Tetrachords

Tetra = 4, chord = ‘string’.

Tetrachords are 4-note scales that span a Perfect 4th (with some exceptions). Many cultures organize melodic ideas around tetrachords and tetrachord combinations, and a great number of tetrachords other than those shown here are also extant. For example, some Arabic tetrachords include quartertones.

Basic Tetrachords:               

     Interval Names:      P1 m2 M2 m3 M3 P4 A4/d5 

     Major (Maj)          1  .  2  .  3  4  .

     Minor (min)          1  .  2  3  .  4  .

     Phrygian (phryg)     1  2  .  3  .  4  .

     Harmonic (harm)      1  2  .  .  3  4  .

     Whole Tone (W.T.)    1  .  2  .  3  .  4

                  P = perfect, M = major, m = minor

                  A = augmented, d = diminished

Tetrachord Combinations: 

Tetrachords can be combined to create heptatonic (7-note) scales and modes. The lower tetrachord spans from the root to the P4, the upper tetrachord spans from the P5 to the octave. The following is a list of the most common tetrachord combinations, but any combination of two tetrachords yields a 7-note scale, except for W.T. + W.T., which makes the 6-note whole-tone scale. (Know bold tetrachord combinations for mid-term test)

Lower T.C.            +        Upper T.C.    = Heptatonic mode

Interval:     P1  m2  M2  m3  M3  P4 A4d5 P5  m6  M6  m7  M7  P8

Maj + Maj     1   .   2   .   3   4   .   5   .   6   .   7   8 = Major/Ionian

Maj + min     1   .   2   .   3   4   |   5   .   6   7   .   8 = Mixolydian

min + Maj     1   .   2   3   .   4   |   5   .   6   .   7   8 = Ascending Melodic minor                                                                    /Jazz minor

min + min     1   .   2   3   .   4   |   5   .   6   7   .   8 = Dorian

min + phryg   1   .   2   3   .   4 |   5   6   .   7   .   8 = Natural minor/Aeolian

min + harm    1   .   2   3   .   4 |   5   6   .   .   7   8 = Harmonic minor

phryg+phryg   1   2   .   3   .   4 |   5   6   .   7   .   8 = Phrygian

W.T.+ Maj     1   .   2   .   3   . 4   5   .   6   .   7   8 = Lydian

W.T.+ W.T.    1   .   2   .   3   . 4/5 .   6   .   7   .   8 = Whole-tone scale

Ear Training: Major & Minor Tetrachord Comparisons

• Sing tetrachords

• Compare intervals (MA/mi 2nds, MA/mi 3rds)

• Qualia (class to describe)

Interval #Semitones/  Qualia   Tonal Tendency     Song Associations

         size-in-cents 

mi2  1    100         rough    strong pull to root   ‘Theme from Jaws’

MA2  2    200         tense    resolves to root      ‘Do, Re, Mi’

mi3  3    300         stable   pull to MA2           ‘Oh, Canada’

MA3  4    400         stable   soft pull to MA2      ‘Taps’

P4   5    500         open     strong pull to MA3    ‘Here Comes the Bride’

A4   6    600         angular  push to P5            ‘Simpson’s Theme’

P5   7    700         stable   resolves to root      ‘Jeopardy Theme’