Real Imitation and Double Counterpoint

1
Real Imitation andDouble Counterpoint

• Interchangeable Voices

2
Real Imitation at the 8va and 10th

• Repetition is the immediate restatement in the
  same voice at the same pitch level (or an octave
  displaced).
• Sequence is the immediate restatement in the same
  voice at a different pitch level.
• Imitation is the immediate restatement in a
  different voice at the same or a different pitch
  level.

3
Real Imitation at the 8va and 10th

• Imitation can be an incidental device or a
  structural component.
• Fugues and inventions are termed imitative
  pieces.
• These pieces begin with points of imitation.
• In two-part compositions the imitation rarely
  continues the imitation beyond the initial
  statement of the subject in the second voice.

4
Real Imitation at the 8va and 10th

• Imitation at the octave is most common.
• There is no problem keeping the intervallic
  relationships the same.
• Imitation at the 5th is the second best choice.
• The dominant key sets up the return to the tonic.
• In minor it is the minor v as a key and not the
  major V as a chord.
• Fugues require a dominant answer.

5
Real Imitation at the 8va and 10th

• The imitation in inventions can be either motivic
  or thematic imitation.
• The initial idea in motivic imitation tends to be
  just a motivic figure.
• Usually implies a single harmony.
• They are very short -- less than a measure,
  usually.
• Often the opening motive and its imitation or
  restated at the dominant level before resolving
  to tonic.
• See the C major (1) and E minor (7) Two-Part
  Inventions.

6
Real Imitation at the 8va and 10th

• In thematic imitation, the initial idea is more
  like a subject.
• It tends to imply a simple progression (I - V or
  I - ii - V).
• It is usually one to two measures long.
• See the D minor (4) Two-Part Invention.
• The second voice entering in the dominant key in
  real imitation is called the answer.
• Sometimes the opening statement is accompanied.
• See the B minor (15) Two-Part Invention.

7
Double Counterpoint at the 8va

• Invertible Counterpoint is another technique to
  achieve recurrence and development.
• In two-parts, both are serving a double function,
  hence Double Counterpoint.
• Double Counterpoint at the octave is very common.
  
• Once the octave is exceeded, intervals no longer
  invert.

• Intervallic Inversion Chart
• 3 2 1 2 3 4 5 6 7 8 9 10
• 10 9 8 7 6 5 4 3 2 1 2 3

8
Double Counterpoint at the 8va

• Consonance inverts to consonance dissonance to
  dissonance.
• The fifth must be treated as a dissonance since
  it inverts to a fourth.
• Notice the intervals add up to 9 (the magic
  number).
• Instead of inverting and then transposing, raise
  and lower the respective voices by numbers that
  total 9.

9
Double Counterpoint at the 8va

• Two-voice counterpoint usually needs to be
  inverted at multiple octaves since the voices are
  usually separated spatially.
• The magic numbers for 2 and 3 octaves are 16 and
  23.
• The answer and accompanying counterpoint will
  likely occur in switched relation so they need to
  be written in Double Counterpoint.

10
Counterpoint at the Tenth

• Counterpoint at the tenth is used less frequently
  because of two main problems
• Thirds and sixths invert into octaves and fifths,
  therefore parallel thirds invert into parallel
  octaves.
• Suspensions do not invert into suspensions (i.e.
  7-6 4-5, etc.). See Ex. 15-10, pg. 187.

11
Counterpoint at the Twelfth

• Counterpoint at the twelfth is more common.
• The problem interval is the sixth, which inverts
  to a seventh, and therefore needs to be treated
  as a dissonance.

Intervallic Inversion Chart 3 2 1 2
3 4 5 6 7 8 9 10 11 12 13 14 14
13 12 11 10 9 8 7 6 5 4 3 2
1 2 3
12
Counterpoint at the Twelfth

• Thirds and tenths are very common.
• The 4-3 suspension becomes 9-10 and 2-3 becomes
  11-10.
• Often the invertible counterpoint is constructed
  so that it will work in multiple intervals.
• Thirds at the octave invert into sixths, and at
  the twelfth invert into tenths.