here on Music SE regarding modulation, including

• Help with tonicization, modulation and modal interchange
• When did the half-step/whole-step modulation in the middle of a song become popular?
• How to train recognizing chords by ear ?
• How many types of modulation are there?

...but I'm still baffled by "West of Hollywood". This song seems to throw all the rules governing tone-center changing and modulation right out the window. And yet IMO, the song never sounds confusing or disjointed (Potter's sax solo surely plays a part in maintaining the integrity of the song).

So, my questions are:

• Is there a modulation style/technique (concurrent with contemporary music theory) present in "West of Hollywood"?
• Can anything be gleaned from the tonic relationships I've noted in the above chart?
• Is there some subtle, seldom-used, or "secret" formula or music-theory "hack" Becker and Fagen used to pull this off? (I wouldn't put it past them--these two musicians are clever and cunning!) ;-)

Thanks for your time and consideration!

Answer 1

One possible explanation is the role of common tones among the chords.

In the above example, you'll see that there is precisely one common tone between each adjacent chord. The common tones are shown with filled-in noteheads; there are two in each chord because one is the common tone with the prior chord, the other the common tone with the next chord. The X noteheads show chord tones not common with either the preceding or succeeding chord.

Playing this at the piano will make the connections really obvious!

These common tones help to smooth out the chord progressions. In most cases, there is a net movement of only two semitones between the chords. Between the first two chords, for instance, D moves to E♭ and B moves to B♭, a total of just two semitones. (In fact, some theorists will claim that, since D to E♭ is ascending and B to B♭ descending, the voice leading actually cancels itself out, resulting in a net movement of zero half steps.)

In other cases, there is a net movement of three semitones. From A minor to E minor, for instance, we see C to B (one half step) and A to G (two half steps). But no chord progression moves any more than three half steps at a time.

Great question, and great piece; Steely Dan is really terrific! If you're really interested in an academic approach to Steely Dan's music, you may want to check out this article by Walt Everett. (For what it's worth, he doesn't address this piece much, only calling it a part of a "highly experimental" album and that the piece doesn't "settle into any particular scale-degree functions." See pp. 214--215.)