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Jazz Theory and Practice
Module 1, a, b, c:
Tetrachords and Scales
A. The basic tetrachords, and other scale 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 even by themselves (“licks”) are often used as a source for jazz
improvisation, 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 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 it doesn’t fall
within 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 tritone tetrachord, the Lydian,
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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
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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
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!)
Return to the menu, and try the PLAY/SING and WRITE exercises
for Module 1a.