Applications / Pedagogy / Guided Tours / Exercise 3A



Try your hand at building some of these "Natural Canon" tetrad swings -
           in different keys, and
           in different dispositions.
      on 2 staves (treble and bass clefs),
           with 2 lines in each clef.
                (Remember that the Fundamental Bass is left out.)
 The functions of a chord will be designated by their Orbit numbers -
           Orbit 0,Orbit 1,Orbit 2,Orbit 3,
      Don't forget to place them beside each note.
 Each exercise will indicate -
      the Key (always a major key),
      the disposition of the orbits of the first chord, placed in ascending order.




The Voice-leading-A Swing
With the chords TONIC-DOMINANT-TONIC-DOMINANT
 1. In G (on G6) -Orbit 1(G),Orbit 2(B),Orbit 3(E),Orbit 0(D)
 2. In F -Orbit 1,Orbit 0,Orbit 3,Orbit 2

With the chords TONIC-COUNTER-TONIC-COUNTER
 3. In C (on C+7) -Orbit 0(C),Orbit 1(G),Orbit 2(E),Orbit 3(B)
 4. In D -Orbit 0,Orbit 3,Orbit 2,Orbit 1

The Voice-leading-B Swing
With the chords DOMINANT-TONIC-DOMINANT-TONIC-DOMINANT-TONIC
 5. In D (on A7) -Orbit 1(E),Orbit 3(G),Orbit 0(A),Orbit 2(C#)
 6. In Bb -Orbit 3,Orbit 1,Orbit 0,Orbit 2

With the chords COUNTER-TONIC-COUNTER-TONIC-COUNTER-TONIC
 7. In G (on C6) -Orbit 3(A),Orbit 2(E),Orbit 0(G),Orbit 1(C)
 8. In F -Orbit 2,Orbit 3,Orbit 0,Orbit 1

The Voice-leading-C Swing
With the chords TONIC-DOMINANT
 9. In F (on F6) -Orbit 3(D),Orbit 2(A),Orbit 1(F),Orbit 0(C)
With the chords TONIC-COUNTER
 10. In D -Orbit 0,Orbit 3,Orbit 2,Orbit 1
     NOTE the wider dispositions in exercises 9 and 10 (with Voice-leading C).
You might enjoy "closing" any of these examples by not procuring theMOTRIXof the last chord -
      simply resolve3-2,2-1,1-1,0-0.
Let us know if you have any problems.

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