Applications / Pedagogy / Guided Tours / Exercise 3C



Circle Exercises

There is a considerable difference between Swings and Circles -
      1. the Swing has no Metamorphosis (what we will eventually call "Metamorphosis 0"),
           always keeping the sameCOMMON TONE,
                which the Circle constantly changes, and
      2. the Swing has no rhythmic structure, no beginning, no end,
           whereas the Circle (with its TONIC chord at both ends) has both beginning and end.
 This rhythmical structure of the Circle will enable us to be more demanding in these exercises,
      by clearly differentiating between Orbit Lines andPerformance Voices.
 In these "Natural Canon" Tetrad Circles, we will -
      (a) In the given Key, with the specified Voice-leading and Metamorphosis (in this case always 1),
           establish the 4 Orbit lines (possibly the Fundamental Bass) in any disposition.
      (b) Substitutions -1(3),0(3), or1(0), will then be added to these Orbit Lines.
      (c) With the given disposition of the DOMINANT chord at the end of the Circle
                (always placed in ascending order),
           establish the Performance Voices (S, A, T, B) on 2 staves (treble and bass clefs).
                (Remember that the Fundamental Bass may be left out.)




With Voice-leading A
1. (a) Voice-leading-A Circle in F withFB, and Orbit chain3-2-10for the 3 upper lines
      (b) No substitutions of Incompleteness
      (c) Disposition of the DOMINANT chord at the end,FB, 10, 3, 2
     Keep the Fundamental Bass close to the Tenor voice (between the unison and the octave), and
           at the end, resolve 10-0 (in the Tenor voice).
 2. (a) Voice-leading-A Circle in D with Orbit line01, and Orbit chain3-2-10for the 3 other lines
      (b) No substitutions of Incompleteness
      (c) Disposition of the DOMINANT chord at the end,2, 01, 10, 3
     Keep the Bass voice low,
      keep the Tenor voice close to the Alto voice,
           (there is no objection to it being far from the Bass voice) and
      at the end, resolve 10-0 (in the Alto voice) and 01-1 (in the Tenor voice).
 3. (a) Voice-leading-A Circle in C withFB, and Orbit chain3-2-10for the 3 upper lines
      (b) Apply entire incompleteness01(3)to eachOrbit 3(G replacing B at the beginning)
      (c) Disposition of the DOMINANT chord at the end,FB, 01(3), 10, 2
     NOTE - Each chord is a real triad in root position.
With Voice-leading B
4. We'll do this one the old way, starting at the beginning of a Voice-leading-B Circle in D.
      A 4-voice canon with the orbit chain2-10-01-3
               (a V-shape upward jump of a sixth in the procuration01-3),
           with the entries in the order : Soprano (on F#), Alto (on B), Tenor (on E), and Bass (on A).
                At the end, resolve01-1(in the Soprano voice).
                     The last chord should be disposed : F#-D-A-D.
           Adjacent voices will occasionally be a tenth apart.
 5. (a) Voice-leading-B Circle in A with Orbit chain01-3-2-10for the 4 lines
      (b) Apply partial incompleteness10(3)-3to eachOrbit 3(A-G# at the beginning)
           removing all need for the V-shape Procuration ofOrbit 3.
      (c) Disposition of the DOMINANT chord at the end,10, 01, 3, 2
          Use the Fundamental Bass (in the Bass voice) in the middle and at the end.
                The last chord should be disposed : A-A-C#-A (no E, blame the Fundamental Bass).
With Voice-leading C
6. (a) Voice-leading-C Circle in Bb with Orbit chain3-2for 2 lines,
           and10-01,01-10, for the other 2 lines.
      (b) Apply partial incompleteness10(3)-01(3)-3to eachOrbit 3
          (Bb-F-A replacing Bb at the beginning)
      (c) Disposition of the DOMINANT chord at the end,3, 01, 10, 2
          One, or both, of the non-canonic lines10-01,01-10could be omitted.
           TheFBcould be added.
 7. (a) Voice-leading-C Circle in D with Orbit chain3-2for 2 lines,
           and01-10, 10-01for the 2 other lines.
      (b) Disposition of the DOMINANT chord at the end,2, 10, 01, 3
     (c) Apply entire incompleteness -
            01(10)to theCOMMON TONEof each odd-numbered chord,
                producing a deceptive triad on the Off-beat of each cell, and
            10(3)to theMOTRIXof each even-numbered chord,
                producing a real triad on the Beat of each cell.
      NOTE -
           We have here the triads F#m / G, Em / F#m, D / Em, C#m-5 / D
                habitually notediii, IV, ii, iii, I, ii, vii, I
           iii, ii, Iappear twice
                first as a deceptive triad and then as a real triad
            IVappears only once as a real triad
            viiappears only once as a deceptive triad
            V, iido not appear at all.
      Academically,viiis often considered as a form ofV, and
            iiiis often considered as a form ofI
               but the principle of deceptive triads is never generalized.

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