Module 14: Modern harmony and rhythmLesson 3advanced⏱ 90 min + 25 min daily for three weeks

Triad pairs and intervallic improvisation

Improvise with two major triads a whole step apart, the hexatonic scales they form, pairs taken from melodic minor over altered and Lydian-dominant chords, and lines built from 4ths and octave displacement.

Why two triads are better than one scale

Bebop lines are built from chord tones, approach notes and scales, and they sound like bebop. From the mid-1960s a different melodic logic appeared in the playing of John Coltrane, Wayne Shorter, Woody Shaw and later Michael Brecker and Kurt Rosenwinkel: lines made of triads, two at a time, with wide intervals and an open, almost rootless quality. The device is the triad pair: two triads with no notes in common, usually major triads a whole step apart, alternated to build a line. Six notes, two shapes, and a sound that is unmistakably modern.

Why it works: a major triad is the most consonant, recognisable shape in Western music, so a line made of triads sounds strong and intentional even when the triads are not the chord of the moment. And because the two triads share no notes, the ear hears a six-note scale (a hexatonic) rather than a sequence of arpeggios; that scale is missing one note of the parent seven-note scale, which is usually the one that would have pinned the line down to conventional harmony.

Prerequisites: the close-position triad shapes on strings 3-2-1 and 4-3-2 from Triads, the arpeggios from Seventh-chord arpeggios in position, and the upper-structure triads lesson, which showed that the useful triads over a dominant come in whole-step pairs.

Adjacent diatonic triad pairs

Take any major scale and its modes. Among the seven diatonic triads, the two major triads that lie a whole step apart (IV and V of the parent major scale) share no notes. Over a chord that uses that scale, alternating them gives a hexatonic line that leaves out the parent's 3rd degree.

The table shows the pairs you will use most, which chord each pair lives over, the scale the engine checks the line against, and the note the pair leaves out.

Notice that the same pair, F and G, serves three different chords. That is the whole economy of the method: one pair, learned thoroughly, is vocabulary over every chord whose scale contains it. The omitted note matters as much as the ones you play. Leaving out the 7th over Fmaj7#11 means the line never says "major seventh"; it says "Lydian", which is lighter and more modern.

The F and G pair over Fmaj7#11

Practise a pair first as a mechanical sequence (triad up, next triad down, in every inversion) and only then as a line. The étude below alternates F and G in close position through the 7th-to-10th fret region, then breaks the pattern in the last two bars so that it sounds like a phrase rather than an exercise.

\tempo 132
.
\ts 4 4
:8 8.5{ch "Fmaj7#11"} 7.4 10.4 9.4 7.3 8.2 10.2 8.1 | 10.1 7.1 8.2 10.3 10.4 7.4 9.4 7.3 | 7.3 8.2 10.2 8.1 10.1 8.1 10.2 8.2 | :2 10.3 :4 7.4 r |

Then move the pair, not the position: the same two triad shapes one whole step higher (G and A) are the pair for Gmaj7#11, Em7 and A7sus4; one whole step lower (Eb and F) for Ebmaj7#11, Cm7 and F7sus4.

Pairs from melodic minor

Melodic minor contains two major triads a whole step apart, on its 4th and 5th degrees, and because melodic minor is the parent of both the altered scale and Lydian dominant, those two triads are the pair for the most important modern dominant sounds.

Ab melodic minor is the parent of G altered (its 7th mode), and its 4th and 5th degrees carry the Db and Eb major triads. Over G7 those two triads supply b5, b7, b9 (Db) and b13, root, #9 (Eb): every alteration in one pair. The omitted note is B, the 3rd of G7, which is why the sound is so dark and why it needs a resolution to make sense.

\tempo 132
.
\ts 4 4
:8 11.4{ch "G7alt"} 10.3 9.2 9.1 11.1 8.2 8.3 8.4 | 9.1 9.2 10.3 11.4 8.4 8.3 8.2 11.2 |

The same two scale degrees of G melodic minor give C and D major: the pair over C7#11 (Lydian dominant, the 4th mode). Here the omitted note is Bb, the 7th, so the line sounds like a bright major triad pair with an F# in it, which is exactly how Wayne Shorter's dominant chords sound.

