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 key features that must be considered—one metric and one harmonic: the differentiation between strong beats and weak beats, and the introduction of the passing tone dissonance.
As in first species, the counterpoint line should be singable, have a good shape, with a single climax and primarily stepwise motion (with some small leaps and an occasional large leap for variety). However, a second-species counterpoint should be even more dominated by stepwise motion than in first species, because there are less sticky situations that would require a leap. If the counterpoint must leap, prefer to do so from strong beat to weak beat (within the bar) rather than from weak beat to strong beat (across the barline). 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.
As in first species, begin a second-species counterpoint above the cantus firmus with do or sol. Begin a second-species counterpoint below the cantus firmus with do. Unisons are permitted for the first and last dyads of the exercise.
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 is preferred (and easier). Regardless of rhythm, the first pitch in the counterpoint should follow the intervallic rules above.
The final pitch of the counterpoint must always be do, as in first species.
The penultimate note of the counterpoint should be ti if the cantus is re, and re if the cantus is ti, as in first species.
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. Which option you use will depend on how you are approaching the final bar.
Strong beats (downbeats) should always be consonant, and should not be unisons. As in first species, prefer imperfect consonances (thirds and sixths) to perfect consonances (fifths and octaves).
Motion across bar lines (from weak beat to strong beat) follows the same rules as first species counterpoint. For instance, if a weak beat is a perfect fifth, the following downbeat must not also be a perfect fifth.
Likewise progressions from downbeat to downbeat must follow principles of first-species counterpoint. The following are some examples, but not an exhaustive list:
Hidden or direct fifths/octaves between successive downbeats are allowed.
Weak beats should exhibit a mixture of consonant and dissonant intervals. Among consonances, unisons are permitted on weak beats when necessary to make good counterpoint between the lines. Any dissonance must follow the pattern of the dissonant passing tone, explained below. Also explained below are a number of standard patterns for consonant weak beats. Chances are high that if your weak beats do not fit into one of the following patterns, there is a problem with the counterpoint, so use them as a guide both for composing the counterpoint, and for evaluating it.
The following patterns (whose terms are either standard or taken from Salzer & Schachter's Counterpoint in Composition) should guide your use of weak-beat notes in a second-species counterpoint line. A good general practice is to start with a downbeat note, then choose the following downbeat note, and finally choose a pattern below that will allow you to fill in the space between downbeats well.
Most of these are used as examples in the demonstration video at the bottom of the page.
All dissonant weak beats must be dissonant passing tones, so called because the counterpoint line passes from one consonant downbeat to another consonant downbeat by stepwise motion. The melodic interval from downbeat to downbeat in the counterpoint will always be a third, and the passing tone will come in the middle in order to fill that third with passing motion.
A consonant passing tone outlines a third from downbeat to downbeat, and has the same pattern as the dissonant passing tone, except that all three tones (downbeat, passing tone, downbeat) are consonant with the cantus. A consonant passing tone will always be a sixth or perfect fifth above/below the cantus.
A substitution also outlines a third from downbeat to downbeat. However, instead of filling it in with stepwise motion, the counterpoint leaps a fourth and then steps in the opposite direction. It is called a substitution because it can substitute for a passing tone in a line that needs an extra leap or change of direction to provide variety. Like the consonant passing tone, all three notes in the counterpoint must be consonant with the cantus.
A skipped passing tone outlines a fourth from downbeat to downbeat. The weak-beat note divides that fourth into a third and a step. Again, all three intervals (downbeat, skipped passing tone, downbeat) are consonant with the cantus.
An interval subdivision outlines a fifth or sixth between successive downbeats. The large, consonant melodic interval between downbeats is divided into two smaller consonant leaps. A melodic fifth between downbeats would be divided into two thirds. A melodic sixth between downbeats would be divided into a third and a fourth, or a fourth and a third. Not only must all three melodic intervals be consonant (both note-to-note intervals and the downbeat-to-downbeat interval), but each note in the counterpoint must be consonant with the cantus.
A change of register occurs when a large, consonant leap (P5, sixth, or octave) from strong beat to weak beat is followed by a step in the opposite direction. It is used to achieve melodic variety after a long stretch of stepwise motion, to avoid parallels or other problems, or to get out of the way of the cantus. It should be used infrequently. And as always, each note must be consonant with the cantus.
A delay of melodic progression outlines a step from downbeat to downbeat. It involves a leap of a third from strong beat to weak beat, followed by a step in the opposite direction into the following downbeat. It is called a "delay" because it is used to embellish what otherwise is a slower first-species progression (motion by step from downbeat to downbeat).
A consonant neighbor tone occurs when the counterpoint moves by step from downbeat to weak beat, and then returns to the original pitch on the following downbeat. If the first downbeat makes a fifth with the cantus, the consonant neighbor will make a sixth, and vice versa.
In the following video, I illustrate the process of composing a second-species counterpoint. This video provides new information about the compositional process, as well as concrete examples of the above rules and principles.