Intro to Counterpoint

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Contents:

Basics

First Species Counterpoint Examples in First Species Second Species Counterpoint Examples in Second Species Third Species Counterpoint Examples in Third Species Fourth Species Counterpoint Examples in Fourth Species

Basics

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Counterpoint is the musical technique of setting one or more lines of music against each other in a pleasing way. Every era of history has its own style of counterpoint, and

the ability to identify these styles is one way to make intelligent guesses about the age and composer of a piece. However, most counterpoint written since the year 1600 has had at least some basis in the style of counterpoint that prevailed during the 16th century, in the music of composers like Palestrina, Lassus and Victoria. This style has been studied by composers since then, and in studying 16th-century counterpoint, you are following in the footsteps of Bach, Mozart, Beethoven and nearly every other great composer of the last four-hundred years.

Your textbook, Tonal Harmony, Fifth Edition, has chosen to not include a section on counterpoint, but my experience as a teacher of music theory has shown me that students who study the basics of counterpoint during their early experiences often have an easier time later on in the theory sequence.

In addition to studying a specific style, we will also be following a specific method of learning to write in that style. The exercises you will be doing would have felt very familiar to Mozart, Beethoven and many later composers, because they are based on a book by J.J. Fux called Gradus ad Parnassum from 1725. While many other texts on 16th-century counterpoint have been written since then, most of them look to Fux as a model, and even the ones that don’t still adopt much of his approach.

There are several basic principles to remember as you compose counterpoint: All lines are of equal importance and strive for independence from each other. The use of dissonance is tightly controlled.

Chords are not as important as the motion between notes. As a result, you will be thinking horizontally instead of vertically.

If you do not understand those basic principles, you may wish to seek additional help in class or during office hours. With that, let’s begin.

Motion Between Voices

In counterpoint, we will be very concerned with the motion between two voices. There are four types of motion, shown in the examples below. Study the examples carefully and memorize the four types of motion.

Think about what each of these means:

Introduction to

Counterpoint

by Matthew C. Saunders, DMA

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Oblique motion: One voice moves up or down while the second voice repeats the same note.

Similar motion: Both voices move in the same direction, but by different intervals. If the top voice moves up a second, the bottom voice moves up, but by some interval larger than a second.

Parallel motion: Both voices move in the same direction and move the same distance.

Notice two things about these definitions.

1. We are concerned only about the number of the interval (third, fifth, etc). Major and minor intervals aren’t as important right now.

2. The four types of motion are listed in an order such that the type that maintains the most independence (contrary) is given first and the type that maintains the least independence (parallel) is given last.

First Species Counterpoint (Note against Note)

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We will begin with the simplest counterpoint to write, note against note, or first species. One of the challenges of writing counterpoint is that you must think of several different qualities at the same time. It is not unlike solving a Sudoku puzzle or playing Scrabble.

You will always be given a cantus firmus consisting of a melody composed of just whole notes. In composing a counterpoint exercise, you may not change the cantus

firmus, just as you may not change any of the material you are given in other theory assignments.

As is traditional, we will think in “cut time,” where the whole-note gets two beats. In the music of Palestrina, barlines were not included—the music was not divided into measures, and exercises in many counterpoint books still omit them. The study of counterpoint in this way is an abstract, simplistic way of thinking about music, with the fuss and details and complexity stripped away. We choose the whole note as our basic beat because it is the easiest note to write, but we could just as easily choose any other note-value.

Given your cantus firmus, you will then compose a melody that harmonizes with it by following the rules below. After each rule, an explanation is given in italics. Some of these rules are specific for first species counterpoint and will change later. Other rules apply as long as we are writing in this “style.”

1. In first species counterpoint, you may write one and only one note in your new melody for each note in the cantus firmus.

This is a “rule of the game” that will be superseded later. For now, you will write one whole note for every whole note you are given.

2. The first note and the last note must form either an octave or unison with the cantus firmus. a. If you choose an octave for the first note, the last note must be an octave. b. If you choose a unison for the first note, the last note must be a unison.

This rule forces you to have a sense of unity to your composition. It will later be superseded when we compose for more than two voices.

3. The next to last note of your melody should help to prepare a cadence.

a. If the last note is a unison, the next to last note should create a third. Each voice should move by step to the unison. b. If the last note is an octave, the next to last note should create a sixth. Each voice should move by step to the octave.

c. The last note should be approached from a half-step below by one of the voices. An sharp on the next-to-last note may be needed for this. You may also need a sharp on the third-to-last note to prevent an augmented second (the origin of melodic minor)

A cadence is a musical stopping point. The two options above are typical of this time period and this style. In your study of other styles, you will find other cadence patterns. Rule 3c intensifies the feeling of a cadence at the end of the line.

4. The harmonic intervals between the beginning and the next-to-last note may be major or minor thirds, major or minor sixths, perfect or augmented fifths, perfect octaves or perfect unisons. Use thirds and sixths the most. If you use an augmented fith, both voices must move by contrary motion and by second to form a third on the following note.

Note that for now you are only using consonant intervals and the tritone.

5. Your melody should move mostly by seconds.

a. Thirds are permitted, but should not be used as frequently as seconds.

b. If you choose to leap by a fourth or more, the note following the leap should move in the direction opposite the leap. c. You should not leap by a tritone (diminished fifth or augmented fourth) or by a descending minor sixth.

d. Use accidentals only to avoid augmented seconds or at the cadence.

