The first half note exists on the downbeat of the measure. Because of this, it must be consonant with the cantus firmus. The second half note exists on the upbeat. Because of this, it may be dissonant with the cantus firmus if we both approach and leave it by stepwise motion. If the upbeat is approached or left by a skip, the pitch must be consonant with the cantus firmus. Thus, the only dissonance that can exist in this species is diminution. Diminution is filling in the space between two notes that are a melodic third apart from each other.
Works of second species (binary meter) will always resolve in a specific way. If the counterpoint resolves to an octave, the penultimate measure will contain a 5th followed by a major 6th in relation to the cantus firmus (except when the diatonic 5th is a tritone). If the counterpoint resolves to a unison, the penultimate measure will contain a 5th followed by a minor 3rd in relation to the cantus firmus (except when the diatonic 5th is a tritone). The final pitch of the counterpoint must match the rhythm of the cantus firmus (in our case, it will be a whole note).
There are several additional rules that must be observed when composing in second species. One such rule is that successive strong beats may not contain parallel fifths or octaves unless the weak beat contains a leap of a 4th or greater. Leaps of a third between successive strong beat parallelism are not substantial enough to erase the strong beat parallel motion from our tonal memory. Another is that a half rest can be used in place of the first note. In this case the upbeat pitch must be consonant with the cantus firmus. Finally, a leap of a minor sixth or an octave may be used to avoid issues in a place where it is impossible to achieve contrary motion.
The rules covered above reflect the differences between second and first species counterpoint. Other than these differences, all the other rules of first species counterpoint apply to second species counterpoint. In addition, the same melodic rules for composing a good cantus firmus apply to composing a good work of second species counterpoint. I would also recommend the same tips for composing that I gave in the lesson on first species. For this reason, it is essential to study this topic in the proper sequence in order to gain a proper understanding. If you have not done so already, please refer to the previous lessons on counterpoint (parts 1-3) to aid in your understand of this lesson.
Based on the rules and tips presented in this lesson, you should be prepared to compose your own second species counterpoint exercises. For more guidance, please refer to the end of the accompanying video where I compose an example of second species counterpoint both in binary and ternary meter. Continued practice will grant you valuable insight into the nature of melodic motion and the way multiple melodies react harmonically.
This Learning Music With Ray video discusses the topic of second species counterpoint. In this video I discuss the rules that govern composing a work of second species counterpoint. I also provide some helpful tips that will make your experience composing second species counterpoint easier. Finally, I compose a line of second species counter point both in binary and ternary meter in order to provide a live demonstration of the principles discussed in the video.