Definition
A tetrachord is a sequence of four notes contained within a perfect fourth. The two outer notes are fixed, the two inner ones are movable. Born in ancient Greek theory, it is still a very powerful tool today: almost all heptatonic scales are two tetrachords joined together (plus a connecting tone, or with one note in common).
Greek tetrachords and the three genera
In Greek theory (Aristoxenus) tetrachords are described descending and come in three genera:
- Diatonic: tone – tone – semitone (descending A G F E).
- Chromatic: minor third – semitone – semitone (A F# F E).
- Enharmonic: major third – quarter tone – quarter tone.
The Greek “Dorian” tetrachord, read ascending, is E F G A (semitone – tone – tone): this is why the Greek Dorian harmonia corresponds to our Phrygian. The names of the church modes (Glarean, Dodecachordon, 1547) do not coincide with the Greek ones: a historical confusion worth knowing about.
Modern tetrachords (ascending)
| Name | Steps | Example on C | On G |
|---|---|---|---|
| Major | T – T – S | C D E F | G A B C |
| Minor | T – S – T | C D Eb F | G A Bb C |
| Phrygian | S – T – T | C Db Eb F | G Ab Bb C |
| Harmonic (or Arabic, “hijaz”) | S – 1½ – S | C Db E F | G Ab B C |
| Lydian (tritone) | T – T – T | C D E F# | — |
In practice the scale is built with a lower tetrachord on 1 and an upper tetrachord on 5, separated by a tone (F–G).
Scales as sums of tetrachords
| Scale | Lower (1–4) | Upper (5–8) |
|---|---|---|
| Major (Ionian) | major C D E F | major G A B C |
| Mixolydian | major C D E F | minor G A Bb C |
| Dorian | minor C D Eb F | minor G A Bb C |
| Aeolian (natural minor) | minor C D Eb F | Phrygian G Ab Bb C |
| Phrygian | Phrygian C Db Eb F | Phrygian G Ab Bb C |
| Melodic minor | minor C D Eb F | major G A B C |
| Harmonic minor | minor C D Eb F | harmonic G Ab B C |
| Harmonic major | major C D E F | harmonic G Ab B C |
| Phrygian dominant | harmonic C Db E F | Phrygian G Ab Bb C |
| Double harmonic | harmonic C Db E F | harmonic G Ab B C |
| Neapolitan minor | Phrygian C Db Eb F | harmonic G Ab B C |
| Neapolitan major | Phrygian C Db Eb F | major G A B C |
Lydian (C D E F# + G A B C) and Locrian (C Db Eb F + Gb Ab Bb C) do not fit the scheme “two perfect tetrachords separated by a tone”: Lydian has a tritone tetrachord, Locrian has the diminished fifth. This is precisely what makes them the two “extreme” modes.
The tetrachord and the circle of fifths
The upper tetrachord of C major (G A B C) is the lower one of G major (G A B C + D E F# G): to move to the key with one more sharp, you raise the 7th degree of the new upper tetrachord. This explains why each new sharp is the new leading tone.
Tetrachords around the world
- In Arabic and Turkish music the blocks are called jins (plural ajnas) and can have 3, 4 or 5 notes: jins Rast, Bayati, Hijaz, Saba, Nahawand, Ajam, Kurd. A maqam is a chain of ajnas (see the card on maqam).
- In flamenco the Andalusian cadence (Am–G–F–E) descends along a Phrygian tetrachord A–G–F–E.
- In rock and metal the “phrygian” riffs (E–F) and “hijaz” riffs (E–F–G#–A) are literally tetrachords played on the low string.
Example in a song
“Misirlou” (in Dick Dale's 1962 surf version) revolves entirely around the harmonic tetrachord E F G# A on the guitar's low string: it is the most recognizable “Middle Eastern” color in rock.
Exercise
- Compose a 2-bar bass riff using only a harmonic tetrachord on E; then add the Phrygian upper tetrachord (B C D E) and you get Phrygian dominant.
- Take a melody in C major and replace the upper tetrachord with the harmonic one (Ab and B): you get harmonic major.
- Build the twelve scales of the table on D and check their notes.
Related topics
Major scale and minor scales; The modes of the major scale; Maqam: introduction; Phrygian dominant; Double harmonic scale.