These rules are meant to help you write in a vocal style. Music is easily singable when it follows the above guidelines.

6. You must use parallel motion very carefully because it obscures the independence of the voices. a. Parallel thirds and sixths are acceptable in groups of two or three.

b. Parallel fifths and octaves are forbidden in this style. Always. Forever. Period.

This rule seems arbitrary but actually has a justification grounded in the science of acoustics. Ask me sometime.

c. A perfect fifth may move to a diminished fifth, but not the other way.

This rule also seems arbitrary but it also has a musical justification. The diminished fifth (or tritone) must always be left by contrary motion, creating a third (the voices will move inward). To do otherwise confuses our sense of mode or key.

d. A corollary to rule 6b: Fifths should be moved into by contrary or oblique motion, not similar motion.

This is true in the 16th-century style, but not in later or earlier styles. This is referred to as “hidden fifths,” because the voice that moves further could be filled in with passing tones and the result would be parallel fifths.

9. The overall shape of your melody should have a single high-point, preferably in the second half of the line.

This rule can be best justified on aesthetic grounds—it is more interesting to have the high point closer to the end.

All of these rules have justifications and reasons. The theorists of the 16th and later centuries worked out reasons that music “had” to be this way, and many of them make much sense. The rules, however, provide a procedure for writing exercises, not actual music. The best composers of the 16th century followed the rules scrupulously but still produced amazingly beautiful pieces of music that spoke deeply and meaningfully to the people who heard them. Later composers learned these rules as a starting point and

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then let good taste and creativity be their guide as to when to break them. Some rules were rarely broken: for example, from the thirteenth century to the early twentieth century, parallel fifths were considered poor form and generally in bad taste. A composer such as Beethoven wrote them only when he was trying to evoke a pastoral or unschooled mood, as in the first few bars of his sixth symphony.

Examples in First Species

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We begin with a cantus firmus. Remember that these are exercises in following the rules, not in showing off musical ideas. By this simplicity you will learn the discipline that will allow you to express your more creative ideas. Don’t try to be a genius; just try to be right.

Here is a cantus firmus (c.f.). It has a single high point and moves mostly by step. The line that you write to go with it should be similar.

A good approach is to write the first note (unison or octave) and a cadence before proceeding. Notice that I have also given the number of the interval between the two voices.

Once the first note and the cadence are in place, begin to work backwards from the end and forward from the middle. If it helps, sketch in the permissible notes as you work. In measure 2, I can have E4, but that is an awkward leap of a seventh (E5 would be parallel octaves). I could write B4, but that would follow an octave with a fifth, and I’m trying to have lots of thirds and sixths. That leaves C5 and G4. C5 allows a stepwise move, while G4 is a leap by fifth right off the bat. I choose C5.

In measure 8, I could have either F4 or A4, but F4 would be a leap of an augmented fifth. With both of those notes, I know that I will be going up after measure 9 to cadence, so I would not be recovering the leap in the opposite direction. C5 is a possibility but leads to C#5, and that kind of chromatic movement is not a part of this style. Stay within the major and minor scales! F5 to C#5 would be a diminished fourth, an awkward leap at best, so D5 is the best choice.

In measure 3, I could move back up to either D5 or E5, but this threatens to make my line stagnant and always hanging around the place it started. E4 is a leap of a minor sixth, which is not stylistically appropriate. Either B4 or G4 is a good choice, and I choose B4 to save a dramatic leap for later.

In measure 7, G5 is not a good choice because I cannot recover that leap (the following measure moves downward). The other choices are all fairly good, but I will avoid D5 and G4 because they would create a perfect fifth or a perfect octave (respectively), and I would rather have thirds and sixths. B4 and E5 are both good choices, but for the sake of the contour of my line, I will choose E5 and probably have it be the high point of the melody.

In measure 4, I have many options. D4 would create a leap of a descending sixth, which is somewhat awkward. F4 would be a leap of a tritone, which is definitely to be avoided. D5, C5 and A4 are all workable options, depending on the composer’s intent. I could continue the downward progress of my line with A4, or I could change direction with C5 or D5. I choose C5 because it allows me to write a perfect interval, the fifth, that I haven’t used yet, and it makes my line more interesting with a change of direction and contrary motion with the cantus firmus.

In measure 6, I also have many choices. At this point, I need to consider what the actual high point of my line will be—Is E5 going to be my top note, or will I go higher? Consider my options: A5 would be a leap that I can’t recover without going back to later measures and making changes. F5 would be a sixth with the cantus, which would make a row of four sixths: This is too many sixths in a row. F4 would create a leap of a seventh, which is awkward. This leaves A4, C5 and E5. Since it appears that E5 will be the high point of my line, it does not make sense to repeat it. To choose C5 would mean that measures 4-6 would just be a rocking back and forth between C5 and something else, which isn’t very interesting. But if I write A4, I will have a dramatic, yet idiomatic leap that I will then be able to recover over the next few measures. I choose A4.

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For measure 5, there are several choices, but the one that immediately makes the most sense is to smoothly connect measures 4 and 6 with B4. Note that D5 would create parallel fifths with measure 4 and G4 would create parallel octaves with measure 6. The other options require leaps in succession, but B4 makes a wonderfully smooth line. Consider the final result:

I would strongly recommend taking this and all the following examples to a piano. You should play through both lines, play one line while singing the other, and then find a partner and sing the exercise as a duet.

