Theory On Tap
Lesson 10, More Jazz Progressions

Introduction

In lesson 6, we covered the grand and glorious II/V/I progression, which is the most common set of chords in jazz. We also discussed how these "two-fives" may not always be in the key of the song. They often are relative to the "key of the moment" -- and it's very handy to be able to spot these two-fives and their related keys, so you'll have a better idea of what to play. And, you were shown some three note voicings that illustrated how the notes of the II-7/V7/Imaj7 chords can smoothly move from one chord to the next. That technique of smooth movement is called voice leading.

Now on to some new stuff:

Tritone Substitutions

Jazz players are a pretty non-conformist bunch. Not only do they insist on playing whatever the heck they want during solos, they don't even put much stock in the chords that are written. Very often, they'll substitute one chord or set of chords for another. One of the most popular substitutions is the tritone substitution. Check out the following chords:

II-7  V7   Imaj7
 D-7  G7   Cmaj7
| / / / / | / / / / |   original version

II-7  ♭II7  Imaj7
 D-7  D♭7   Cmaj7
| / / / / | / / / / |   new version, using a tritone substitution

We learned in lesson 6 that the most important notes of a seventh chord are the third and the seventh. The cool thing about a dominant seven chord (like the G7 above) is that its third and seventh can swap jobs, becoming the seventh and third of a new chord. That new chord is a tritone (flat fifth or sharp fourth) away. In the original example, G7 has B as its third, and F as its seventh. In the new version, the D♭ has F as its third and B as its seventh. The G7 and the D♭7 can be substituted for each other since they both share those notes, and thus both lead the ear to the Cmaj7.

Note: technically, the seventh of a D♭7 chord is C♭. It's still the same note as B, though. Notes like these that are spelled differently, but have the same pitch, are enharmonic to each other.

When playing three-note voicings on the Stick, like you learned in lesson 6, a tritone substitution couldn't be any easier to play. Just move the bass note down in half steps instead of fifths:

          II-7                ♭II7                Imaj7

    |---|---|---|---|   |---|---|---|---|   |---|---|---|---|
    |---|---|---|-X-|   |---|---|---|-X-|   |---|---|-X-|---|
mel |---|---|---|-X-|   |---|---|-X-|---|   |---|---|-X-|---|
    |---|---|---|---|   |---|---|---|---|   |---|---|---|---|
    |---|---|---|---|   |---|---|---|---|   |---|---|---|---|

    |---|---|---|---|   |---|---|---|---|   |---|---|---|---|
    |---|---|-X-|---|   |---|-X-|---|---|   |-X-|---|---|---|
bas |---|---|---|---|   |---|---|---|---|   |---|---|---|---|
    |---|---|---|---|   |---|---|---|---|   |---|---|---|---|
    |---|---|---|---|   |---|---|---|---|   |---|---|---|---|

But why stop at substituting the V7 chord? You can also replace the II-7 chord with the II chord that's relative to the new dominant chord. In other words, substitute the II-7 with a minor 7 chord that's also a tritone away:

II-7  ♭II7  Imaj7
 D-7  D♭7   Cmaj7
| / / / / | / / / / |     Tritone substitution on the V7 only

♭VI-7  ♭II7  Imaj7
 A♭-7  D♭7   Cmaj7
| / / / / | / / / / |     Tritone sub on the entire II/V progression

That last example would look like this:

          VI-7                 ♭II7                Imaj7

    |---|---|---|---|   |---|---|---|---|   |---|---|---|---|
    |---|---|---|---|   |---|---|---|-X-|   |---|---|-X-|---|
mel |---|---|-X-|---|   |---|---|-X-|---|   |---|---|-X-|---|
    |---|---|-X-|---|   |---|---|---|---|   |---|---|---|---|
    |---|---|---|---|   |---|---|---|---|   |---|---|---|---|

    |---|---|---|---|   |---|---|---|---|   |---|---|---|---|
    |---|---|---|---|   |---|-X-|---|---|   |-X-|---|---|---|
bas |---|-X-|---|---|   |---|---|---|---|   |---|---|---|---|
    |---|---|---|---|   |---|---|---|---|   |---|---|---|---|
    |---|---|---|---|   |---|---|---|---|   |---|---|---|---|

Notice that the first chord, a minor 7, looks just like the II-7 we all know and love, except that it's been moved right one string and down (lower in pitch) one fret. That's the easiest way to visualize a tritone on the Stick. For better voice leading, you'll probably want to invert the RH for that first chord, that is, move the lower RH note one octave higher. You'll notice something cool about how the RH moves to each chord. (No, I'm not telling. You'll have to pick up the Stick and try it yourself.)

