Module 11: Harmony II: substitution and reharmonisationLesson 2advanced⏱ 90 min + two weeks of daily practice

Tritone substitution

Replace any dominant with the dominant a tritone away, understand why the guide tones make it work, voice-lead the result into chromatic bass lines, and use substitute ii–Vs and tritone-sub turnarounds in every key.

Why two dominants can do the same job

Every dominant seventh chord contains one tritone, the interval between its 3rd and its 7th, and that tritone is the engine of the chord: it is the unstable interval that wants to collapse into the 3rd and root of the target. Now look at what happens a tritone away. G7 has the guide tones B and F. Db7 has the guide tones F and Cb, and Cb is the same key on the piano as B. The two chords share their tritone, which means they share the two notes that do all the work, so either of them can resolve to C. This is tritone substitution: any dominant chord can be replaced by the dominant seventh whose root is a tritone (three whole steps, six frets) away. The substitute is written bII7 when it replaces V7, because its root is a half step above the tonic.

Read the table across. The 3rd of G7 is the 7th of Db7, and the 7th of G7 is (enharmonically) the 3rd of Db7. Every other note is different: the substitute swaps the root and 5th of G7 for two notes a half step above the tonic and the 5th. Those two new notes are what give the substitution its sound: a chromatic bass line (Dm7 to Db7 to C) in place of the cycle-of-fifths bass (D to G to C), and a darker, more dissonant dominant that still resolves cleanly.

The rule for finding the substitute is easy to state and easy to get wrong under pressure, so practise it: the tritone sub of any dominant is the dominant seventh on the note six frets away (up or down, it is the same note). G7 becomes Db7, C7 becomes Gb7 (or F#7), D7 becomes Ab7, A7 becomes Eb7, E7 becomes Bb7, B7 becomes F7, and each of those pairs works in both directions.

Hearing it: the same guide tones, two different basses

The quickest way to convince your ear is to play the shared guide tones with each bass note in turn. In the example, the first two bars are G7 resolving to Cmaj7 with a shell voicing from Module 4; the last two bars are Db7 resolving to the same Cmaj7. The 4th and 3rd strings play exactly the same frets under both dominants. Only the bass note changes, and it changes everything about the colour while changing nothing about the resolution.

\tempo 72
.
\ts 4 4
:1 (3.6 3.4 4.3){ch "G7"} | (8.6 9.4 9.3){ch "Cmaj7"} | (9.6 9.4 10.3){ch "Db7"} | (8.6 9.4 9.3){ch "Cmaj7"} |

Notice how the Db7 resolves. Its root falls a half step to C, and the two guide tones resolve exactly as they did under G7. Everything moves down by step or stays still. That is why the substitution is so smooth in the bass and why bass players love it: the line D–Db–C is the most natural thing a walking bass can do.

The turnaround with a tritone sub: I–VI7–ii–bII7

The first place to use the substitution is the turnaround you learned in the previous lesson. Cmaj7 | A7 | Dm7 | G7 becomes Cmaj7 | A7 | Dm7 | Db7, and the bass in the last two bars descends chromatically into the tonic. Here it is with drop-2 shapes on strings 5–4–3–2, with and without the substitution so that you can hear the difference in the same register.

\tempo 100
.
\ts 4 4
:2 (3.5 5.4 4.3 5.2){ch "Cmaj7"} (4.5 5.4 2.3 5.2){ch "A7"} | (5.5 7.4 5.3 6.2){ch "Dm7"} (5.5 5.4 4.3 6.2){ch "G7"} | (3.5 5.4 4.3 5.2){ch "Cmaj7"} (4.5 5.4 2.3 5.2){ch "A7"} | (5.5 7.4 5.3 6.2){ch "Dm7"} (4.5 6.4 4.3 6.2){ch "Db7"} | :1 (3.5 5.4 4.3 5.2){ch "Cmaj7"} |

The voice leading from Dm7 to Db7 is worth staring at: the root-position Dm7 shape and the root-position Db7 shape are the same fingering apart from the 2nd string, and that string is the F that both chords share (the minor 3rd of Dm7 and the major 3rd of Db7). From Db7 into Cmaj7, the bass falls a half step, the 4th-string note falls a half step, the 3rd-string Cb (B) is already the 7th of C and stays, and the F falls a half step to E. Four voices, three half-step moves and one common tone. This is the sound of bebop comping.

Substituting every dominant: the chromatic turnaround

The A7 in the turnaround is a dominant too, so it can also be substituted: A7 becomes Eb7. And the ii chord can be replaced by the related ii of the substitute, or simply by a dominant on the same root (II7 instead of ii7), which can then be substituted as well: D7 becomes Ab7. Do all three and the turnaround I–VI7–II7–V7 becomes I–bIII7–bVI7–bII7: Cmaj7 | Eb7 | Ab7 | Db7, four chords whose roots fall by whole and half steps instead of leaping in 5ths. This is the chromatic turnaround, the one Tadd Dameron and Bud Powell used, and once you can hear it the original cycle-of-fifths version sounds almost plain.

\tempo 110
.
\ts 4 4
:2 (3.5 5.4 4.3 5.2){ch "Cmaj7"} (4.5 5.4 3.3 4.2){ch "Eb7"} | (3.5 4.4 1.3 4.2){ch "Ab7"} (2.5 3.4 1.3 2.2){ch "Db7"} | :1 (2.5 2.4 0.3 1.2){ch "Cmaj7"} |

Play this slowly and watch the top note: it descends by step the whole way, which is the main reason the chromatic turnaround sounds so good on guitar. You are not obliged to substitute everything. The most common real-world versions are I–VI7–bvi7–bII7 (only the ii–V is replaced), I–bIII7–ii–bII7 (the VI7 and V7 are replaced, the ii stays), and I–VI7–ii–bII7 from the previous section. Try all of them and listen to how the amount of chromaticism changes.

