Module 11: Harmony II: substitution and reharmonisationLesson 3advanced⏱ 90 min + two weeks of daily practice

Diminished chords and passing harmony

Use diminished seventh chords as chromatic passing chords, as rootless dominant 7b9 chords and as auxiliary colour on a static chord, and exploit their symmetry so that one shape covers four chords.

Why one chord does four jobs

The diminished seventh chord is the most economical chord in jazz. It has four notes stacked in minor 3rds, it repeats itself every three frets, it contains two tritones instead of one, and it can be heard as a passing chord, as a dominant without its root, or as a colour on a chord that is not moving at all. Pianists and arrangers lean on it constantly; guitarists often avoid it because the shapes look unfamiliar. By the end of this lesson you should have exactly one shape per string set in your hands and know four things to do with it.

You met the chord as viiº7 of harmonic minor in minor-key harmony and as #IVº7 of the jazz blues in the blues lesson. This lesson explains why those two uses are the same thing.

Symmetry: one dim7 is four dim7s

Build a diminished seventh on B and look at its notes. Then build one on each of its other three notes.

Spelled strictly, the four chords use different note names, but on the fretboard they are the same four pitches in a different order. A dim7 chord has no root in the practical sense: any of its notes can be called the root, and the chord symbol on the chart is usually chosen for the bass line, not for the theory. What this means for your hands is that every dim7 shape is also a shape for the dim7 chords three, six and nine frets away. Learn one drop-2 fingering on strings 5–4–3–2 and you can play every diminished chord there is by sliding it in three-fret steps.

Look at the frets: the four inversions are one fingering moved up three frets at a time. In Module 9 you will see the same property in the diminished scale; here you only need the chord.

Diminished as a rootless dominant 7b9

Now put the four notes of Bdim7 next to G7b9.

Bdim7 is G7b9 without the G. That is the single most useful fact in this lesson. A dim7 chord built on the 3rd of a dominant is the top four notes of that dominant's 7b9, so whenever a chart says G7b9 you can play a Bdim7 shape and let the bass player supply the root, and whenever a chart says Bdim7 resolving to C you can think "G7b9" and play your dominant vocabulary. The chord in bar 2 of the example below is G7b9 played as four Bdim7 shapes, one per beat, sliding up three frets each time. All four are the same chord, so the symbol does not change, and all four resolve to C.

\tempo 90
.
\ts 4 4
:1 (5.5 7.4 5.3 6.2){ch "Dm7"} | :4 (2.5 3.4 1.3 3.2){ch "G7b9"} (5.5 6.4 4.3 6.2) (8.5 9.4 7.3 9.2) (11.5 12.4 10.3 12.2) | :1 (10.5 10.4 9.3 12.2){ch "Cmaj7"} |

Because the symmetry works in both directions, one diminished chord is the rootless 7b9 of four dominants: Bdim7 (= Ddim7 = Fdim7 = Abdim7) is the top of G7b9, Bb7b9, Db7b9 and E7b9. The table shows the same thing from the other side: Cdim7 lives inside four different 7b9 chords. When you are improvising, this is why a diminished arpeggio works over any of four dominants, and when you are comping, it is why a single dim7 shape can harmonise an entire 7b9 line.

Passing diminished chords

The classic use of dim7 is as a chromatic passing chord between two diatonic chords whose roots are a whole step apart. The diminished chord fills the half step in the bass and its other notes move by half step into the next chord. Between I and ii in C the passing chord is C#dim7; between ii and iii it is D#dim7. This progression, I–#Iº7–ii–#IIº7–iii, is the opening of many swing-era tunes and the standard way to harmonise a rising bass line.

\tempo 100
.
\ts 4 4
:2 (3.5 5.4 4.3 5.2){ch "Cmaj7"} (4.5 5.4 3.3 5.2){ch "C#dim7"} | (5.5 7.4 5.3 6.2){ch "Dm7"} (6.5 7.4 5.3 7.2){ch "D#dim7"} | :1 (7.5 9.4 7.3 8.2){ch "Em7"} |

Now apply the rootless-dominant idea to this and the passing chords stop being mysterious. C#dim7 is A7b9 without its root, and A7 is V7/ii from lesson 1. D#dim7 is B7b9 without its root, and B7 is V7/iii. An ascending passing diminished chord is a secondary dominant 7b9 with the bass moved from the root up to the 3rd. That is why it sounds like it is pulling towards the next chord: it is a dominant.

The descending version works between iii and ii: Em7 | Ebdim7 | Dm7, often continuing into G7 and C. In this direction the diminished chord is not a dominant of the chord that follows (Ebdim7 contains the notes of D7b9, which points at G, not at Dm7); it is a pure chromatic connector, and the ear accepts it because the bass and two inner voices all fall by half step. Charts spell it either Ebdim7 or D#dim7 depending on what is easiest to read; the engine's strict spelling in the table below shows why nobody writes it out with double flats.