Sus Chords and Slash Chords

       major triad           sus chord

    |---|---|---|---|    |---|---|---|---|
    |-X-|---|---|---|    |-X-|---|---|---|
mel |---|---|-X-|---|    |---|---|---|-X-|
    |---|---|---|-X-|    |---|---|---|-X-|
    |---|---|---|---|    |---|---|---|---|

In the second example, we've raised the third one fret. That's called a "suspended fourth", and that what the "sus" means. We call the fourth "suspended" because it's traditionally supposed to resolve back down the third. But in jazz, anything goes. For proof of that, listen to Herbie Hancock's "Maiden Voyage", which consists entirely of sus chords that never resolve.

Note: Although you most often will suspend the fourth, It's perfectly legal to have a "sus2" chord, which moves the third down a whole step. Also, don't let anyone tell you that the fourth takes the place of the third. In jazz you can get away with playing the third and fourth together, if you voice the chord tastefully.

A common way to voice a V7sus chord is to play a IV triad in the RH, and play the V root note in the LH. Here's one way to play that:

       V7sus or IV/V

    |---|---|---|---|
    |---|-X-|---|---|
mel |---|---|-X-|---|
    |---|---|-X-|---|
    |---|---|---|---|

    |---|---|---|---|
    |---|-X-|---|---|
bas |---|---|---|---|
    |---|---|---|---|
    |---|---|---|---|

VI/V is known as a "slash" chord, for obvious reasons. You play the chord above the slash, but put the single note underneath the slash in the bass. In the key of C, our slash chord would be "F/G", which you would pronounce "F slash G" or "F with G in the bass". No matter how you say it, it's a great substitution for a Gsus chord.

Note: Remember, I don't intend for you to play an F chord *and* a G chord on top of each other. The bottom note is just the bass note. Multiple triads played on top of each other (called polychords) will be covered in more depth in a later lesson. Be aware that although this is the notation style employed in most fake books, some people *do* use a slash to indicate a polychord.

Slash chords are very handy at indicating the inversion of chord. You would never see "C major, first inversion" in a jazz chart, but you would see "C/E". Slash chord are also an easy way to play seventh chords using triads, as you learned back in lesson 4. But the question remains, why does F/G substitute for G7sus? Look at the notes in each chord:

    G7sus               F/G                D-7/G

      F  ← 7th          C  ← 4th          C  ← 4th
      D  ← 5th          A  ← 9th          A  ← 9th
      C  ← 4th          F  ← 7th          F  ← 7th
      G  ← root         G  ← root         D  ← 5th
                                          G  ← root

With the F/G, we got rid of the fifth (which is the least important note, remember?), and added a ninth. (What's a ninth? We'll get to that.) If you were dead-set on putting that fifth back in, you could play the third chord, a D-7 chord over a G root note. Which leads us to...

Universal Truth #979: "A single V7sus chord can substitute for an entire major key II/V progression." Why? Because it contains many of the notes of the II-7 and the V7, rolled up into one handy-dandy chord.

Tensions

In lesson 4, part 2, you learned that a triad can be derived from a scale or mode by choosing every other note, until you have three notes. Each note is a third away from the other. In other words, a C major triad is C-E-G, because it's made up of every other note in a C major scale. Taking that concept further, you learned that you can add another third on top, making it a 7th chord. Going even further, you were introduced to chord extensions beyond the 7th, namely the 9th, 11th and 13th. (This stuff is important, so if it seems fuzzy, go back and reread Rick's lesson. I'll wait...)

Let's dig into that concept of extended voicings a bit more. Take a look at this C major scale, which repeats a bit. I've added numbers on top, representing the scale degree, or "note number":

1  2  3  4  5  6  7      8  9  10 11 12 13
C  D  E  F  G  A  B      C  D  E  F  G  A
                       [ one octave higher ]

So it stands to reason that if you played C-E-G-B-D, that D is called a ninth. If you added yet another third on top of that, an F, it's an eleventh. Still another third, the A, gives you the thirteenth. These added notes, beyond the seventh, are called "tensions" in jazz theory.

