Lesson 5c - 2:1 Counterpoint and Embellishing Shapes

In second-species counterpoint, the counterpoint line moves in half notes against a cantus firmus in whole notes. This 2:1 rhythmic ratio leads to two new “fundamental musical problems” – one metric and one harmonic:

  • the differentiation between strong beats and weak beats
  • the introduction of the passing tone dissonance.

The introduction of harmonic dissonance into second species adds to the variety of the musical texture. However, it brings a tension that must be balanced with consonance to promote a cohesive tonal progression, and it requires careful attention in order to maintain smoothness in and out of the dissonance.

If we consider first-species counterpart the most “basic” interaction between two melodies, adding this second note against a harmony also provides an opportunity to begin discussing the shapes and patterns that composers use to embellish a simple melody.

Goals for this topic

Use the following examples of second-species (2:1) counterpoint to develop guidelines for writing in this style. Each of the following examples is in the major mode and has the counterpoint above the cantus firmus, but again, be aware that these two characteristics are not indicative of all counterpoint; we are using a simplified structure as our introduction.

As you develop your rules for second-species counterpoint, look only at the counterpoint (CP) line; the cantus firmus (CF) was provided, so the counterpoint line was written by following the stylistic rules.

Generally, your rules should be divided into three categories:

  • Acceptable harmonic intervals (intervals between lines)
    • Strong beats versus weak beats
      • Are dissonances viable? If so, when?
    • Starting and ending intervals
    • Approaching the final pitch
    • Approaching and leaving perfect intervals
    • Number of times that an interval size can be used consecutively
      • Differentiate between perfect and imperfect consonances
  • Constructing a melodic line
    • Length
    • Starting and ending pitches
    • Approaching the final note
    • Repeated pitches
    • Melodic intervals
      • Leaps
      • Resolutions following leaps
      • How would you describe the motion surrounding any dissonant intervals?
    • Range
    • Climax (position in melody and frequency)
  • Acceptable motion between lines
    • Acceptable types of motion

Conclusions

Second Species Counterpoint

Instead of the 1:1 ratio in first species between pitches of the cantus firmus and counterpoint, second species has a 2:1 ratio–most often notated as two half notes for every one whole note. This creates a pattern of strong and weak beats and consequently a series of rules that are defined by the contrapuntal place in the measure.

  • Strong beats occur “on the beat”, meaning that they align with every change of pitch in the cantus firmus.
  • Weak beats are “off the beat” meaning that they occur in the middle of each pitch in the cantus firmus.

Harmonic Intervals:

Second species counterpoint also allows for a key element that is not an option in first species: dissonance. Strong beats must still only use consonances. Weak beats may use dissonance, although there are many restrictions.

For our studies, we will start the counterpoint with a rest on the strong beat followed by a perfect interval on the weak beat. From that point forward, you will follow these harmonic rules:

Consonances:

  • may occur at any point
  • strong beats will always be consonant
  • imperfect consonances are generally preferred because they do not cause issues when used in parallel motion

Dissonances:

  • only on weak beats
  • approached by step

Starting and Ending Intervals:

  • starts on P5, P8, or unison
  • ends on P5 or P8

Perfect Intervals

  • approached by parallel motion
  • same perfect interval (e.g. P5 to P5) can never occur consecutively, nor can they occur on consecutive strong beats

Motion Between Lines

passing motion (P): motion approached by step and left by step in the same direction

neighbor motion (N): motion approached by step and left by step in the opposite direction

  • these two types of motion are the only way you can use dissonant intervals in a line of counterpoint in 2nd species
  • neighbor motion is only allowed for dissonances as lower neighbor motion

appoggiatura (APP): motion approached by leap and left by step in the opposite direction