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Counterpoint


Counterpoint (pl. contrapuntist) is the study of two or more individual lines of music written above each other and played simultaneously.

The art of counterpoint has been developed from as early as the 9th century, and since it has come to be categorized into five different species, each with their own set of rules.

But before studying the different species, one must learn the difference between consonant and dissonant intervals and the rules of motion.


Intervals

When working with counterpoint, it is necessary to look at the harmoniousness of intervals which are divided into perfect consonant, imperfect consonant, and dissonant:

Perfect Consonant Imperfect Consonant Dissonant
Unison Thirds Seconds
Fifth Sixths Fourth
Octave Tritone
Sevenths

Motions

Motion is the study of linear movement between two or more lines of music. There are three different types of motion: direct, contrary, and oblique.

Direct Motion

Direct motion results when both lines of music move in the same direction.

Contrary Motion

Contrary motion is when one line of music moves in one direction and the other to the contrary.

Oblique Motion

Oblique motion is when one line of music remains stationary, and the other moves up or down by step or skip.

When using these motions, it is important to follow the following set of rules:

  • First rule: From one perfect consonance to another perfect consonance one must proceed in contrary or oblique motion
  • Second rule: From a perfect consonance to an imperfect consonance one may proceed in any of the three motions
  • Third rule: From an imperfect consonance to a perfect consonance one must proceed in contrary or oblique motion
  • Fourth rule: From one imperfect consonance to another imperfect consonance one may proceed in any of the three motions

Usually, before beginning to write counterpoint, a cantus firmus (a set melody) is required as the basis to which the composer adds to.


First Species

In the first species of counterpoint, both lines of music consist only of semibreves (whole notes).

The following is a list of rules for the first species:

  • Consonant intervals are only permitted
  • If the cantus firmus is in the lower part, the first interval may be a unison, fifth, or octave
  • If the cantus firmus is in the upper part, the first interval must be a unison or octave
  • The last interval may only be a unison or an octave
  • More imperfect than perfect consonances should be used in the body
  • Unison cannot be used in the body
  • A tritone is not permitted (diminished fifth/augmented fourth)
  • Contrary and oblique motion should be used as much as possible
  • A skip of a major sixth is prohibited
  • A tenth into an octave by contrary motion is prohibited at the beginning of a bar
  • A consonance into an octave by skip is prohibited
  • If the cantus firmus is in the lower part, the second last interval should be a major sixth
  • If the cantus firmus is in the upper part, the second last interval should be a minor third

Figure 1: The first species of counterpoint with the cantus firmus at the bottom.

Figure 2: The first species of counterpoint with the cantus firmus at the top.


Second Species

In the second species, there are two minims (half notes) against one semibreve (whole note).

The same set of rules applies from the first species unless mentioned below:

  • It is permissible to begin with a minim rest, starting the counterpoint on the upbeat (which must be a perfect consonance)
  • The downbeat must be a consonant
  • The upbeat may be a dissonant if it moves from the proceeding note and to the next note stepwise
  • If the upbeat moved by skip, it must be a consonant
  • The skip of a third cannot prevent the succession of two fifths or octaves on the downbeats
  • The skip of a minor sixth or an octave is permitted if there is no possibility of contrary motion and the two parts have been led so close together that one does not know where to take them
  • If the cantus firmus is in the lower part, the second last bar should consist of a fifth followed by a major sixth
  • If the cantus firmus is in the upper part, the second last bar should consist of a fifth followed by a minor third

Figure 3: The second species of counterpoint with the cantus firmus at the bottom.

Figure 4: The second species of counterpoint with the cantus firmus at the top.


Third Species

In the third species, there are four crotchets (quarter notes) against one semibreve (whole note).

The same sets of rules apply from the previous species unless mentioned below:

  • If four crotchets in a bar follow each other ascending or descending stepwise, the first one has to be a consonant, the second may be a dissonant, and the third must again be a consonant. The fourth one may be a dissonant if the fifth note (in the new bar) is a consonant
  • The previous point does not hold if the second and fourth notes are consonant, in which case the third is always a dissonant
  • Another alternative to the first point is ‘cambiata’ - beginning with a consonant, the second a dissonant, and the third a consonant by the skip of a third
  • If the cantus firmus is in the lower part, these are the possibilities for the second last bar:
  • If the cantus firmus is in the upper part, these are the possibilities for the second last bar:

Figure 5: The third species of counterpoint with the cantus firmus at the bottom.

Figure 6: The third species of counterpoint with the cantus firmus at the top.


Fourth Species

In the fourth species, there are two minims (half notes) against a semibreve (whole note), and the minims are tied together over each barline. This species is also known as ‘ligature’ or ‘syncopation.’

The same sets of rules apply from the previous species unless mentioned below:

  • Every bar can be consonant or dissonant:
    • Consonant bar: Both minims are consonant intervals
    • Dissonant bar: The downbeat is a consonant and the upbeat a dissonant
  • Dissonant intervals must always be resolved descending stepwise to next consonance
  • One may replace ligature with an untied minims anywhere ligature cannot be introduced. The ligature must start up again whenever the opportunity rises

If the cantus firmus occurs in the lower voice:

  • The interval of a third on the upbeat followed by a second on the downbeat is permitted
  • The interval of a tenth on the upbeat followed by a ninth on the downbeat is permitted
  • The second last bar should consist of a seventh followed by a sixth

If the cantus firmus occurs in the upper voice:

  • One may use from the downbeat: a second to the third, a fourth to the fifth, or a ninth to the tenth
  • A seventh to the octave is not permitted, and the seventh may be omitted with a minim rest
  • The second last bar should consist of a second followed by a third, followed by unison in the final bar

Figure 7: The fourth species of counterpoint with the cantus firmus at the bottom.

Figure 8: The fourth species of counterpoint with the cantus firmus at the top.


Fifth Species

The fifth species of counterpoint, rather than a strict number of notes against each other, is the combination of all previous species to make a unique melodic line. This species is also known as ‘florid counterpoint’ as its composition should flourish and make a line of excellences.

There are only a few new points of order for this species:

  • Great use of oblique motion or ligature should be made when approaching the downbeats
  • Although passable, two crotchets (quarter notes) at the beginning of a bar without a ligature following is considered weak counterpoint

Figure 9: The fifth species of counterpoint with the cantus firmus at the bottom. The interval are bar numbers have been left out here for your understanding.

Figure 10: The fifth species of counterpoint with the cantus firmus at the top.


Also see Voices | Texture.


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