\tempo 132
.
\ts 4 4
:8 10.4{ch "C7#11"} 9.3 8.2 8.1 10.1 10.2 7.2 7.3 | 7.4 11.3 10.2 10.1 12.1 8.1 8.2 9.3 | :4 10.4 :8 7.3 10.2 :4 8.2 :8 9.3 10.4 | :1 12.1 |

A ii-V-I étude from pairs

Pairs can be chained through a progression. Over the ii the étude uses the two triads inside Dm9 (F and A minor); over the V, the Db and Eb pair; over the I, C and D, which asks for a Lydian I chord, written here as Cmaj13#11. The V bar is checked against G7alt with allow=Db: the engine's 7alt symbol has no b5, and Db is the b5/#11 that the Db triad brings from the altered scale.

\tempo 132
.
\ts 4 4
:8 8.5{ch "Dm9"} 7.4 10.4 9.3 7.3 10.3 5.2 7.3 | 11.4{ch "G7alt"} 10.3 9.2 9.1 11.1 8.2 8.3 8.4 | 9.3{ch "Cmaj13#11"} 8.2 10.2 10.1 8.1 7.2 9.3 7.3 | :2 8.2 :4 10.4 r |

When you transpose, do not transpose the frets. Work out the pair for each chord from its root (for the V7alt: the major triads on the b5 and the b13; for the Lydian I: the triads on the root and the 9th), find them in the position you are in, and rebuild the line. That is slower and it is the point: the method is a way of thinking, not a lick.

Intervallic lines: 4ths and octave displacement

Triad pairs give you wide intervals almost by accident. Two more techniques make wide intervals the deliberate material of the line.

Lines in 4ths

A melodic line built from diatonic 4ths has the same floating, modal quality as the quartal voicings: the line is a broken-up version of the chords. On guitar, diatonic 4ths in one position lie across adjacent strings at the same or neighbouring frets, so these lines are easier to finger than they are to hear. Start with cells of four ascending 4ths, then reverse and vary them.

\tempo 120
.
\ts 4 4
:8 7.4{ch "Dm7"} 7.3 8.2 8.1 9.4 9.3 10.2 10.1 | 10.1 10.2 9.3 9.4 8.1 8.2 7.3 7.4 | 5.4 5.3 6.2 7.1 :4 10.1 :8 8.1 10.2 | :2 7.3 r.2 |

Octave displacement

Take a plain scale and move every second note up or down an octave. The pitches are the ones a beginner plays; the contour is not. Practise it on one scale until the string skipping is clean, then apply it to a line you already know: any bebop phrase becomes "modern" when two of its notes jump an octave.

\tempo 100
.
\ts 4 4
:8 5.5{ch "Dm7"} 5.2 3.4 3.1 7.4 7.1 10.4 10.1 | 10.1 10.4 7.1 7.4 3.1 3.4 5.2 5.5 | :4 5.5 r :8 5.2 3.4 3.1 7.4 | :2 7.1 r.2 |

Exercises

1. Mechanical pairs. F and G triads on strings 3-2-1, then 4-3-2, alternating in all three inversions, ascending and descending, 80 bpm in eighths. Then G and A, then Eb and F.
2. Fmaj7#11 étude as written at 100, 120, 132 bpm; then play two choruses of free improvisation on Fmaj7#11 using only the six notes.
3. Altered pair. Db and Eb over G7alt for two bars, resolving to any Cmaj7 phrase; then over C7alt (Gb and Ab), F7alt (B and Db), Bb7alt (E and Gb). Say the triads aloud before each key.
4. Lydian-dominant pair. C and D over C7#11; then F and G over F7#11; then Bb and C over Bb7#11.
5. ii-V-I étude in C as written, then in F and Bb from the progression table.
6. 4ths and displacement études as written; then apply octave displacement to a ii-V-I line from Approach notes and enclosures: displace two notes per bar.

Quiz