Species Counterpoint (part 2 – Rules of Polyphonic Motion)

        Before studying the specific rules of each species of counterpoint, there are some basic principles of polyphonic motion that we should understand.  The first concept among these principals is the fact that there are three types of polyphonic motion.  They are direct motion, contrary motion and oblique motion. 

        Direct motion consists of two or more parts moving in the same direction (ascending or descending) by step or skip.  Whether the parts move in equivalent intervals (all steps, all skips, equal distances) is irrelevant.  The only relevant factor to qualify polyphonic motion as direct is that the parts move in the same direction. 

  

      Contrary motion consists of two parts moving in opposite directions (ascending and descending) by step or skip.  Again the interval of movement is irrelevant since the classification of contrary motion is only contingent on the direction of the motion.  This type of polyphonic motion can only occur between two parts since there are only two directions of motion (ascending or descending).  A third part would have to duplicate one of these two types of motion, and thus be an example of direct motion with that part. 

        Oblique motion consists of one part moving (by step or skip) while the other part remains stationary.  The stationary part could be a single pitch with a rhythmic value that is longer than the pitches of the moving part, or it could be repeated rhythmic occurrences of the same pitch.  As we will discuss in future lessons, the rhythmic value of a piece of counterpoint may vary from that of the cantus firmus only in certain species. 

        Now that we understand the three possible types of polyphonic motion, we can discuss the four fundamental rules of polyphonic motion.  They are listed below:

1. From one perfect consonance to another perfect consonance one must proceed in contrary or oblique motion.
2. From a perfect consonance to an imperfect consonance one may proceed in any of the three motions.
3. From an imperfect consonance to a perfect consonance on must proceed in contrary or oblique motion.
4. From one imperfect consonance to another imperfect consonance one may proceed in any of the three motions.

These four rules can be boiled down to two basic principles.  When we are traveling to an imperfect consonance, we may use any type of polyphonic motion.  However, when we are traveling to a perfect consonance, we must avoid direct motion.      

        As a result of these rules, composers find it more desirable to utilize imperfect consonances in their polyphonic writing.  This results in less restriction on the types of motion that they can employ.  In addition, imperfect consonances are perceived to be more harmonious than perfect consonances.  The pure quality of perfect consonances cause them to sound hollow or empty.  The impure quality of imperfect consonances cause them to sound rich and full.    Therefore, the majority of harmonic consonances within a polyphonic work should be imperfect otherwise the work will seem to lack harmony. 

       However, a work of counterpoint must start and end with a perfect harmonic consonance in relation to the cantus firmus.  To be more specific, all works of counterpoint must end with either a unison or octave.  In addition, any work of counterpoint that is composed below the cantus firmus must begin with a unison or octave.  Works of counterpoint composed above the cantus firmus may also begin with a fifth. 

This cannot be done with counterpoint that is composed below the cantus firmus because a fifth below would result in an obscuring of the perceived key.  Another rule of polyphonic motion is that all counterpoint must remain in the same key as the cantus firmus.  A starting interval that is a fifth below the cantus firmus could be perceived as a Do – Sol relationship in which the counterpoint is starting on the tonic even though it is actually a Fa – Do relationship in which the cantus firmus is starting on the tonic.  This dilemma could obscure the perceived key of the polyphonic work, and is thus avoided. 

The perfect fourth is considered to be a consonant interval when examining two pitches outside of any other musical context.  Remember, the perfect fourth is an inversion of the perfect fifth, and is thus heard as a similar interval.  However, within various musical contexts the state of this interval is more complex.  The best way to understand consonance and dissonance in polyphonic music is to think of consonant intervals as stable in relation to the key, and dissonant intervals as unstable in relation to the key.  Therefore, any interval of a fourth that requires resolution is considered to be dissonant. 

Since the perfect fourth is and inversion of the perfect fifth, Do – Fa relationships can easily be misperceived as Sol – Do relationships (as discussed earlier).  Any polyphonic situation that obscures the identity of the key would be considered dissonant, and in need of resolution.  In works containing three or more voices, additional pitches may help to support the integrity of the key and cause an interval of a perfect fourth to be considered consonant.  However, in two part compositions the perceived dissonance of the perfect fourth would be unavoidable. 

Now that we have an understanding of the basic principles of polyphonic motion, we are better prepared to discuss the specific rules of each species of counterpoint.  In future lessons on each species, please review the principles of this lesson.  Once we apply these principles through the practice of polyphonic composition, they will become easier to understand and retain.   

