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’

Pitch-Tetrachord exercise

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