Introduction to 2-part Modal Counterpoint
As a prelude to the writing of chordal, 3- and 4-part tonal music, we will briefly engage in the practice of modal counterpoint for 2 voices.
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.
In this semester, we make the simplest of beginnings. In the second semester course, this topic is covered in considerably more detail.
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 system of tonality, 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.
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 inversions of each other). Dependent 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). 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.
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.
Rules of Motion
Finally, there are rules of motion when writing species counterpoint.
They are:
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 main rule for species counterpoint is to strictly avoid the following:
- Direct 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.
Writing Species Counterpoint: examples and procedures
Our last task, which will serve as a preparation for the upcoming work
in functional harmony, involves composing a second melody above a fragment
of a chant melody. This is known, again, as counterpoint,
which comes from the Latin term punctum contra punctum or “note
against note.” It is the discipline of writing notes that harmonize one
another according to fixed rules of consonance and dissonance. These rules
have been listed in the section above.
The point of this study is not to become fluent in modal counterpoint (that
is a semester’s course in itself, and a lifetime of practice), but to simply
begin to place notes together in the vertical dimension according
to the fixed rules of the style, so as to better understand how notes are
to be combined when we begin to create chords and melody according to more
modern usage.
The practice is straightforward. In first species counterpoint,
you simply add a melody above or below a given cantus firmus,
and you make certain that these intervals are perfect or imperfect consonances,
and you make certain that the voice leading, the way in which
any interval moves from one to the next, follows the rules of motion on
page 46. In essence, this means making sure that you do not move into a
perfect interval, a fifth or an octave, by direct motion. Here are some
examples of incorrect motion:
Direct motion between imperfect consonances (thirds and sixths) are permissible
and, indeed, an important part of the style. Ideally, you want to add a
countermelody to a cantus firmus that employs a combination of
direct and indirect motion, with an occasional use of oblique motion when
that proves necessary. Examples of this species are below.
In second species counterpoint, two notes are created
for every one note in the cantus firmus. This allows the composer
a greater degree of melodic freedom. Third species involves
the use of three to one counterpoint, but we will not bother with that
species, as it is a simple expansion of the second species.
Fourth species counterpoint introduces a controlled use of
dissonance. In this style, a the countermelody is composed in second species
style, but offset by a half a beat. This results in a situation where
sometimes the cantus firmus moves into a dissonant relationship with
the held over countermelody note, requiring the countermelody to resolve the
dissonance into another consonance. This in turn could become a dissonance
to the next note in the cantus firmus, requiring another resolution.
This will be made clear in the examples below.
By learning to write modal counterpoint in these three styles, you will
be well prepared for the more complex task of writing in four part harmony
using the rules of tonality. Study the examples below. You will given assignments
this week that will require you to write in accordance with these models.
For all the exercises, we will work with exactly the same two cantus
firmi, one in the Dorian mode and the other in the Mixolydian mode.
We do so because these two modes stand in the clearest relationship to
the minor and major scale, respectively, which informs our work from the
next chapter onwards. By appreciating the Dorian mode, with its characteristic
raised 6th (the B natural), and the Mixolydian mode, with its characteristic
lowered 7th (the F natural), you will gain a better appreciation for the
world of tonality, the topic of the remaining chapters. Notice that the
notes which give these two modes their characteristic sound, the B and
the F, are the very notes of the tritone, and it was through their alteration
(Bb and F#) that the system of major and minor scales came to be.
The cantus firmi (which are fragments of Gregorian chant) are:
You will notice that the characteristic notes, the B and F, are not present
in the cantus firmi. These allows you to add them in your countermelody
and to notice the effect on the sound of the mode when you do so.
What follows are examples of first, second and fourth species counterpoint,
based on the these cantus firmi. Use them as examples when you
write your exercises for class assignments.
In all your species counterpoint writing, always write in the
interval number between the notes, so that you are assured of having perfect
and imperfect intervals. NOTE: it is common to have an interval of a tenth,
which is simply a third plus an octave. Make sure you understand
how, in the following examples, the interval of a tenth is indeed just
a third plus an octave.