The cantus firmus has its high point in measure 6, and the new line peaks in measure 7. The new line moves only by steps, except for one leap, and after that leap, there is stepwise motion in the opposite direction. The last three measures (the cadence and its approach) bring the emphasis back to D, which hasn’t appeared since the beginning. The intervals formed between the cantus firmus and the new voice are mostly thirds and sixths, and in no place do fifths and octaves appear next to each other.

Another Example

Here is the same cantus firmus, but this time, we will write a line below it instead of above. To make this clearer, I have moved it up an octave and put it in treble clef.

Here is my solution to this exercise, with intervals given between the notes:

I am not completely happy with my results. I have followed the hard-and-fast rules, but the contour of my line is somewhat jagged. Notice, however, that it still has a single high point (F3), and that my two leaps larger than a third (C3-F3 and E3-A2) are both followed by stepwise motion in the other direction. More stepwise motion would have been nice, but it simply wasn’t possible without a long string of thirds that would ruin the independence of the line. The leaps in my new line occur at places where the

cantus firmus is moving stepwise, which helps the overall effect of the line. Notice that at the cadence, both voices must approach the final note by step, and they must move

in contrary motion. This will continue to be true as long as we are writing in only two voices.

Second Species Counterpoint

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So far in our study of counterpoint, we have only set note-against-note, traditionally referred to as first-species counterpoint. In first species, no dissonance is allowed between voices. This week, we will introduce our first use of dissonance with second-species counterpoint. The study of 16th-century counterpoint has much to do with the control of dissonance, and learning to use dissonant intervals in specific but effective ways that allow the underlying harmony to be clear and coherent.

As you compose second-species counterpoint, keep in mind that many of the same principles apply: All lines are of equal importance and strive for independence from each other.

The use of dissonance is tightly controlled.

Chords are not as important as the motion between notes.

As a result, you will often be thinking horizontally instead of vertically. With that, let’s begin.

Types of Dissonance

Many of the same rules from first species counterpoint will still apply to second species. The addition is the permitted use of some forms of dissonance. It is important to be aware of how these dissonances are treated. There are other ways to write dissonance, but for now, these will be the only ones permitted.

Neighbor tone: (NT) A voice or line moves up or down by step from a consonance to a dissonance, and then back to the same note, which remains a consonance. Passing tone: (PT) A voice or line moves up or down by step from a consonance to a dissonance, and proceeds by step in the same direction to another consonance. In addition, there is another type of embellishment that is permitted in second-species counterpoint.

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Writing Second Species Counterpoint (Note against Note)

Remember that, for now, it is more important to follow the rules of counterpoint than to be extremely creative. If you have a creative urge and would like to compose freely, you should do that, but not in your counterpoint assignments.

As before, you will be given a cantus firmus consisting of a melody composed of just whole notes. Remember that the cantus firmus cannot be changed. Given your cantus firmus, you will then compose a melody that harmonizes with it in the following manner:

1. In second species counterpoint, you will write two notes for every note in the cantus firmus, except for the last note.

This is a “rule of the game” that will be superseded later. You will be writing mostly half-notes in second species.

2. The first note and the last note must form either an octave or unison with the cantus firmus. a. If you choose an octave for the first note, the last note must be an octave. b. If you choose a unison for the first note, the last note must be a unison.

This rule forces you to have a sense of unity to your composition. It would be superseded later if we studied composition in more than two voices.

3. The next to last note of your melody should help to prepare a cadence.

a. If the last note is a unison, the next to last note should create a third. Each voice should move by step to the unison. b. If the last note is an octave, the next to last note should create a sixth. Each voice should move by step to the octave. c. On the last note should be approached from a half-step below by one of the voices. An accidental may be needed for this.

A cadence is a musical stopping point. The two options above are typical of this time period and this style. In your study of other styles, you will find other cadence patterns. Rule 3c intensifies the feeling of a cadence at the end of the line.

4. The interval formed between the voices on the downbeat of every measure must be a consonance—unison, third, fifth, sixth or octave.

Downbeats must be consonances in second-species.

5. The interval formed between the voices on the second beat of every measure may be either a consonance or a dissonance.

a. If the interval is a consonance, be careful not to write parallel fifths or octaves between the second beat of the measure and the downbeat of the next measure or between consecutive downbeats.

b. If the interval is a dissonance, it must be either a passing tone or a neighbor tone and must resolve correctly in the next measure.

This is the new part for second-species counterpoint.

6. Your melody should move mostly by seconds.

a. Thirds are permitted, but should not be used as frequently as seconds.

b. If you choose to leap by a fourth or more, the note following the leap should move in the direction opposite the leap. c. You should not leap by a tritone (diminished fifth or augmented fourth) or by a descending minor sixth.

d. Use accidentals only to avoid augmented seconds or at the cadence. e. All dissonances must be approached and left by step, never by skip or leap.

These rules are meant to help you write in a vocal style. Music is easily singable when it follows the above guidelines.

7. You must use parallel motion very carefully because it obscures the independence of the voices. a. Parallel thirds and sixths are acceptable in groups of two or three.

b. Parallel fifths and octaves are forbidden in this style. Always. Forever. Period.

Parallel fifths or octaves can be between downbeats or between an upbeat and a downbeat.

c. A perfect fifth may move to a diminished fifth, but not the other way.

