The second species of species counterpoint sees the counterpoint line move twice as fast as the cantus firmus. This introduces the ideas of strong versus weak beats.

Strong beats are always consonant. Weak beats may be consonant or dissonant. Dissonance may occur on weak beats may arise through passing motion. Consonant weak beats connect two consonant strong beats to create a succession of 3 consonances. These can be of many types:

consonant passing tone: two steps in the same direction to outline a third.

substitution: leap a fourth, then step in the opposite direction.

skipped passing tone: a third and a step in the same direction to outline a fourth.

interval subdivision: two leaps in the same direction to divide a larger melodic interval, for example, with two thirds to make a fifth.

change of register: a large, consonant leap (perfect fifth, sixth, or octave) from strong beat to weak beat, followed by a step in the opposite direction.

delay of melodic progression: leap a third, then step in the opposite direction.

consonant neighbor tone: step in one direction, then step back to the original tone.

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, and 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 tonal fusion, and it requires careful attention in order to maintain smoothness in and out of the dissonance.

Here are the complete examples of second-species counterpoint from Part I of Gradus ad Parnassum, annotated (as before) with the interval that the counterpoint line makes with the cantus firmus. For the complete examples from Gradus ad Parnassum as exercises, solutions, and annotations, see Gradus ad Parnassum Exercises.



Example 1. All second-species exercises from Gradus ad Parnassum.

The Counterpoint Line

As in first species, the counterpoint line should be singable and have a good shape, with a single climax and primarily stepwise motion (with some small leaps and an occasional large leap for variety). However, because a first-species counterpoint had so few notes, in order to maintain smoothness in other aspects of the exercise, the melody frequently employed small leaps. In second species, the increase in notes and the added freedom involving the use of dissonance makes it easier to move by step without causing other musical problems. Thus, a second-species counterpoint is even more dominated by stepwise motion than in first species. If the counterpoint must leap, take advantage of the metrical arrangement to diminish the attention drawn to the leap: leap from strong beat to weak beat (within the bar) rather than from weak beat to strong beat (across the bar line) when possible. Also, because there are more notes in a second-species line, there should usually be one or two secondary climaxes—notes lower than the overall climax that serve as “local” climaxes for portions of the line. This will help the integrity of the line by ensuring that it has a coherent shape and does not simply wander around.

Beginning and Ending

Beginning a second-species counterpoint

As in first species, begin a second-species counterpoint above the cantus firmus with do (\hat1) or sol (\hat5). Begin a second-species counterpoint below the cantus firmus with do (\hat1).

A second-species line can begin with two half notes in the first bar, or a half rest followed by a half note. Beginning with a half rest establishes the rhythmic profile more readily, making it easier for the listener to parse, so it is often preferable. It is also easier to compose. Regardless of rhythm, the first pitch in the counterpoint should follow the intervallic rules above.

Ending a second-species counterpoint

As in first species, you should end with a clausula vera: the final pitch of the counterpoint should be do (\hat1); the penultimate note of the counterpoint should be ti (\hat7) if the cantus is re (\hat2), and re (\hat2) if the cantus is ti (\hat7).

The penultimate bar of the counterpoint can either be a whole note (making the last two bars identical to first species) or two half notes. This allows you to begin your clausula vera on either the strong beat or the weak beat of the penultimate measure.

Strong Beats

The inclusion of dissonance in a musical texture creates new musical problems that need to be addressed. Because the philosophy of species counterpoint is to present only a small number of new musical difficulties with each successive species, second-species counterpoint introduces dissonance in a very limited way.

Strong beats (downbeats) in second species are always consonant. As in first species, prefer imperfect consonances (thirds and sixths) to perfect consonances (fifths and octaves), and avoid unisons.

Because motion across bar lines (from weak beat to strong beat) involves the same kind of voice motion as first species (two voices moving simultaneously), follow the same principles as first-species counterpoint. For instance, if a weak beat is a perfect fifth, the following downbeat cannot also be a perfect fifth.

Likewise, progressions from downbeat to downbeat must follow the principles of first-species counterpoint described in the previous chapter, such as:

Do not begin two consecutive bars with the same perfect interval.

Do not outline a dissonant melodic interval between consecutive downbeats. (Exception: if the counterpoint leaps an octave from the str