\tempo 100
.
\ts 4 4
:2 (5.4 7.3 5.2 7.1){ch "Em7"} (4.4 5.3 4.2 5.1){ch "Ebdim7"} | (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"} |

#IVº7 in the blues

The most famous passing diminished chord is the one in bar 6 of the jazz blues. In F, bar 5 is Bb7 (IV7), bar 6 is Bdim7 (#IVº7) and bar 7 returns to F7, usually with the 5th in the bass so that the bass line goes Bb–B–C. Three of the four notes of Bb7 are also in Bdim7 (the table at the top of this lesson shows that Bdim7 contains D, F and Ab), so only the root moves, up a half step. Then the whole chord resolves into F7. Here are bars 5–8 of an F blues with drop-3 shapes on strings 6–4–3–2, the way a guitarist in a trio would play them.

\tempo 110
.
\ts 4 4
:1 (6.6 6.4 7.3 6.2){ch "Bb7"} | (7.6 6.4 7.3 6.2){ch "Bdim7"} | (8.6 7.4 8.3 6.2){ch "F7"} | :2 (8.6 7.4 9.3 8.2){ch "Am7"} (8.6 7.4 7.3 7.2){ch "D7"} |

For soloing, the rootless-dominant idea tells you what to play: Bdim7 is the top of G7b9, so a G7b9 line works, but so does a plain Bdim7 arpeggio, which is what most players actually use because it sits so well against the Bb7 before it. The line below plays Bb7 chord tones, then the diminished arpeggio with only one note changed, then F7 chord tones. Hear how the single note that changes (Bb to B) is the whole story of bar 6.

\tempo 120
.
\ts 4 4
:8 8.4{ch "Bb7"} 7.3 6.2 9.2 6.1 9.2 6.2 7.3 | 9.4{ch "Bdim7"} 7.3 6.2 9.2 7.1 9.2 6.2 7.3 | 6.2{ch "F7"} 5.1 8.1 5.1 6.2 8.3 5.3 7.4 | :4 10.4 7.4 :2 r |

Auxiliary diminished: colour on a chord that stays put

The fourth use is different in kind. An auxiliary (or "common-tone") diminished chord is a dim7 built on the same root as the chord you are already on, used to decorate it without going anywhere: Cmaj7 | Cdim7 | Cmaj7. Nothing resolves in the functional sense; three notes step away and come back while the bass holds. The sound is characteristic of early jazz, of Ellington, and of ballad intros, and it is the chord behind a lot of "Imaj7 to Iº7" moves in standards. Over a dominant it works the same way: G7 | Gdim7 | G7.

\tempo 72
.
\ts 4 4
:1 (3.5 5.4 4.3 5.2){ch "Cmaj7"} | (3.5 4.4 2.3 4.2){ch "Cdim7"} | :2 (3.5 5.4 4.3 5.2){ch "Cmaj7"} (3.5 4.4 2.3 4.2){ch "Cdim7"} | :1 (3.5 5.4 4.3 5.2){ch "Cmaj7"} |

How do you tell an auxiliary diminished from a passing one on a chart? Look at the bass: if the dim7 has the same root as the chord before or after it, it is auxiliary; if its root is a half step between two chords, it is passing. And if it is a half step above a dominant's root and resolves down, it is probably the rootless 7b9 of a tritone sub, which is an exercise for the end of this lesson.

Fingering the diminished chord

A few practical points, because the shapes are the reason most guitarists under-use this chord:

• On strings 5–4–3–2 the drop-2 shape is a four-fret box with the index finger on the 3rd string. The same chord on strings 4–3–2–1 is the familiar "dim7 on the top strings" box, two adjacent pairs of frets. Learn both; the top-string version is the one for chord melody.
• Because the chord repeats every three frets, you never need to move more than one fret to find the nearest shape for any dim7. Decide by the bass line, not by the chord name.
• When a dim7 lasts a whole bar, play two different inversions in the bar (as in the G7b9 example) rather than holding one. It is what pianists do and it keeps the bar alive.
• For a 7b9 chord with no bass player, use a shell (root, 3rd, 7th) and add the b9 on top, or play the dim7 shape with the root in the bass on the 6th string: that is the drop-3 7b9 voicing you will find in the chord dictionary.

Exercises

1. One shape, four chords. Play Bdim7 on strings 5–4–3–2 in all four positions (frets 2, 5, 8, 11), naming the chord by its bass note each time. Then the same on strings 4–3–2–1.
2. Rootless 7b9. Play Dm7 | G7b9 | Cmaj7 with the four diminished shapes in bar 2, in all keys around the cycle. Then say which dim7 you are using for each 7b9 chord (the one on its 3rd).
3. Ascending passing chords. Play I–#Iº7–ii–#IIº7–iii in all keys, drop-2, 90 bpm. Then play the same thing thinking "I, A7b9, ii, B7b9, iii" and notice it is the same fingering.
4. Descending passing chords. Play iii–bIIIº7–ii–V–I on strings 4–3–2–1 in all keys. Keep the top voice falling by step.
5. Blues bars 5–8. Play the F blues example, then transpose to Bb, C, G and Eb. Add the line over Bb7 | Bdim7 | F7 and transpose it with the chords.
6. Auxiliary. Play Imaj7 | Iº7 | Imaj7 and V7 | Vº7 | V7 in five keys, slowly, with a bass note held.
7. Analysis. Take the chord list from lesson 1. For each dim7 chord you can find in your tunes, decide: passing up, passing down, auxiliary, or rootless 7b9. Write the dominant it stands for where there is one.

Quiz