This rule also seems arbitrary but it has a musical justification. The diminished fifth (or tritone) must always be left by contrary motion, creating a third (the voices will move inward). To do otherwise confuses our sense of mode or key.

d. A corollary to rule 7b: Fifths should be moved into by contrary or oblique motion, not similar motion.

This is true in the 16th-century style, but not in all later or earlier styles. This is referred to as “hidden fifths,” because the voice that moves further could be filled in with passing tones and the result would be parallel fifths.

8. Repetition between notes in your new line is not permitted.

Repetition was acceptable in first-species, but in second species, it too closely resembles a type of embellishment that comes later, the suspension, which has very specific rules of its own.

9. The overall shape of your melody should have a single high-point, preferably in the second half of the line.

This rule can be best justified on aesthetic grounds—it is more interesting to have the high point closer to the end.

Remember that these rules provide a procedure for writing exercises, not actual music. You are writing music that is the equivalent of batting practice for a baseball player—a relatively easy task without all the pressure and challenge of the full situation. When we add additional voices, lyrics, specific instruments and freedom of rhythm, if you know your counterpoint, you will find the task of free composition to be much easier. For now, accept the rules as somewhat arbitrary limitations that will allow you to develop control and craft in your later compositions.

Examples in Second Species

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Write the first note (unison or octave) and a cadence.

Notice that the next-to-last note of the cantus has two half-notes against it. The second half-note is the required note to create a proper cadence for this exercise: an octave must be preceded by a sixth that resolves stepwise in both voices. The first half-note is consonant with the cantus, as required. Both notes are sharped to intensify the feeling of completion at the end (a use of the melodic minor scale). The other options for the first half-note in this measure are all unacceptable: D4 would create a leap of a tritone, while B4 would cause parallel octaves with the downbeat of the next measure. As with first-species, once the first note and the cadence are in place, begin to work backwards from the end and forward from the middle, considering allowable notes on the downbeat. If it helps, sketch in the permissible notes as you work. In measure 2, there are several options. C5 would create parallel octaves with the downbeat of measure 1. E4 is a large leap, while G4 would not allow me to place a dissonance between A4 and G4 (on the second half of measure 1). A4, however, allows an imperfect consonance and will let me write a neighbor tone between the downbeats of measure 1 and 2.

In measure 8, C5 would guarantee an unrecovered leap or some other vocal awkwardness. G4 would create parallel fifths between the downbeats of measures 8 and 9. E4 is consonant, but presents problems of what note to place between it and the F#4 in measure 9. A4 is the best choice because the second note in measure 8 can then be E4, which leads smoothly to the cadence.

For the second beat of measure 1, I chose B4, which creates an upper neighbor dissonance. G4 would have worked as well, but B4 has the advantage of resolving using contrary motion, and thus increasing the independence of the voices.

In measure 3, there are many options for the downbeat. D5 requires a leap upward of a fourth, and I don’t wish to move this high this soon. It is also an octave by similar motion, and is not particularly effective. B4 would be an excellent choice for first species, but I am concerned that my melody might hover around one or two pitches, which isn’t very interesting. A4 presents the same problem. D4 would require a leap that I am not yet ready to use, and again, I would prefer a third or a sixth to an octave. My choice, then, is F4, with an eye to perhaps using G4 as the second note of measure 2.

In measure 7, I have to consider the overall shape of my line—where is my highpoint, and how do I get down from it? Thus, while F4 would be a good choice, I reject both that note and D4 for considerations of contour. I hope to come down from my high point by step, and so D5, which would require a skip somewhere in this measure, is out. B4 presents the problem again of being only a step away from the next downbeat, requiring a consonant skip for the second note, which would create two leaps, both unrecovered. A4, however, can allow a neighboring tone on the second beat of this measure, and it is my choice.

For the second note in measure 8, my choices are fairly limited. C5 would create an awkward leap of a tritone, and A4 would be a non-permitted repeated note. G4 would create parallel fifths with the downbeat of the next measure. A leap to E4, however, would be immediately recovered and would set up the rising voice of the cadence very nicely.

For the second note of measure 2, I have decided to use a consonant skip down to E4 instead of a passing tone on G4. This is in consideration of the rising stepwise pattern in the cantus firmus in measures 2-4, as will be shown momentarily. In this situation, there is no completely stepwise solution that doesn’t circle aimlessly around a few notes or create unacceptable parallels or forbidden dissonances. My reasoning will become clear in the next example, but the leap down to E4 allows a stepwise recovery on the down beat of measure 3 and lets me preview a register that I will need at the cadence.

In measure 4, I can quickly eliminate C5, because of the large leap and my earlier decision to delay the high point of my line for later. B4 is also problematic because it would create a fifth by similar motion, which is not found in this style. E4 would almost certainly have to be preceded by D4 in the previous measure, which would create parallel octaves. G4 is the best choice.

In measure 6, my options are more open. G4 would create parallel fifths with the next measure, and E4 would result in similar fifths. But either A4 or C5 would allow a properly resolved dissonance on the second beat. My choice is C5, on purely aesthetic grounds because it allows the line to have a high point just after the middle of the exercise.

In measure 7, I have the choice of two consonant skips (D5 or F4), or either an upper or lower neighbor (B4 or G4). A4 would be a repeated note, and is thus not available. I choose G4 and the lower neighbor because it is actually a dissonance (a fourth). B4 would be acceptable, but would lessen the impact of the high point of the line occurring in measure 6.