Technically, tensions are an octave higher, but in jazz you can voice a chord pretty much any way you want. A handy formula to remember is that the the ninth corresponds to the second note in the mode, the eleventh to the fourth, and the thirteenth to the sixth.

To get you started, here's a chart of ninth chords, derived from the C major scale:

Mode	notes (R,3,5,7,9)	type of chord	example
Ionian	C, E, G, B, D	Major 7, add 9	Cmaj7 (9)
Dorian	D, F, A, C, E	Minor 7, add 9	D-7 (9)
Phrygian	E, G, B, D, F	Minor 7, flat 9	E-7 (b9)
Lydian	F, A, C, E, G	Major 7, add 9	Fmaj7 (9)
Mixolydian	G, B, D, F, A	Dominant 9	G9
Aeolian	A, C, E, G, B	Minor 7, add 9	A-7 (9)
Locrian	B, D, F, A, C	Minor 7, flat 5, flat 9	B-7 (b5,b9)

Notice that the ninths, like all tensions, are usually notated in parenthesis. It can get a little confusing. Even though the second and the ninth are the same, a "9" by itself, not in parenthesis, means a dominant seventh chord, with the second/ninth added. Even though the sixth and the thirteenth are the same, you usually only call dominant chords "thirteenth chords", and reserve "sixth" chords for major and minor. To make things even worse, the word "fourth" is used when referring to major and sus chords, but minor and dominant chords would get the word "eleventh". Whew!

Exercise #1: What are the notes in the following chords (answers at the end):

1. Dmaj7 (9)
2. F-7 (9)
3. E9

ALT CHORDS Look back at the chord for the Locrian mode in the chart above. Notice how, to fit the mode, we've lowered the fifth and ninth of the chord. Notes that have been "flatted" or "sharped" are called "altered" notes. When you venture outside the standard, major scale, you'll run across several altered notes in your chords. In fact, you'll almost never come across an unaltered eleventh in a major or dominant chord, usually it's raised. Flat and sharp nines, flat fives, and flat thirteens are some other common and useful altered notes to know.

So what's the difference between a flat thirteen and a sharp five? On an enharmonic basis, nothing, the note, after alteration, is the same in both cases. But if the chord is notated as a sharp five, that means the raised fifth takes the place of the perfect fifth normally found in the chord. (And unlike the perfect fifth, you won't be able to leave it out of the voicing without changing the character of the chord.) You most often see flat fives on minor seventh chords. A flat thirteen, on the other hand, indicates that you should play a dominant seventh chord with a lowered thirteenth in it. You can actually get away with sneaking in the perfect fifth, if you voice it so that the fifth and the flat thirteenth aren't right next to each other.

MINOR TWO-FIVES So far, we've been dealing with chords based on modes of the major scale. There's a whole truckload of jazz standards that are in minor keys though, and our friend the II/V/I progression has a home there, too. Check out this chord progression, which sounds suspiciously like the beginning to Thelonious Monk's "'Round Midnight":

    I       ?           II      V          I
   Eb-7    C-7b5       F-7b5   Bb7(alt)   Eb-7
|   /   /   /   /   |   /   /   /   /   |  /  /  / etc...