       
         This Learning Music With Ray video gives an overview of the basic rules of polyphonic motion that govern all polyphonic composition. After gaining an understanding of these rules, one will be better prepared to study the specific rules of each species of counterpoint. The video starts by discussing the three types of polyphonic motion. I then cover the four fundamental rules of polyphonic motion. Next, I discuss the difference between perfect and imperfect consonance in polyphonic music. Finally, I go on to discuss other miscellaneous rules of polyphonic motion, and the dissonant nature of the perfect 4th in polyphonic music. 

Species Counterpoint (part 1 – Cantus Firmus)

What Is Species Counterpoint?

      Species counterpoint is a method that has been used for many years to teach polyphonic musical composition.  The method is modeled after the compositional works of Palestrina.  This method of study was propelled forward in our modern musical culture primarily by the Johann Joseph Fux’s book entitled Gradus Ad Parnassum.  The starting point for this method is creation of a fixed melody or cantus firmus.  Next, the student composes additional melodic lines as harmony parts to the cantus firmus.  Each species of counterpoint implements a different set of rules that the harmony line must follow in relation to the cantus firmus.

Why Study Species Counterpoint?

What makes a melody beautiful?  Why do certain harmonies sound nice, and others do not?  In tonal music, there are certain melodic and harmonic characteristics that are considered beautiful and expressive.  The study of species counterpoint helps composition or music theory students to understand, identify and replicate these characteristics. 

What Is A Cantus Firmus?

A cantus firmus is a pre-existing fixed melody that forms the basis or foundation of a polyphonic composition.  One of the best ways to familiarize yourself with the parameters of a well written cantus firmus is to study pre-existing examples.  Here is an example of a cantus firmus:

        

        

          There are several basic rules that we must follow when composing a cantus firmus.  These rules can be observed in the existing literature of great cantus firmi.  They are:

1. Cantus firmi do not extend beyond the range of a tenth, and they usually remain within the range of an octave.
2. Most cantus firmi are 8-16 notes in length,
3. Cantus firmi begin and end on the tonic.
4. Cantus firmi usually approach the final tonic by step.
5. Cantus firmi contain a single climax.
6. Cantus firmi contain no rhythmic variation (they are composed of all whole notes).
7. Cantus firmi contain mostly stepwise motion, but have some jumps (usually small).
8. Leaps larger than a fourth are followed by stepwise motion in the opposite direction.
9. Cantus firmi do not contain more than two leaps in a row, and consecutive leaps are usually in opposite directions.
10. The intervals between consecutive pitches in a cantus firmus are always melodic consonances.

Consonance & Dissonance

Webster’s defines consonant as:  being in agreement or harmony; free from elements making for discord.  It defines dissonant as:  a mingling of discordant sounds; especially: a clashing or unresolved musical interval or chord.  A simple explanation of these terms would be that consonant intervals create pure harmonies while dissonant intervals create impure or even clashing harmonies.

I covered the concept of consonance and dissonance in my Learning Music With Ray: Musical Intervals lesson.  However, the basic consonant and dissonant intervals discussed in that lesson are harmonic intervals.  A harmonic interval is the distance between two pitches that are heard at the same time.  A melodic interval is the distance between two pitches that are heard consecutively.  The rules for melodic consonance differ slightly from harmonic consonance.  Like harmonic consonance, melodic intervals that are perfect, major/minor thirds or major/minor sixths are considered consonant.  However, diatonic steps are also considered to be melodic consonance. 

When you watch a good movie, sporting event or read a good fiction, what happens?  It starts slow, then some issue develops that puts you on the edge of your seat.  Finally it reaches a climax and then resolves.  The same thing happens in good music.  Dissonance is used to create conflict, then consonance is used to resolve the conflict.  Learning to control the flow of tension and release in musical composition is an important key to creating beautiful and expressive music. 

The study of species counterpoint helps us to understand the nature of musical tension and release, in addition to other musical laws and tendencies.  To start studying species counterpoint, one must first study the nature and composition of a cantus firmus.  Continued study of existing cantus firmi, along with practice composing cantus firmi according to the rules listed above, will aid you in these studies.

       

          This Learning Music With Ray video discusses is meant to open a series I will be teaching on species counterpoint.  In this first lesson, I will give a brief description of what species counterpoint is.  I will also discuss the illusive concepts of musical expression and beauty.  I will explain how the study of species counterpoint can aid in understanding the construction of expressive and beautiful music.  Finally, I go on to discuss what a cantus firmus is, and the rules that form the basis for its composition.