Examples of Species Counterpoint
First Species
In this species, also known as 1:1 counterpoint, you simply write a melody either above or below the fixed voice which forms a perfect or imperfect consonance, note by note. As you do so, you try to give the emerging countermelody a smooth, singable motion. In order to accomplish this, follow these simple rules:
- The countermelody should primarily move stepwise
- When jumping, leaps of a third (upwards or downwards) should be the most common.
- Sometimes a leap of a fifth is acceptable, and a leap upwards of a minor sixth is acceptable once only within an exercise.
As long as you keep within these rules and strive as much as possible for stepwise movement or leaps of a third, the melody will be musical and serve as a good countermelody to the fixed voice.
The Cadence
There is one final item to consider, which is the cadence of each
exercise. A cadence refers to how a piece of music, or a musical phrase,
comes to a close. In the case of these exercise, they all end with a perfect
unison or octave and be preceded by either a sixth or a third, moving in contrary
motion into the final measure. Study the examples to clarify this
point.
Also study these examples (and the examples in the other species) to see
that the fifth is never approached by direct motion, but always by contrary
or oblique motion.
Examples
Here is an example of first species counterpoint in Dorian, one above the cantus
firmus, and one below. (Note, there is one error in the graphic: the
9th measure of the first example should of course be labelled a sixth, not
a 10th.)
And here is an example in Mixolydian.
Second Species
We now take the same chants and create another countermelody that moves
in a 2:1 relationship to the cantus firmus. Here, the note that
falls within the half-measure, on the weak beat, can be dissonant to
the fixed voice, as long as the intervals that fall on the downbeats of
the measures are consonances. These half-measure notes can, of course,
also be consonant.
Notice again that fifths and octaves are never approached in direct motion,
and notice that the final cadence is approached in contrary motion into
an octave or unison.
In these cadences, you will notice that the countermelody is given a sharp
in parenthesis (#) on the penultimate note. That is because in this style
it is always appropriate to raise the leading tone on the final cadence,
though not absolutely necessary. I personally prefer the lowered leading
tone, as it sounds more “modal” and exotic, but I include the sharp here
in case it is more to your taste, and because in most theory treatises
on counterpoint, you are expected to do so.
Dorian:
Fourth Species
This species introduces the concept of syncopation and suspension. The
second note of each measure is tied into the following measure, sometimes
creating a dissonance with the next note of the cantus firmus, requiring
resolution. What is at work is a retardation of the next note,
which becomes a dissonance that resolves into a consonance. Without the
retardation, you would have a simple motion of consonances. The contrast
can be seen in the following two examples.
The first four measures involve retardation, creating a suspension that resolves into a dissonance. The second four measures show it without the suspension.
The first example is known generically as a 4-3 suspension, while the second
example shows a 3-2 suspension (or in this case, with the added octave,
a 10-9), followed by a 7-6 suspension.
This species is essential training for musicians and composers, because
here we begin to learn the art of controlled dissonance, which results
in an ability to create tension and resolution within a piece of music.
Without such tension, the music holds little interest to the listener,
though of course with too much dissonance, it can become overwhelming and
impossible to listen to. Notice the tension and resolution in these
examples, especially in the measures where there is a continual sequence
of dissonances falling into consonances.
One example in Dorian will suffice to understand this species:
Here is another example of fourth species. It indicates how the voice on the downbeat is a preparation (P) and how the not that has been tied over the barline is the suspension (S). When the S is alone, it is a dissonant suspension, and when the S is in parenthesis, it is a consonant suspension.
Assignments
You will be asked to write a few examples of these species of counterpoint,
and you should refer to these examples often for guidance, trying
as best you can to hear what you are writing. While this can be
a somewhat mechanical exercise, it can still do wonders to train
your ear if you are listening carefully to what you are putting
on the page, and is essential practice for writing good four part
music, a task which will occupy you for most of the remainder of
this course. Here are some guidelines for doing this work.
Guidelines for Composing Species Counterpoint
These Guidelines have been moved to a new page, with updated on material on the fourth species:
4G.2 Guidelines for Composing Species Counterpoint
Composing a Canon
Beginning modal counterpoint concludes with a study on writing a canon. This deserves a new page.
NEXT: 4G Writing a modal canon.