Tritone Substitution

The previous lesson treated symmetrical scales. An even structure has no center and looks the same from any note. That was framed negatively as a loss of center, but it also has a use.

There is a symmetrical component inside the dominant seventh as well: the tritone.

Where the tension of a dominant seventh comes from

G7 is G B D F. Of those four notes, the ones demanding resolution are B and F.

• B (the third) is the leading tone, rising a half step to C
• F (the seventh) is the dissonance, falling a half step to E

Measure the distance between them and B to F is a diminished 5th — a tritone. What makes a dominant seventh a dominant seventh is neither its root nor its fifth but this tritone.

And a tritone is symmetrical. At six half steps it is exactly half of the twelve-half-step octave, so inverting it produces another tritone. B to F is a diminished 5th and F to B is an augmented 4th; both are six half steps.

That symmetry is what a tritone substitution is.

Move the root by a tritone

Move the root G of G7 by a tritone and you get Db. A dominant seventh on Db is Db7 = Db F Ab Cb.

Setting the two side by side:

	G7	Db7
Root	G	Db
Third	B	F
Fifth	D	Ab
Seventh	F	Cb (= B)

Both B and F appear in each chord, and their roles have swapped. The B that was the third of G7 is the seventh (Cb) of Db7. The F that was the seventh of G7 is the third of Db7.

The resolving force of a dominant seventh comes from its tritone. With that tritone preserved entire, Db7 wants to resolve to the same place, and it can therefore be used in place of G7.

Note the spelling of the seventh: Db7’s seventh is Cb, not B. Being at the seventh, its letter has to be C — the principle established back in Unit 0. Lead sheets usually print B, and the two sound identical, but Cb is the correct spelling.

Check

What is the tritone substitute for C7?

Gb7G7Db7F7

Check answer

The bass slides by half step

The practical effect of a tritone substitute has less to do with color than with the motion of the bass line.

In C major, ii – V – I is Dm – G7 – C, whose roots descend by perfect 5ths: D – G – C (equivalently ascending fourths).

Replace the V with its substitute and it becomes Dm – Db7 – C, whose roots go D – Db – C, descending by half step.

ii–V–I against ii–♭II7–I

▶ii – V – I▶ii – ♭II7 – I

Check: Both begin on the same Dm and arrive at the same C. In the first the bass leaps by a fifth; in the second it descends by half step. The upper voices are nearly identical and the shared tritone is unchanged, so the sense of resolution is the same. Only the way the bass walks has changed. Jazz and city pop use it constantly for that smoothness.

bass D – G – C

The key point is that it works without changing the upper voices. As Fig. 2 showed, F and B belong to both chords, so those two parts can simply be held. Substituting the bass alone produces the tritone substitution.

The tensions trade places

One further property demonstrates the relationship.

The root and fifth of Db7 are the same notes as the altered tensions of G7.

Note of Db7	Relative to G7
Db (root)	♯11
Ab (fifth)	♭9

So G7(♭9, ♯11) and Db7 overlap in a substantial share of their sounding notes. The previous lesson derived altered tensions from the half-whole diminished scale; they can equally be explained as the chord tones of a tritone substitute.

One phenomenon admitting two explanations is a sign that both are viewing the same underlying symmetry from different angles. Two dominant sevenths joined by a tritone were sharing one tension from the start.

♭II7 against ♭II6

Recall the Neapolitan chord of Unit 8. Its root was Db as well.

Chord	Type	Standard position	Function
Neapolitan ♭II6	major triad	first inversion (bass on F)	subdominant
Tritone substitute ♭II7	dominant seventh	root position (bass on Db)	dominant

The root is the same Db, and whether a seventh is present reverses the function. Adding the seventh Cb (= B) supplies a leading tone and converts the chord to a dominant.

The treatment of the bass is opposite too. The Neapolitan uses first inversion to put the subdominant F in the bass, projecting subdominant character. The tritone substitute uses root position to put Db in the bass, projecting the dominant character of a half-step descent.

Two chords on the same root take different roles purely through type and bass. Unit 3’s point that an inversion is the same chord in another guise, and that changing the bass changes the meaning, is recovered here in its sharpest form.

Check

What tells you a chord built on Db is functioning as a tritone substitute rather than as a Neapolitan?

The preceding chord is DmDb is in the bass and the chord contains the seventh CbDb is the highest noteThe chord has three voices

Check answer

▶ Compare the notes of G7 and Db7 in the chord finder Enter the two chords in turn and look for shared notes. Two of the four match, and those two turn out to be the third and the seventh Chord Finder →

That completes Unit 9. Thickening chords with extensions, holding color with modes, cutting gravity with symmetrical scales, and replacing chords by substitution. None of it breaks the rules of classical harmony; all of it takes the mechanism apart and reuses the pieces.

The next unit is ear training, where the structures learned so far get practiced by ear alone, without a score.