composing species counterpoint


Step 1 - Understand rules of melodic and harmonic consonance and dissonance

Melodic consonance and dissonance

Melodic consonant intervals are:

•       All perfect intervals (P4, P5, P8)

•       All diatonic steps (M2, m2)

•       Major and minor thirds

•       Major and minor sixths

 

Melodic dissonant intervals are:

•       Sevenths

•       All augmented and diminished intervals

Harmonic consonance and dissonance

Imperfect consonances:

•       Major and minor thirds

•       Major and minor sixths 

Perfect consonances:

•       All perfect intervals except the perfect fourth (P1, P5, P8)

  

Harmonic dissonant intervals:

•       All diatonic steps (M2, m2)

•       All augmented and diminished intervals

•       All sevenths

•       Perfect fourths


Step 2 - Compose the Cantus Firmus

Cantus Firmi should have the general characteristics of:

•       be singable (a reasonable range for an average singer)

•       smoothness

•       melodic integrity

•       variety

•       motion towards a goal/resolution

smooth-line.jpg

To achieve this use the following rules and constraints:

•       length of about 8–16 notes

•       all whole notes

•       all note-to-note progressions are melodic consonances

•       the leading tone progresses to the tonic

•       begin and end on the tonic

•       approach final tonic by step wise motion

•       range (interval between lowest and highest notes) of no more than a tenth, usually less than an octave

•       a single climax (high point) that appears only once in the melody

•       clear logical connection and smooth shape from beginning to climax to ending

•       mostly stepwise motion, but with some leaps (mostly thirds)

•       any large leaps (fourth or larger) are followed by step in opposite direction

•       no more than two leaps in a row; no consecutive leaps in the same direction

 

I endeavoured to compose a different cantus firmi for each species. I composed the first cantus firmus in the bass clef however when I realised that I wanted to play the two lines of counterpoint on guitar I changed to using the treble clef for both the cantus and counterpoint lines.

I found species 4 very tricky and so borrowed a ‘ready made’ cantus firmus.



Step 3 - Compose the counterpoint - first Species

First species counterpoint is whole note against whole note. I composed the cantus firmus in C major.

General principals for composing good counterpoint are the same as for the cantus; look for smoothness, melodic integrity, variety, and motion towards a resolution.

species-1.png

I followed these rules and constraints:

Rules

  • Begin and end with perfect consonances. The first note of the counterpoint should be the tonic or a perfect 5th or octave above the cantus. (There are similar rules for writing below the cantus)

  • The final note of the counterpoint must always be the tonic or an octave above/below the cantus).

  • Approach the final interval by contrary stepwise motion. (Thus, in both major and minor keys, the penultimate bar will either be a minor third or a major sixth between the two lines.)

  • The counterpoint should have a single climax, which should not coincide with climax of the cantus firmus.

  • Keep the two lines within an octave.

  • In general, all harmonic consonances are allowed.

  • Imperfect consonances (3 & 6) are preferable to perfect consonances for all intervals (other than the first and last dyads). Aim for a variety of harmonic intervals over the course of the exercise.

  • Follow every perfect consonance with an imperfect consonance

  • Vary the types of motion between successive intervals (parallel, similar, contrary) with a preference for contrary motion where possible.

Constraints

  • Unisons should only be used for first and last intervals

  • Avoid voice crossing, where the upper voice is temporarily lower than the lower voice, and vice versa. Voice crossings diminish the independence of the lines and make them more difficult to distinguish by ear.

  • Avoid voice overlap, where one voice leaps past the previous note of the other voice. For example, if the upper part sings an E4, the lower part cannot sing an F4 in the following bar. This also helps maintain the independence of the lines.

  • The interval between the cantus and counterpoint at any moment should not exceed a perfect twelfth (octave plus fifth).

  • Never use two perfect consonances of the same size in a row: P5–P5 or P8–P8. This includes both simple and compound intervals. These “parallel fifths and octaves” significantly promote tonal fusion over melodic independence at the same time that the consecutive stable sonorities arrest both the variety and the motion of the exercise.

  • Do not use more than three of the same imperfect consonance type in a row.

  • Never move into a perfect consonance by similar motion. This draws too much attention to an interval which already stands out of the texture.

  • Avoid combining similar motion with leaps, especially large ones.


Step 4 - Second Species Counterpoint

Species 2 counterpoint is whole note against half note. I composed the cantus in A minor. The ascending 6th and 7th are sharpened to create the leading tone (melodic minor).

A 2:1 rhythmic ratio introduces strong and weak beats.

Species 2 includes the similar rules and constraints as Species 1 with the big difference being the inclusion of harmonic dissonance in the passing tone, that is the note that passes from the weak (second/up) beat to the strong (first/down) beat. 

species-2.png

The following additional rules and constraints apply:

Additional Rules

  • First beats are always consonant with a preference to imperfect consonants (3 and 6).

  • Use a mixture of consonant and dissonant intervals on the second beat.

  • Unisons are permitted on weak beats when necessary to make good counterpoint between the lines.

  • As in Species 1 use primarily stepwise motion however when there is a leap, leap from the strong beat to the weak beat within the bar.