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In measure 3, I again face the problem engendered by the series of rising seconds in the cantus. Having chosen a third for the downbeats of measures 3 and 4, I cannot write a passing tone or a neighbor tone. For consonant skips, B4 creates a leap of a tritone that is additionally not properly recovered. D4 is similarly awkward because it creates two leaps in succession. F4 would be a repeated note, so A4 is the best choice. Notice that if I had written G4 as the second note in measure 2, there would be parallel fifths between the two measures on the second beats. While this is not strictly forbidden, it is poor form and should be avoided.

In measure 5, my options are many, remembering that my ultimate goal is the C5 in measure 6. D4 would leave me with the interval of a seventh to cover to get to the next downbeat. G4 would result in parallel octaves with the next downbeat. B4 would allow a passing tone in the previous measure, but there have been many thirds so far, especially on downbeats, and this tends to undermine the independence of the lines. D5 is higher than my intended goal of C5 and would obscure the shape of the line. E4 represents my best option, if it raises issues that may be troublesome later.

In measure 6, the clear choice is B4, a passing tone that allows a nice stepwise descending line from the high point.

The hardest part of writing these exercises is planning a shapely line. For this reason, not all writers of counterpoint choose to work from both ends as I am showing. It can be just as effective to work from one end or the other. No matter what the approach, be prepared to revise and make changes after your first draft.

In measure 4, the obvious choice for the second beat is F4, creating a passing tone.

Measure 5 is the problematic spot. It is much like building a bridge from both sides of the river at the same time and hoping they meet up in the middle. If you have measured correctly, they will, but you may also have to undertake some rewriting to ensure that they do. There is no permissible dissonance that will connect E4 and C5 in this case. This limits my choices to consonant skips. D5 is a leap of a seventh, which is not idiomatic. At any rate, it would replace C5 in measure 6 as the high point, and that isn’t part of my plan. G4 would result in successive leaps of a third and a fourth. This is not a stylistic way to negotiate a sixth, because there are two leaps involved. B4, however, allows a step up to C5 to follow a leap of a fifth. This is an instance when the rule about recovering leaps is momentarily in abeyance. We are driving to the high point of the line, and immediately after the high point is a descending scalar passage. In effect, the leap is recovered, but in a delayed fashion. It would certainly be wrong to go any higher or to follow the C5 by another leap.

Consider the final result:

The cantus firmus has its high point in measure 5, and the new line peaks in measure 6. The new line moves mostly by steps and thirds, and where there are leaps, they are always from a consonance to a consonance. The dissonances used are always approached and resolved by steps, and leaps appear one at a time. Contrary motion is used as much as possible.

More Examples

Here are two solutions below the same cantus firmus. I wasn’t completely happy with either of the results, and I will explain why:

In this exercise, I feel that the shape of the line is somewhat lacking, but that the cantus drove me in this particular direction. The problem is that my new line starts and ends on A4, and never goes any higher than that. The skip of a third between the first two notes of the cantus prevented me from starting up in a stepwise ascending motion and the beginning, and I could never find the right opportunity to get the line higher again. Notice that when writing a cadence in a second-species exercise below the cantus, I can’t put F#3 against B4 – this would be a fourth, and create a dissonance on the downbeat. Thus, I have ended up with two whole notes at the end of my line. It may be tempting to write E3-G#3-A3 in the last two measures, but this is simply not appropriate to the style (or to later styles). The line I wrote has good motion, but to me lacks a suitable contour.

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Even with a great big leap at the beginning (which I was not able to recover properly), the line just seems forced down, down, down. The ascending stepwise motion in much of the cantus firmus seems to guarantee it. Notice that I tried this time beginning on the second beat of the first measure, which is permissible, provided you begin with a unison or octave I couldn’t make a good high point happen, so I drove for a low point instead, with D3 starting my approach to the cadence.

This is how these exercises go sometimes – you don’t always get that perfect shape because much of your decision-making in composing a new line is driven by the cantus

firmus. Just focus on getting as musical a result as you can while staying within the stylistic guidelines (“rules”). If you were writing a piece freely, without regard to the

rules, you would still find yourself up against some of these limitations, but they would be imposed by your musical desires, not by a cantus firmus that someone else wrote.

Third Species Counterpoint

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In first-species counterpoint, we set note against note, one harmonizing note for every note given in the cantus firmus. Then, in second-species counterpoint, we wrote two notes for every note in the cantus firmus and began to use dissonance for the first time. Now, we are beginning to practice third-species counterpoint, which means writing

four notes for every notes of the cantus firmus.

As you compose third-species counterpoint, keep in mind that many of the same principles apply: All lines are of equal importance and strive for independence from each other.

The use of dissonance is tightly controlled—at no point in the 16th-century style was a leap to a dissonant note permitted. Chords are not as important as the motion between notes.

As a result, you will often be thinking horizontally instead of vertically. With that, let’s begin.

Types of Dissonance Remain (mostly) the Same

The types of dissonance used in third-species counterpoint are identical to those permitted in second-species. The purpose of dissonance in both second and thirds species is twofold:

Dissonance in the form of passing tones allows the melody to move more smoothly between consonances, allowing more use of stepwise motion. 1.

