1

Jazz Theory and Practice

Module 1, a, b, c:

Tetrachords and Scales

A. The basic tetrachords, and other melodic patterns

Modules 1 and 2 are about jazz basics: chords and scales. The

chords could have come first, and often do, but chords and scales (or modes) are always linked in the jazz world: every

chord, especially every 7th chord, has a matching scale. Every scale can be broken into parts, or melodic cells. We begin our

study with these short 3-note and 4-note melodic cells, which may stand alone as a melodic source for jazz improvisation, (see

examples of “licks” at the end of this section) but also combine to form larger melodic patterns and scales.

A tetrachord (literally “four strings”) consists of four notes in a

row, and has been recognized as an important musical element

since the music of the Ancient Greeks. Almost 2500 years ago the Greeks defined the tetrachord as the smallest melodic

element, and combined tetrachords to form the “Greater Perfect System” which became the foundation for scales and music

theory. Significantly, a textbook known to many Canadian jazz musicians: Delamont, Gordon: Modern harmonic technique

begins the study of jazz theory with tetrachords.

Most musicians would associate a tetrachord with the bottom half or the top half of a scale or mode. There will be a detailed

introduction to various scales later in Module 1; for the moment a few different scales will show how tetrachords are combined.

The tetrachord is usually contained within a perfect fourth. The

familiar major scale, for example, consists of two identical major

tetrachords; identical because each tetrachord has the same pattern of whole steps (W) and half steps (H):

1a1

Copyright © 2012 Peter J. Clements

2

The pattern of whole steps and half steps in the minor tetrachord

forms the lower half of the minor scale, and many similar scales:

1a2

When two minor tetrachords are joined, they form a dorian

mode (or dorian scale), a scale that sounds very close to the natural minor scale:

1a3

The natural minor scale combines two tetrachords: a minor

tetrachord and a Phrygian tetrachord:

1a4

The Phrygian scale, another scale that sounds very close to a natural minor scale, is composed of two Phrygian tetrachords:

1a5

The harmonic minor scale combines the minor tetrachord and

the harmonic tetrachord. Notice that the harmonic tetrachord

has a larger interval in the middle: a whole step and half step combined (an augmented second):

3

1a6

Any pair of tetrachords may be combined. A Gypsy Minor (Byzantine) scale combines two harmonic tetrachords:

1a7

The four basic tetrachords, then, are Major, Minor, Phrygian, and

Harmonic.

1a8

There is another important four-note cell that is made up entirely of whole steps:

1a9

It is not a tetrachord by the strict definition (since the overall

span is an augmented fourth, not a perfect fourth), but will be included in our study, and we will identify it as the tritone

tetrachord. (Tritone = 3 tones, or whole steps). There are two of the seven common modes (“church” modes) that contain the

4

tritone tetrachord, the Lydian, and the Locrian. The tritone

tetrachord produces a feeling of instability in both modes:

1a10

The whole-tone scale can be seen as two overlapping tritone tetrachords:

1a11

The whole-tone scale contains only whole steps, and has a

strong feeling of instability (there is really no tonic or dominant note) created by the tritones. You will see that the whole steps

are usually written as major seconds, but one of the intervals has to be respelled (as a diminished third) in order to come back

to the beginning note. The scale above could also be written with the sharps rewritten as flats (G-flat, A-flat, and B-flat), but

there would still be one “odd” interval in the scale.

There are two common three-note cells, filling in a perfect fourth

just like the tetrachord, and using just two intervals: a minor third and a major second (or whole step). We will refer to these

as the major trichord, and the minor trichord:

5

1a12

One version (there are several versions!) of the pentatonic scale uses two major trichords:

1a13 Children throughout the world know a chant (sometimes called

“The Teasing Song”) that uses only the notes of the minor trichord:

1a14

The minor pentatonic scale (often used in jazz improvisation) is

made up of two minor trichords:

1a15

A single note inserted between the two minor trichords produces

the common Blues Scale:

1a16

6

The two trichords provide ideal raw material for “licks”: short

melodic cells, typically two bars long, and often used for a call-response improvisation. The “lick” also needs a rhythmic

pattern, usually with some syncopation. Here are some licks using only the trichord pitches.

1a17

Any of the tetrachords are good sources for licks, especially if

they contain a “bluesy” minor 3rd.

1a18

The following chart summarizes the tetrachords and trichords:

TETRACHORD COMPOSITION

(W=whole; H = half step)

Major W W H

Minor W H W

Phrygian H W W

Harmonic H W+H H

Tritone W W W

TRICHORD

Major M2(W) m3(W+H)

Minor m3 M2

7

Something to listen to: Keith Jarrett: “de drums” from the

album Priceless Jazz. (listen for trichords).

Miles Davis: “Blue ‘n’ Boogie” (by Dizzy Gillespie) (The same minor trichord!)

You should be able to find both of these pieces on YouTube.