Counterpoint Study 3: 1:1 Ratio (Part 1)

Counterpoint Study Lesson 3: 1:1 Ratio (Part 1)

Assuming that we know basic harmony, now we should move on to the real lesson of counterpoint. The simplest type of counterpoint is 1:1 ratio. Ratio is defined as horizontal relation between two vertical notes. In the famous book Gradus Ad Parnassum by Johann Fux, ratio can be associated with species. 1:1 ratio means that one particular note is compared with another note with the same value, hence, 1:1 ratio simply means note against note.

There are many rules in counterpoint. These rules make counterpoint sometimes perceived as 'one of the most difficult subject in music theory'. Composing a contrapuntal music should consider these rules. Because our start point in studying counterpoint is from scratch, the type of counterpoint that we are going to study is strict counterpoint. All contrapuntal music that will appear or given in this lesson are subject to these rules. By studying strict counterpoint, I hope we can make a contrapuntal music using the same way Baroque composers composed theirs. In this lesson, I will introduce several rules in 1:1 ratio of counterpoint.

Rule No. 1
Good counterpoint is a counterpoint which has good harmonic structure.

The first rule states that good counterpoints must have good harmonic structures.  In more simple words, good harmonic structure in counterpoint means that the chords in counterpoint must be properly defined. It means that every essential notes (CF and its CP) must form a chord. In two notes counterpoint, chord not always be formed by a triad. Two distinct notes (one represents CF and the other represents CP) can be regarded as a chord. The chord may appear in various positions: root, first inversion, or second inversion.

Rule No. 2
Sometimes use dominant 7th chord.

This rule is more like a suggestion rather than a necessity. To make it clearly, dominant 7th is a major triad chord with an additional minor seventh. Dominant 7th chord is sometimes used as a resolution chord, because of its tendency to change to tonic chord. Since leading tone has also the same tendency, dominant 7th chord sometimes appears together with it.

Rule No. 3
Use 3rd and 6th intervals as frequent as possible.

Rule number 3 is a strong suggestion. It could even be regarded as weak necessity. In most good contrapuntal works, 3rd and 6th intervals appear more often rather than other intervals. The extensive use of these intervals may caused by their characteristic of being consonant. Nevertheless, other consonant intervals (any kind of perfect intervals) do not get the same rule.

Rule No. 4
Octave interval may be used, but not too frequent. If it appears, it should be approached by contrary motion.

As I was saying that consonant intervals other than 3rd and 6th do not have the same rule like rule number 3. Therefore, rule number 4 is the one the consequences which apply to particular perfect interval. I believe that rule number 4 is a self explanatory. The application of rule number 4 can be seen in the picture below.

As you may notice that an octave interval appears on the third bar. The motion from second bar to third bar forms a contrary. Thus, the appearance of octave interval follows the rule number 4.

Rule No. 5
Perfect 5th interval may be used, but not too frequent. If it appears, it should be approached by contrary motion.

Rule number 5 is identical with rule number 4 except that it applies for perfect 5th rather than octave. The picture below shows an example of the application of rule number 5.

In this example, the appearance of perfect 5th in the fourth bar is approached by contrary motion which is formed from third bar to fourth bar.

Exercise
Try to compose counterpoint part for the cantus firmus below by using all the given rules. Notice that because the CF is written in clef F, the CP must be written in clef G. I will post my composition of this exercise on the next update.

Here is my composition for the above exercise. If you find my composition violates any counterpoint rules, please do not hesitate to elaborate.