Both forms of dissonance, passing tone and neighbor tone, allow the melody to be more complex and more ornamented, thus giving it more independence from the

cantus firmus.

2. To review:

Neighbor tone: A voice or line moves up or down by step from a consonance to a dissonance, and then back to the same note, which remains a consonance. Passing tone: A voice or line moves up or down by step from a consonance to a dissonance, and proceeds by step in the same direction to another consonance. In

third-species writing, two dissonances may appear in a row as passing tones provided that neither of them falls on the downbeat and that they are preceded and followed by consonances.

Don’t forget about the use of consonance as an embellishment:

Consonant skip: A voice or line moves up or down by skip or leap from a consonance to a consonance. Leaps should be recovered as in first species.

Writing Third Species Counterpoint (Four Notes against One)

Most beginning composers find the freedom of third species to be helpful—just be careful, for with freedom comes responsibility. For second- or third-species, you should be able to remove the notes not on the downbeat and be left with a correct (except for some bad leaps) first-species exercise.

As before, you will be given a cantus firmus consisting of a melody composed of just whole notes. Remember that the cantus firmus cannot be changed. Given your cantus firmus, you will then compose a melody that harmonizes with it in the following manner:

1. New: In third-species counterpoint, you will write four notes for every note in the cantus firmus, except for last note.

This is a “rule of the game” that will be superseded later. You will be writing mostly quarter-notes in third-species. Most authors of books on counterpoint apply the rules from third-species writing to situations where there are three notes in the new melody for every note in the cantus as well.

2. Unchanged: The first note and the last note must form either an octave or unison with the cantus firmus a. If you choose an octave for the first note, the last note must be an octave.

b. If you choose a unison for the first note, the last note must be a unison.

This rule forces you to have a sense of unity to your composition. It will later be superseded when we compose for more than two voices.

3. Unchanged: The next to last note of your melody should help to prepare a cadence.

a. If the last note is a unison, the next to last note should create a third. Each voice should move by step to the unison. b. If the last note is an octave, the next to last note should create a sixth. Each voice should move by step to the octave. c. On the last note should be approached from a half-step below by one of the voices. An accidental may be needed for this.

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A cadence is a musical stopping point. The two options above are typical of this time period and this style. In your study of other styles, you will find other cadence patterns. Rule 3c intensifies the feeling of a cadence at the end of the line.

4. Unchanged: The interval formed between the voices on the downbeat of every measure must be a consonance—unison, third, fifth, sixth or octave.

Downbeats must be consonances in third-species.

5. Unchanged: The interval formed between the voices on the second beat of every measure may be either a consonance or a dissonance.

a. If the interval is a consonance, be careful not to write parallel fifths or octaves between the second beat of the measure and the downbeat of the next measure.

b. If the interval is a dissonance, it must be either a passing tone or a neighbor tone and must resolve correctly.

6. New: The interval formed between the voices on the third and fourth beats may be either a consonance or a dissonance, but only one of these notes can create a dissonance with the cantus firmus.

If you write passing tones correctly, this will not be a problem.

7. Unchanged: Your melody should move mostly by seconds.

a. Thirds are permitted, but should not be used as frequently as seconds.

b. If you choose to leap by a fourth or more, the note following the leap should move in the direction opposite the leap. c. You should not leap by a tritone (diminished fifth or augmented fourth) or by a descending minor sixth.

d. Use accidentals only to avoid augmented seconds or at the cadence. e. All dissonances must be approached and left by step, never by skip or leap.

These rules are meant to help you write in a vocal style. Music is easily singable when it follows the above guidelines.

8. Expanded: You must use parallel motion very carefully because it obscures the independence of the voices. a. Parallel thirds and sixths are acceptable in groups of two or three.

b. Parallel fifths and octaves are forbidden in this style. Always. Forever. Period. c. A perfect fifth may move to a diminished fifth, but not the other way.

This rule also seems arbitrary but it has a musical justification. The diminished fifth (or tritone) must always be left by contrary motion, creating a third (the voices will move inward). To do otherwise confuses our sense of mode or key.

d. A corollary to rule 7b: Fifths should be moved into by contrary or oblique motion, not similar motion.

This is true in the 16th-century style, but not in all later or earlier styles. This is referred to as “hidden fifths,” because the voice that moves further could be filled in with passing tones and the result would be parallel fifths.

e. There are three ways to write parallel motion: 1. Between downbeats

2. Between the third note of a measure and the following downbeat 3. Between the fourth note of a measure and the following downbeat 9. Unchanged: Repetition between notes in your new line is not permitted.

Repetition in third-species breaks down the flow and momentum of the line.

10. Unchanged: The overall shape of your melody should have a single high-point, preferably in the second half of the line.

This rule can be best justified on aesthetic grounds—it is more interesting to have the high point closer to the end.

Once again, I need to remind you that you are writing exercises. Your work should be as musical as possible, but no one will ever mistake it for actual music because it is so very limited in scope. Remember the analogy of batting practice: it may be fascinating to the observer and very helpful to the player, but no one would ever mistake it for an actual game.

Examples in Third Species

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Again, we begin with a cantus firmus.

Write the first note (unison or octave) and a cadence. Notice that I am choosing the fourth quarter-note of the next to last measure as the place where my cadence will actually take place.

