Counterpoint is the mediation of two or more musical lines into a meaningful and pleasing whole. This depends on many factors—including the quality of each individual line, the harmonic intervals between them at any given moment, the independence of the lines, etc.
Counterpoint is not the construction of harmonic music, but the combination of lines into a pleasing whole. While the intervals between two notes sounding at any given time is critical, the lines cannot suffer. On the other hand, we cannot simply compose two melodies of the same length in the same key and call it counterpoint. A composer must always keep in mind both the integrity of each line and the intervallic relationships between them.
To begin our study of this important factor of musical theory and composition, we will explore first-species counterpoint. In first species counterpoint, a single new line—called the counterpoint—is written above a given cantus firmus. That new line contains one note for every note in the cantus. In other words, both the cantus firmus and the counterpoint will be all whole notes.
In general, the counterpoint should follow the principles of writing a good cantus firmus. There are some minor differences, to be discussed below, but generally a first-species counterpoint should consist of two cantus-firmus-quality lines.
When writing a counterpoint above a cantus firmus, the first note of the counterpoint should be do or sol (a P1, P5, or P8 above the cantus).
When writing a counterpoint below a cantus firmus, the first note of the counterpoint must always be do (P1 or P8 below the cantus).
The final note of the counterpoint must always be do (P1 or P8 above/below the cantus).
Always approach the final interval by contrary stepwise motion. If the cantus ends re–do, the counterpoint's final two pitches should be ti–do. If the cantus ends ti–do, the counterpoint's final two pitches should be re–do. Thus the penultimate bar will either be a minor third or a major sixth between the two lines. This is the case for both major and minor keys.
Like the cantus firmus, the counterpoint should have a single climax. To maintain the independence of the lines and the smoothness of the entire passage, these climaxes should not coincide.
A single repeat/tie in the counterpoint is allowed, but try to avoid repeating at all.
Avoid voice crossing, where the upper voice is temporarily lower than the lower voice, and vice versa.
Avoid voice overlap, where one voice leaps past the previous note of the other voice. For example, if the upper part sings an E4, the lower part cannot sing an F4 in the following bar.
The interval between the cantus and counterpoint at any moment should not exceed a perfect twelfth (octave plus fifth). In general, try to keep the two lines within an octave where possible, and only exceed a tenth in "emergencies," and only briefly (one or two notes).
In general, all harmonic consonances are allowed. However, unisons should only be used for first and last intervals, and imperfect consonances are preferable to perfect consonances for all intervals other than the first and last dyads. In all cases, aim for a variety of harmonic intervals over the course of the exercise.
Never, ever, ever use two perfect consonances of the same size in a row: P5–P5 or P8–P8. This includes both simple and compound intervals. For example, P5–P12 is considered the same as P5–P5. (Two different perfect consonances in a row, such as P8–P5, is allowed, however, but try to follow every perfect consonance with an imperfect consonance if possible.)
Vary the types of motion between successive intervals (parallel, similar, contrary, oblique). Try to use all types of motion (except, perhaps, oblique motion), but prefer contrary motion where possible. It is best for preserving the independence of the lines.
Use similar and parallel motion within the following constraints:
In the following video, I illustrate the process of composing a first-species counterpoint. This video provides new information about the compositional process, as well as concrete examples of the above rules and principles.