The substitute ii–V: bvi7–bII7

A substitute dominant can bring its own related ii chord with it. The related ii of Db7 is Abm7 (the ii of Gb major), so the ii–V Dm7 G7 can become Abm7 Db7, a substitute ii–V that lands on the same Cmaj7. In Roman numerals this is bvi7–bII7–I. You will see it in the last two bars of many bebop heads and in the A sections of tunes whose composers liked a ii–V a half step above the tonic. It also appears as a two-bar "side-step" in solos: play the ii–V a half step up and resolve down.

\tempo 100
.
\ts 4 4
:2 (3.4 5.3 3.2 5.1){ch "Dm7"} (3.4 4.3 3.2 3.1){ch "G7"} | :1 (2.4 4.3 1.2 3.1){ch "Cmaj7"} | :2 (4.4 4.3 4.2 4.1){ch "Abm7"} (3.4 4.3 2.2 4.1){ch "Db7"} | :1 (2.4 4.3 1.2 3.1){ch "Cmaj7"} |

Keep one distinction clear. Dm7 Db7 keeps the diatonic ii and substitutes only the dominant, giving a chromatic bass. Abm7 Db7 replaces the whole ii–V with the one from the key a tritone away, and sounds like a brief sidestep into Gb before the resolution. Both are standard; which one a chart uses tells you what the composer wanted the bass to do.

Tensions on the substitute: why bII7 loves the #11

A tritone sub is normally written and played with a #11, and the reason is in the table at the top of the lesson. The #11 of Db7 is G, which is the root of the chord it replaces; the natural 9 of Db7 is Eb, and the 13 is Bb. All three are notes of C major, so Db7 with a 9 and a #11 sounds like a dominant that belongs to the key even though its root does not. The chord-scale that contains all of them is Db Lydian dominant, the fourth mode of Ab melodic minor, which you will study in Module 9. For now, remember the practical rule: on a tritone sub, play the natural 9 and the #11; on the original V7, play the b9 and the #9 if you want the same notes. Compare the rows of the table below: the b9, #9 and b13 of G7alt (Ab, A# and Eb) are the 5th, 13th and 9th of Db7, and the #11 of G7 is the root of Db7. The two chords are two names for one scale.

Here is a line that uses this. Over Dm7 it is plain chord tones; over Db7#11 it is the chord tones of Db7 plus the #11, and it resolves into Cmaj7 by half steps. Play it, then play the same line and think "G7alt" on the second bar: nothing changes except the name.

\tempo 120
.
\ts 4 4
:8 7.3{ch "Dm7"} 6.2 5.1 8.1 10.1 8.1 5.1 6.2 | 6.2{ch "Db7#11"} 4.3 6.3 6.4 6.3 4.3 6.2 8.2 | 8.2{ch "Cmaj7"} 5.2 5.3 4.3 :2 5.3 |

Where you will meet it

• The last two bars of a bebop tune are frequently I–bIII7–bVI7–bII7 or I–VI7–bvi7–bII7 instead of a plain I–VI–ii–V.
• Bridges of AABA tunes often use a chain of dominants with every second one substituted, so the bass walks down in half steps instead of leaping in 5ths. If you see a chart with dominants a half step apart (E7 | Eb7 | D7 | Db7 | C), you are looking at a backcycle (lesson 1) with alternate chords tritone-substituted.
• A ii–V a half step above the key at the end of a phrase is a substitute ii–V (bvi7–bII7).
• A dominant a half step above its target, anywhere, is a tritone sub of a secondary dominant: Bb7 going to Am7 is the sub for E7 (V7/vi), Eb7 going to Dm7 is the sub for A7 (V7/ii), and so on. In lesson 4 you will see that bVII7 going to I is a different animal (the backdoor), so check where the chord resolves before you label it.

Exercises

1. Name the sub. Say the tritone substitute of every dominant chord around the cycle of fourths: C7–Gb7, F7–B7, Bb7–E7, Eb7–A7, Ab7–D7, Db7–G7, then the reverse. Then do it from random roots.
2. Shared guide tones. Play the shell example (G7, Db7, Cmaj7) in all twelve keys. Keep the two upper notes identical between V7 and bII7 every time.
3. Turnaround with the sub. Play I–VI7–ii–bII7–I with drop-2 on strings 5–4–3–2 in all keys at 90 bpm. Then on strings 4–3–2–1 with your own inversions.
4. Chromatic turnaround. Play I–bIII7–bVI7–bII7–I in all keys. Then mix: substitute only one or two of the chords and decide which version you like in each key.
5. Substitute ii–V. Play Dm7 G7 | Cmaj7 and Abm7 Db7 | Cmaj7 back to back in all keys. Sing the bass line of each before you play it.
6. Lines. Play the line over Dm7 | Db7#11 | Cmaj7 in C, F, Bb, Eb and G. Then write a line over Cmaj7 | Eb7 | Ab7 | Db7 using only chord tones and the #11 of each dominant.
7. Find them. Take the chord list from lesson 1 and find every dominant that resolves down a half step. Label each as a tritone sub and write the chord it replaces above it.

Quiz