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Scale

Tetrachord

A tetrachord is a series of four notes within a perfect fourth. The outer notes stand firmly a fourth apart, the inner ones may lie differently. The concept comes from ancient Greek music theory.

Notes
four
Frame
perfect fourth (five semitones)
Major tetrachord
whole – whole – half
Minor tetrachord
whole – half – whole
Joining
conjunct or disjunct

Four notes within a fourth

A tetrachord fills a perfect fourth with four notes. The two outer notes stand five semitones apart, for example C and F. Where the two inner notes lie decides the kind. The major tetrachord goes whole–whole–half (C D E F), the minor tetrachord whole–half–whole (A B C D), the Phrygian half–whole–whole (E F G A).

The major scale from two tetrachords

C D E F G A B C 1 1 ½ 1 1 1 ½

The lower tetrachord C–D–E–F and the upper G–A–B–C have the same step pattern: whole, whole, half. Between them lies a whole tone, F–G. This joining is disjunct.

Conjunct joining: one note belongs to both

C D E F G A B♭ 1 1 ½ 1 1 ½

Here the first tetrachord C–D–E–F ends and the second F–G–A–B♭ begins on the same F. Both tetrachords share a note. The scale thus has only seven notes and ends not on C but on B♭.

Lament bass: descending tetrachord

3 4

The descending tetrachord from the tonic to the dominant, here in A minor: A, G, F, E. Read downwards it goes whole–whole–half; read upwards (E–F–G–A) it is, by the classification above, the Phrygian tetrachord. In the literature the model is often called the “descending minor tetrachord”, because it steps through the notes of the natural minor scale from tonic to dominant. It is known as a bass model of lament (“lamento”) and is often filled in chromatically.

In the glossary: Hexachord · Scale · Semitone

The connection with the circle of fifths

Splitting the major scale into two equally built tetrachords is more than a memory aid. It explains the circle of fifths. The upper tetrachord of a major scale is at the same time the lower one of the scale a fifth higher. Seen from C major, G–A–B–C is the upper tetrachord of C major and the lower of G major. In G major the upper tetrachord D–E–F♯–G needs only a single sharp. That is why exactly one new sharp or flat is added with every fifth step.

Conjunct and disjunct

If you join two tetrachords there are two possibilities. If they are conjunct they share a note. If they are disjunct a whole tone separates them. The major scale is built disjunct.

Three genera

Ancient theory knew three genera that differ in the position of the inner notes. The diatonic consists of whole tones and semitones. The chromatic has two narrow steps (semitones) and a minor third. The enharmonic has still smaller gaps, namely two quarter tones, and in addition a major third. For the practical music of the West the diatonic remained the standard.

The bass model

In the Baroque the descending tetrachord from tonic to dominant is known as the lament bass model, often filled in chromatically. Famous examples are Purcell's “Dido's Lament” from “Dido and Aeneas” and Monteverdi's “Lamento della Ninfa”.

Practice: At the piano play a major tetrachord on C and then on G. Join the two with a whole tone between them and you have C major. Then begin the second tetrachord on F, the last note of the first, instead of on G: the note sequence C–D–E–F–G–A–B♭ arises from two conjunct tetrachords.