Introduction to 2-part Modal Counterpoint
Contrapunctus or "point against point" (counterpoint) is the art of writing two or more melodies that work in harmony with each other, according to certain fixed rules of interplay. Since strict modal counterpoint, also known as species counterpoint, functions within very defined and easily learned parameters, it is an excellent beginning to the art of composition.
Where does it come from?
Modal counterpoint is an ancient art, first developed in the 12th and 13th Centuries and flourished in Europe through the period of Medieval and Renaissance music, eventually giving way to the major-minor system, tonal counterpoint and functional harmony that will be the focus for the remainder of the semester. The ancientness of the craft is one of the reasons for employing its techniques as a first step in serious composition—it is the foundation of all music to follow.
And we're learning it, why?
2-part modal counterpoint teaches you some important things about how to work with dissonance and consonance, which is to say with tension and relaxation. With practice, you'll get a feeling for how, in a very pared down and direct way, expressive music moves on a wave of tension and release. By working this out within the context of two melodies, you can expand it out into more complex music.
Parameters of Species Counterpoint
Species counterpoint involves composing one or more new melodies above or below a cantus firmus, or fixed voice, which initially were Gregorian chants. We shall also use Gregorian chant as our fixed voice. There were strict rules for creating such countermelodies, and these rules can be summarized in the simplest form as follows, based on the concept of perfect consonances, imperfect consonances and dissonances:
Perfect consonances, which should come as no surprise, are the unisons, octaves and perfect fifths, since these are based on the lowest integer relationships. (The fourth is considered a dissonance in this style, for reasons which will be explained shortly).
Imperfect consonances are the thirds and the sixths (which are of course inversions of each other). They are called "imperfect" because, as we saw on the previous page, their tuning is defined by the ratios 5:4 (major thirds), 6:5 (minor thirds), 5:3 (major sixths) and 8:5 (minor sixths). Since these use integers higher than the Pythagorean-limited ceiling of 4 (the tetractys), they are considered to be less "perfect" than the intervals of the octave and the fifth, which to Pythagorean thought represented the Harmony of the Spheres.
Depending on their position within the scale, these thirds can be either major (comprised of two whole tones) or minor (a whole tone and a half tone).
Depending on their position within the scale, the sixths can also be either major (a perfect fifth and a whole tone) or minor (a perfect fifth and a semi-tone).
Both are equally “imperfect” but both are consonances. Indeed, these are considered to be the “sweet” intervals in this style, and their sonority will be an essential part of our study of tonality.
This is how the major thirds/sixths and the minor thirds/sixths lie within the natural scale. Recall how maj intevals invert to minor intervals and vice-versa. Thirds and sixths invert to each other because the major third interval (5/4) multiplied by the minor sixth interval (8/5) equals 40:20, which is the octave. It's important to remember how these ratios explain the way intervals invert to octaves, since arithmetically they add up to 9.
All other intervals are dissonant:
Seconds are dissonant because of their close proximity to each other.
Sevenths are dissonant because they are only a step away from being an octave.
Tritones, as we know, are the most dissonant and require special treatment.
All dissonances cannot remain so for long, and must be resolved in the proper way to consonances. How this happens is much of what we will be exploring.
Recall that the major second has the ratio of 9:8 and the minor second has the ratio of 243/256!.
Types of Motion
In Species Counterpoint, there are three possible types of motion
Direct motion results when two or more parts ascend or descend in the same direction by step or skip:
Contrary motion results when one part ascends by step or skip and the other descends—or vice versa:
Oblique motion results when one part moves by step or skip while the other remains stationary:
In writing species counterpoint, we concern ourselves with how we move from one pairing of notes to another.
The Central Rule of Motion
The main rule for species counterpoint is to strictly avoid the following:
Direct or parallel motion into a perfect consonance.
That is, you cannot go by direct motion, either by step or by skip, into a perfect fifth, octave or unison. Implied by this one rule are four rules that make the first more explicit:
From one perfect consonance to another perfect consonance one must proceed in contrary or oblique motion.
From a perfect consonance to an imperfect consonance one may proceed in any of the three motions.
From an imperfect consonance to a perfect consonance one must proceed in contrary or oblique motion.
From one imperfect consonance to another imperfect consonance, one may proceed in any of the three motions.
Oblique motion, if used with due care, is allowed with all four progressions.
What to avoid when you write modal counterpoint
So to look at this in manuscript, here's what to avoid:
Avoid parallel perfect fifths and parallel octaves when you write 2-part modal counterpoint:
It's easy to see parallel 5ths and 8vas. Direct motion into a fifth and an octave is a little more subtle.
D5 = direct motion into a fifth from the previous interval.
D8 = direction motion into an octave from the previous interval.
P5 = parallel fifth from the previous interval.
P8 = parallel octave from the previous interval.
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