JT 2.2 - Tetrachords

A tetrachord is four pitches within the span of 5 semitones (the interval called a perfect 4th).

It was the smallest system used in ancient Greek music (around 700 BC) and probably derived from the four notes on the early lyre.
Later, tetrachords were used to construct modes (predecessors of our present scales).

Four tetrachords relevant to our present Western music system and to Jazz are the :

In the following Audio each tetrachord is played three times. First twice slowly, then once at double the speed.

Audio 1


Tetrachords are used for the construction and analysis of 7-note scales.
They are also very helpful in ear training for the aural identification of scales and modes.

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JT 2.3 - The Major scale

The seven notes that now represent the white keys on the piano were first defined mathematically by the Greek scientist Pythagoras (550 BC). From these seven notes various modes were constructed using combinations of tetrachords.

The most important scale in Western music today, the major scale (or Ionian mode), dates back from that era.

The major scale consists of two major tetrachords separated by a whole tone :

In the key of C :

Audio 2

(The first note of a scale is called the tonic.)

These spacings do not only apply to the C major scale, but to the major scales in all 12 keys. (There is a major scale for each one of the 12 notes of the music system.)

Take the F major scale for example :

The F major scale must have a semitone between the 3rd and 4th note of the scale. (the last note of the lower tetrachord). Therefore the B is lowered one semitone to a Bb. (This is easiest achieved by placing a Bb in the key signature at the beginning of the staff.) This produces a semitone between A and Bb and a whole tone between Bb and C. The semitone between the 7th and the tonic of the scale (F) is formed by the white notes E and F. By the way, did you notice that the upper tetrachord of the F major scale is the same as the lower tetrachord of the C major scale (C - D - E - F) ? (You can read more about this in my Scales Book.)

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JT 2.4 - Quiz

A.
1. What is a scale ?

2. What are scales used for ?

3. Which scale contains all twelve notes of the Western music system ?

B.
1. What is a tetrachord ?

2. How many different 7-note scales can you construct by combining any two of the four tetrachords outlined in this lesson ? (Keep a whole tone spacing between each combination of two tetrachords).

3. Try out some of the scales you have constructed and, using one of the scales only, write a small composition or play a free improvisation.

C.
Mark the major scale in all keys on the Keyboard Diagrams.
Use the tone and semitone formula :

Like this for the E major scale :

D.
Write out the major scale in all keys in letter names on the Scale Letters Diagrams.
Write the appropriate number underneath each note name :

1 - 2 - 3 - 4 - 5 - 6 - 7 - 1

Like this for the E major scale :

E.
Write out the major scale for all 12 keys on Manuscript paper.

• Use sharps and flats for individual notes where required.
• Use sharps for the major scales of G, D, A, E, B and F#.
• Use flats for the scales of F, Bb, Eb, Ab and Db.
• Rule for the major scale (and all associated 7-note modes and scales) :
  Each letter name is only used once in each scale.
  (This means using E# instead of F in the scale of F#, and Cb instead of B in the scale of Gb.)

F.
The sharps and flats used in Quiz D reflect the key signature for each major key.
Determine the key signature for each major keys using that data.

JT 2.5 - Ear tests 4 & 5

First listen to Audio Demo.
It plays each tetrachord three times, in the following order :

1. - t - t - s - = Major tetrachord

2. - t - s - t - = Dorian tetrachord

3. - s - t - t - = Phrygian tetrachord

4. - s - ts - s - = Gypsy tetrachord

Ear test 4 - tetrachords.
Each tetrachord is played twice, one note after the other, ascending only.

1. - t - t - s - major tetrachord

2. - t - s - t - Dorian tetrachord

3. - s - t - t - Phrygian tetrachord

4. - s - ts - s - Gypsy tetrachord

Single Items test
Each number plays one of the above tetrachords :

JT 2.6 - Lesson Material