Philomathes: I would not have thought there had been such variety to be used upon so few notes… Master: There be many things which happen contrary to men’s expectations, therefore yet once again try what you can do upon this plainsong… Morley, A Plain and Easy Introduction to Practical Music (1597), 152.
Most of the principles of 1st species still apply here. In writing two notes in the line of 2nd species counterpoint against each whole note in the cantus firmus (CF), the first half note in each measure must be consonant. Now, however, it is possible to introduce dissonance in the second half of the measure in the form of passing tones, and thereby the energy and tension of the line of counterpoint can be greatly enhanced.
It is still necessary to begin on a perfect consonance, but now the line of counterpoint may begin either on the first beat (example 1a), or it may begin with a half-note rest (example 1b).
Beginning the line of counterpoint with a half-note rest encourages the sense of independence between the two lines. The counterpoint will end on the note an octave or unison away from the final note in the CF, as in 1st species, and the penultimate note must be the leading tone or seventh modal degree (example 2a). Occasionally a whole note may be used in the line of counterpoint in the penultimate measure; in this case it will always be the leading tone or seventh modal degree (example 2b).
Dissonant intervals, such as the 2nd, 4th, 7th, 9th, and tritone, can be used on the second half note of a measure if the line of counterpoint moves up or down by step from one consonance to another (example 3).
Such dissonances are called passing tones (P or PT). A passing tone is a stepwise connection between two other tones a third apart.
The neighbor note (N — a stepwise connection between two instances of the same note) may be used if and only if it is consonant with the CF (example 4).
Don’t let the line of counterpoint leap into or out of a dissonant interval, since this leaves the dissonance hanging, unfulfilled and unresolved (example 5).
Big leaps — any leap larger than a 3rd — over the bar line (from 2nd beat to the subsequent strong beat) are more problematic than leaps within the measure, since the second beat then has a tendency to “dangle,” and the goal of the leap sounds as though it had been shot out of a cannon. If you must leap over the barline, follow the leap with an immediate change of direction — this will ameliorate the dangling sensation.
Large leaps within the measure should also be followed with a change of direction: this keeps the line of counterpoint from extending its register too low or too high (example 6).
A large melodic interval (P5, major or minor 6th, or P8) can be broken into two smaller leaps; this is a useful technique for slowing down registral expansion.
A P5 can be traversed by using two consecutive leaps of a 3rd (example 7a); a 6th can be traversed by using two consecutive leaps of a 3rd and a P4, or a P4 and a 3rd (7b); and finally, a P8 can be traversed by leaping a P5 and a P4, or a P4 and a P5 (7c).
Any other combination of consecutive leaps (P4 + P4, 3rd + P5, for example) will result in a dissonant outline (7d), and is therefore forbidden. As always with leaps, all intervals formed against the CF must be consonant. When you use two smaller leaps to gain a larger interval, the first of the two leaps should not be recovered. Once the goal is reached, however, an immediate change of direction should occur.
Directly adjacent (parallel) P5s and P8s are, as before, forbidden under any circumstances (example 8a). P5s and P8s on successive strong beats, mitigated by only one intervening half note, are to be strenuously avoided (8b). P5s and P8s on successive weak beats, however, are acceptable, as long as they do not form a sequence (8c).
The line of counterpoint may move by leap as long as both vertical intervals formed with the CF are consonant (example 9).
The unison can now be used, but only on the second half of the measure, in the middle of an exercise, and it must be left by step in the opposite direction from its approach (example 10a). If you leave it with a skip, it is as though the line of counterpoint has fallen temporarily into a black hole (example 10b).
The leap of a P8 or an ascending m6 (never a descending 6th, nor an ascending M6, since these are relatively difficult to sing) will prove useful to change the counterpoint’s register from time to time in these exercises, especially when the voices are getting too close together (example 11).
Like 1st species, the 2nd species counterpoint line should achieve a unique (unrepeated) climax which is not simultaneous with the high point of the CF.
It is always helpful to sketch in a possible climax when beginning to write the line of counterpoint; this will help to avoid such common problems as painting oneself into a registral corner (being too high or too low relative to the close of the exercise, with insufficient time to recover), and arriving at a climactic point on a weak beat.
Repeated notes (example 12a), tied notes (12b), sequences (12c), and repetitions of groups of notes (12d) are all off limits in 2nd species.
To summarize, the second half note in the counterpoint has several functions: consonant (example 13a) and dissonant passing tone (13b); to change register quickly within the measure (13c); to break a large leap into two smaller and less obtrusive ones (13d); and to avoid potential voice leading errors (13e).
Here are four examples of second species counterpoint for your review. Identify each example’s mode, write the vertical intervals between the staves (numbers only, not qualities), play one line and sing the other, switching parts in order to gain full fluency in the reading of each clef, and to get personal experience with the elegance of simple melodic lines.
2nd species EXERCISES:
1) What are the basic characteristics of 2nd species counterpoint? Consider rhythm, melodic behavior, and harmonic behavior (the behavior exhibited by the two parts together).
2) Describe and graph (or illustrate in notation) ascending and descending passing tones.
3) Write the harmonic interval quantities between the staves for all of the 2nd species examples at the end of the chapter, and circle all dissonant harmonic intervals. Label passing tones with the letter “P” above the counterpoint note.
4) Add a line of 2nd species counterpoint above and below CFs chosen by your instructor. Circle all dissonant harmonic intervals, and label passing tones with the letter “P.”
Finally, many instructors (and I am one of them) go directly to 4th species counterpoint from 2nd species, returning to 3rd species later, time permitting. This is particularly helpful if the instructor has a limited amount of time to introduce these fundamental concepts of handling consonance and dissonance. Since suspensions are so critically important as an expressive device, and 4th species continues the 2:1 rhythmic relationship introduced in 2nd species, it is a natural follow-up to 2nd species. With its cornucopia of new flourishes and fripperies, 3rd species can wait.
Go to 4th species … or