  • A dissonant passing tone on the second beat should be followed by an imperfect consonant.

  • Include one or two secondary climaxes.

Additional Constraints

  • Avoid unisons of the first beat

  • Avoid leaps from the weak beat to the strong beat across the bar.

  • Do not begin two consecutive bars with the same perfect interval.

  • Do not have a dissonant melodic interval between consecutive downbeats. 

  • Do not begin more than three bars in a row with the same imperfect consonance.


Step 5 - third Species Counterpoint

In third-species counterpoint, the counterpoint line moves in quarter notes against a cantus firmus in whole notes. I composed the cantus in G mixolydian.

This 4:1 rhythmic ratio creates a still greater differentiation between beats than in second species: strong beats (downbeats), moderately strong beats (the third quarter note of each bar), and weak beats (the second and fourth quarter notes of each bar).

Third species also introduces the neighbour tone dissonance. This is when a dissonant harmonic interval is preceded and followed by two consonant interval. The double neighbour is when beats 1 and 4 in the counterpoint are the same tone, and beats 2 and 3 include the notes a step higher and a step lower than the original tone.

Species 3 follows the same rules and prohibitions as species 1 and 2, with the general principal that a dissonant harmonic interval on the weaker beats should lead to a consonant interval, preferably imperfect, on the strong downbeat.

species-3.png

These additional rules and constraints relate to the added complexity of the 4:1 rhythmic ratio.

Rules 

•       Beats 2–4 should exhibit a mixture of consonant and dissonant intervals to promote variety.

•       Among consonances, unisons are permitted on weak beats when necessary to make good counterpoint between the lines.

•       Any dissonance must follow the pattern of the dissonant passing tone or the dissonant neighbour tone.

•       Progression towards higher and higher peaks.

Constraints

•       The pitches that begin consecutive downbeats must not make a dissonant melodic interval.

•       Avoid parallels tones and patterns across bars


Step 6 - fourth Species Counterpoint

In fourth-species the counterpoint line is a half note against the cantus firmus whole note but it is offset by two beats with each down beat half note tied across the bar line to the following up beat. This creates syncopation across the bar. There are very specific intervalic rules that make fourth-species tricky to compose. I borrowed a pre-made cantus firmus from Salzer & Schachter* in C major.

The tie across the bar introduces the suspension. The suspension can either be dissonant or consonant however the aim for fourth species is to have as much dissonant suspension as possible.

species-4.png

The following rules and constraints apply (these rules apply for writing above the cantus):

Rules

  • Always begin with a half rest.

  • Begin with an unison, octave or perfect fifth. 

  • When the suspended down beat is dissonant it must always followed by a downward step and harmonic consonance.

  • Possible dissonant suspensions above the cantus firmus are 7–6, 4–3, and 9(2)–8. These are the only options that start on a dissonance and resolve down by step to an allowable consonance.

  • Using these suspensions as much as possible will cause the counterpoint line to move downward in stepwise motion.

  • When the bar starts with a consonant interval the cantus can go up or down and it can leap.

  • At least one or two upward leaps will be necessary to counteract the downward motion.

  • Must finish with 6-7-6 suspension.

Constraints

  • Suspensions in fourth species follow similar rules to intervals of resolution in first species. For example, similar to the prohibition against using two octaves or two fifths in a row in first species, do not use two 9–8 or 4–5 suspensions in a row. Following the same principle, do not use the “consonant suspension” 6–5 twice in a row, since its interval of “resolution” is a fifth. Use 7–6 and 4–3 (above) liberally, but no more than three times in a row (like thirds and sixths in first species).

  • avoid any configuration that would create two fifths or two octaves on consecutive weak beats in fourth species (called “after-beat” fifths or octaves).

  • Avoid 2-1 suspensions

  • No overlapping lines - the counterpoint always stays above the cantus.


Step 7 - fifth Species Counterpoint

Species 5 counterpoint is about combining the previous four species together. The counterpoint should begin with a suspension and end with 6-7-6 suspension as in fourth species. Eighth notes can be used.

After following the rules and constraints of species 1-4 I decided to allow myself some freedom to compose a counterpoint tune that broke with some of the species constraints but was influenced by my experience of composing within them. I wanted to compose in an altered Phrydgian mode, which is a mode often used in Eastern music, and commonly in Klezmer (Eastern European folk music) by which it is known as the ‘Avha Raba’ or ‘Fregyish’ mode. This mode alters the Phrydgian mode by raising the third one step. The seventh can also be raised. I have also used some dotted rhythms.

I have written two counterpoint pieces in this way. I have noted the harmonic intervals between notes when they occur on the beat, or when there is a suspension. Other notes I have treated as passing tones. The first uses a cantus firmus in 3/4 time using whole notes. For the second composition I abandoned the cantus firmus and re-wrote that line against the counterpoint line. I attempted to follow the general counterpoint principals of smoothness, independence of lines, melodic integrity and motion towards a goal.

species-5.png

Chen Hui playing “Fifth Species Inspired” counterpoint.

species-5.1.png