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I’m going to think about how I hope to get to measure 2 – the most useful thing is to think of notes in groups of five – from a downbeat to a downbeat. My choices to harmonize with A2 would be C4, E4, F4, A4, C5 and E5 (the notes I could move to from G4 without awkward leaps). A4 would create parallel octaves, and E5 would create a fifth by similar motion. If you want a challenge, try to find a way to get to C5 in this situation—there aren’t any good answers! C4, however, can be gotten by descending steps, a wonderfully fluid way to start this line.

To finish measure 9, I will need to approach the F#4 from below: A4 cannot appear on the first or third beat because it would create parallel octaves, and if it appears on the second beat, it would create an awkward line. Similarly, if G4 precedes the F#, it must itself be preceded by another F#, causing a wobbly, uncertain approach to the cadence. The best bet is to begin the measure on C4 and move up by step.

By the beginning of measure 3, I should have recovered some of the distance I moved down in measure 1—remember that I am heading for a high point somewhere near the middle of the piece. My choices to harmonize with the D3 are D4, F4, A4, B4 and D5 (assuming no large leaps and upward motion). I choose F4 because it is higher, but not too high, and forms an imperfect consonance. I fill in measure 2 with quarter-notes that follow the rules: a consonant skip and a neighbor tone. Notice that since the third quarter-note is dissonant (a fourth), the fourth quarter-note is consonant. Also notice that although I am using several fifths, none of them create parallel fifths because of their placement within the measure. If measure 2 had begun with E4, I would have parallel fifths.

I chose a first note (E4) for measure 8 that will allow contrary motion between the downbeats and will prepare my C4 at the beginning of measure 9. Very quickly, you will realize that there are a limited number of ways to get from one downbeat to the next in third-species, and your choice will often be dictated by the motion of the cantus

firmus. In this respect, writing species-counterpoint is a lot like playing Sudoku or tic-tac-toe. Once certain decisions are made, other decisions become inevitable. The

pattern of quarter-notes in measure 8 is a good way to get to a downbeat that is down a third from the previous downbeat.

To fill in measure 3, I am still aiming for a high point, and I’m seeing that the end of my line is running fairly low, so I’ve decided to move up stepwise to C4 at the beginning of measure 4. A stepwise run in contrary motion like this is always an option when the cantus moves by step and is very helpful in getting your line to have a good contour. The falling fifth in the cantus firmus between measures 7 and 8 can be problematic, and to have my line run stepwise in the same direction could sap its independence. On the other hand, if I move in a stepwise run in the opposite direction, I will go to A3, meaning that I would need to consistently move down in measures 4-6 when I should be moving up at least part of the time. I am also avoiding the G4 in light of the approaching cadence—I want that note to be a surprising return to home when it appears in the last measure. Thus, my solution in measure 7 allows me to emphasize other pitches and more or less remain where I am.

In measure 4, I realize that if this line is to have a high point, it needs to be here, which is not the ideal spot, but reasonable enough. If I choose D5 as the downbeat of measure 5, I will have the opportunity to write still higher notes in measure 4, but not run so high that I can’t get back down. In the end, E5 is my high point, approached by step and left by skip, which is recovered in the next measure. This is an example of certain choices having consequences later on: I chose in measure 9 to have the long approach from below, which was the result my choosing to have four quarter-notes in that measure instead of two quarters and a half-note. The consequence has been that I had to stay low to avoid the G4, and thus pushed my high point closer to the beginning of the line.

In measure 6, like measure 7, by beginning and ending the measure on the same consonance, I am essentially in a holding pattern: I have slowed down the harmonic motion of the exercise in order to accommodate my need to remain in a fairly similar range. The best solution? Probably not. I can always try it again, and have learned something for the experience.

For once, though, connecting the two ends of the line isn’t a problem. Measure 5 practically writes itself! Consider the final result:

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The cantus firmus peaks in measure 6, while my new line peaks in measure 4. Perhaps I should have tried to peak in measure 7, which would have resulted in a completely different solution! Try it for yourself to see what happens.

One of the difficulties about third-species counterpoint is controlling the contour of the line. Because there are so many notes, it is possible to move from register to register very rapidly, especially if you don’t use mostly stepwise motion. Have a single high point in mind and aim for it.

It is also helpful to consider your exercise as a first-species problem: it should work out perfectly, except that the contour will be off (because you’ve been filling in leaps with passing tones). Here is the example striped of its fancy quarter-notes:

Another Example

Here is another solution below the same cantus firmus.

I’ve managed to get the high point a little bit later, the first note in measure 5, but still not ideal. The need to approach the final note (G3) from below really has put a cramp in my style. One solution to this problem might be to start on a unison instead of an octave and think in terms of a low point instead of a high point. I’m not satisfied with measure 6 because not only do I have that leap down to G3, I wasn’t able to recover it in the other direction. So I was able to have my high point at the expense of a smooth line later on in the exercise. There is a lot of F3 in measures 7 and 8, which makes the F#3 in measure 9 somewhat jarring. It is very tough to avoid this, though—a challenge for you students!

I said it before, but here it is again: this is how these exercises go sometimes – you don’t always get that perfect shape because much of your decision-making in composing a new line is driven by the cantus firmus. Just focus on getting as musical a result as you can while staying within the stylistic guidelines (“rules”). If you don’t like the result, feel free to erase and start over. You won’t be the only composer to have ever done that! We have Beethoven’s counterpoint exercises (he saved everything), and they are covered with red ink just like your papers will be soon and mine were when I was a student (a shout of to my 16th-century counterpoint teacher, Dan “Flying V” Trueman, now on faculty at Princeton). This is how we learn, and a teacher’s critical eye can always find something to “fix.” Keep at it!