	It's common for minor jazz tunes to have a dominant V chord as we see here. This would indicate that we're in harmonic minor, right? But if we're in harmonic minor, shouldn't the first chord be Eb-(maj7), instead of Eb-7? Truth is, we're in natural minor for some chords, and harmonic for others. As you learned in the two previous lessons by Grant Green on minor scales and chords, most music tends to use chords from various types of minor scales. Even in a mostly major song, like "Stella by Starlight", you may still find some minor two-fives. Just as in a major key, being able to spot them will help you decide what scale to play, and what tensions to add. In a minor II/V/I, you're likely to see:
	Position Chord Suggested Tensions I minor7 9 II minor7, b5 b9 V dom7 b9, #9, b13
	Usually, when soloing in a minor key like this, you can play natural minor on the I chord, then switch to harmonic minor for the II/V.
	MODAL INTERCHANGE You may have wondered about that C-7b5 chord up there, the one I put a question mark over. The chord could come from melodic minor (ascending), but playing melodic minor's natural seventh there sounds pretty awful in context with everything else. It's not derived from Eb natural minor or Eb harmonic minor either, so where does it come from? You might want to go ahead and take some aspirin for this one--it's a doozy.
	As it turns out, the entire first bar is an example of "modal interchange". For that one bar, we're actually in Eb Phrygian, and the C-7b5 is the VI chord. By the time we get to bar two, we're back in Eb minor. The Eb-7 chord really exists in both "worlds" and serves as a sort of anchor point for the ear. If you're familiar with the rest of "'Round Midnight", you may also notice that it goes back into Phrygian with an Ab7 in bar three (right where I put "etc..."). Steely Dan's "Doctor Wu" is another good example of modal interchange, going from Ionian to Aeolian and back in the chorus.
	PUTTING IT ALL TOGETHER Your final exam is to analyze the following song, identifying the key of the moment, minor and major II/V progressions, and other fun stuff. For extra credit, try reharmonizing the tunes with a few chord substitutions.
	These chords sound a heck of a lot like the jazz standard "Autumn Leaves". If this were a real chart, you'd see that the key signature has one sharp. The numbers below are bar numbers for later reference, and the colons are supposed to be repeat signs. Good Luck!
	A-7 D7 Gmaj7 Cmaj7 |:/ / / / | / / / / | / / / / | / / / / | 1 2 3 4 F#-7b5 B7 E-7 | / / / / | / / / / | / / / / | / / / /:| 5 6 7 8 F#-7b5 B7(b9) E-7 | / / / / | / / / / | / / / / | / / / / | 9 10 11 12 A-7 D7 Gmaj7 | / / / / | / / / / | / / / / | / / / / | 13 14 15 16 F#-7b5 B7(b9) E-7 Eb7 D-7 Db7 | / / / / | / / / / | / / / / | / / / / | 17 18 19 20 Cmaj7 B7(b9) E- | / / / / | / / / / | / / / / | / / / / | 21 22 23 24
	ANSWERS Exercise #1 Dmaj7 (9): D, F#, A, C#, E F-7 (9): F, Ab, C, Eb, G E9: E, G#, B, D, F#
	Song Analysis II V I IV A-7 D7 Gmaj7 Cmaj7 |:/ / / / | / / / / | / / / / | / / / / | 1 2 3 4 II V I F#-7b5 B7 E-7 | / / / / | / / / / | / / / / | / / / /:| 5 6 7 8 II V I F#-7b5 B7(b9) E-7 | / / / / | / / / / | / / / / | / / / / | 9 10 11 12 II V I A-7 D7 Gmaj7 | / / / / | / / / / | / / / / | / / / / | 13 14 15 16 II V II V(ts) II V(ts) F#-7b5 B7(b9) E-7 Eb7 D-7 Db7 | / / / / | / / / / | / / / / | / / / / | 17 18 19 20 VI V I Cmaj7 B7(b9) E- | / / / / | / / / / | / / / / | / / / / | 21 22 23 24
	Notes: The key signature and the first four bars put us firmly in the key of G. At bar 5, we suddenly switch to the key of E minor, which is the relative minor of G major. It might be tempting to just call the F#-7b5 a VII chord, and the E-7 a VI chord, but the dominant B7(b9) strongly suggests E harmonic minor for that section. We go back to G major for bars 13-16, then back to E minor for the rest of the song, taking a brief side trip into D major and C major, in bars 19 and 20 respectively.
	Bars 19 and 20 are tricky. Resist the urge to consider the E-7 in bar 19 to be a I in E minor, or a VI in G major, although it's both of these. It actually serves a more important role as part of a two-five into the D-7 of bar 20. That D-7 is in turn part of a two-five into the Cmaj7 of bar 21. In each two-five, the tritone substitute of the V7 chord is used. You would expect the E-7 and Eb7 to resolve to Dmaj7, but it throws you a curve ball, going to still another two-five. These "cascades" of two-fives are common in jazz.
	That section would be a good spot for some reharmonization. You could replace the two-five in bar 19 with a single sus chord, and "un-tritone" the Db7 in bar 20. That would give you:

 G/A       D-7  G7
| / / / / | / / / / |
19        20

But of course, that's just a suggestion. In the end, the theory doesn't matter a bit--it all comes down to playing what your ears want to hear.