Fourth Species Counterpoint

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In first-species counterpoint, we set note against note, one harmonizing note for every note given in the cantus firmus. Then, in second- and third-species counterpoint, we began to embellish this texture using melodic ornaments called passing tones, neighbor tones and consonant skips. The downbeat of each measure still had to be a consonance. Fourth-species counterpoint allows us to embellish the texture using a type of rhythmic displacement called a suspension.

As you compose fourth-species counterpoint, keep in mind that many of the same principles apply: All lines are of equal importance and strive for independence from each other.

The use of dissonance is tightly controlled—at no point in the 16th-century style was a leap to a dissonant note permitted. Chords are not as important as the motion between notes.

As a result, you will often be thinking horizontally instead of vertically. With that, let’s begin.

And Now for Something Completely Different

A fourth-species exercise can be thought of as a special type of first-species exercise with one of the parts shifted by half of a measure. In order to accomplish this, we require a new type of dissonance, the suspension.

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A suspension has three parts:

1. A consonant preparation (P) that occurs on the beat before the downbeat with the suspension. There is usually a tie from this note across the bar line.

2. The suspension (S) itself in which the newly composed voice remains on the same note as the previous beat but the cantus firmus moves to create a dissonant

interval.

3. A consonant resolution (R) created when the newly composed voice moves down by step.

There are four types of suspensions, three for use above the cantus firmus and one for use below. They are classified by the intervals formed between the voices on the downbeat and its resolution.

a. The 4-3 suspension has a fourth between the two voices on the downbeat. The top voice then moves down to create a third.

b. The 7-6 suspension has a seventh between the two voices on the downbeat. The top voice then moves down to create a sixth.

c. The 9-8 suspension has a ninth or (rarely) a second between the two voices on the downbeat. The top voice then moves down to create an octave or a unsion.

d. The 2-3 suspension is used when the newly composed voice is below the cantus firmus. It has a second on the downbeat, and the bottom voice moves down to create a third.

It is very common to see chains of suspensions when the cantus firmus moves downward by step. You should look for opportunities to write suspensions in chains as you compose. The 4-3, 7-6 and 2-3 suspensions can all be written in chains; the 9-8 suspension cannot because it would cause parallel octaves between the two voices. The resolution of a 9-8 suspension must be followed by the cantus firmus and the new voice moving in contrary motion.

Not a Suspension:

There are two suspension-like figures. One involves a sixth on the downbeat with a fifth on the following note (for writing above the cantus), and the other has a fifth on the downbeat with a sixth on the following note (for writing below the cantus). It can be useful because it can help to maintain the feel of the fourth-species passage, but it is not a suspension. However, it cannot be used in a chain because the “resolutions” would imply parallel fifths.

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Writing Fourth Species Counterpoint (Rhythmic Displacement)

Fourth-species counterpoint is much more limited and formulaic than the first three species because the goal is to include as many suspensions as possible. In those places where the cantus firmus will not allow a suspension, you will revert to the rules for second-species counterpoint.

As before, you will be given a cantus firmus consisting of a melody composed of just whole notes. Remember that the cantus firmus cannot be changed. Given your cantus firmus, you will then compose a melody that harmonizes with it in the following manner:

1. New: In fourth-species counterpoint, you will write two notes for every note in the cantus firmus, except for last note.

This is a “rule of the game” that will be superseded later. You will be writing mostly halfr-notes in fourth-species.

2. Revised: The first note and the last note must form either an octave or unison with the cantus firmus. Because the tendency in fourth-species writing is to move downward, you may begin with an octave and end with a unison.

This rule forces you to have a sense of unity to your composition. It will later be superseded when we compose for more than two voices.

3. Unchanged: The next to last note of your melody should help to prepare a cadence.

a. If the last note is a unison, the next to last note should create a third. Each voice should move by step to the unison. b. If the last note is an octave, the next to last note should create a sixth. Each voice should move by step to the octave. c. On the last note should be approached from a half-step below by one of the voices. An accidental may be needed for this.

A cadence is a musical stopping point. The two options above are typical of this time period and this style. In your study of other styles, you will find other cadence patterns. Rule 3c intensifies the feeling of a cadence at the end of the line.

4. New: The interval formed between the voices on the downbeat of every measure may be dissonant if it is part of a suspension. Otherwise, it must be a consonance —unison, third, fifth, sixth or octave.

5. Revised: The interval formed between the voices on the second beat of every measure may be either a consonance or a dissonance.

a. If the interval on the downbeat is a consonance, the second beat may be either consonant or dissonant, following the rules of second-species writing. b. If the second beat is the preparation of a suspension, it must be consonant. The suspended voice will remain on this note on the following downbeat (it may either be ties across the barline or simply repeated).

c. If the second beat is the resolution of a suspension, it must be consonant and the suspended voice will be a step lower than the previous downbeat. d. The second beat may be both a resolution of a suspension on the previous downbeat and the preparation for a suspension on the next downbeat. 6. Unchanged: Your melody should move mostly by seconds.

a. Thirds are permitted, but should not be used as frequently as seconds.

b. If you choose to leap by a fourth or more, the note following the leap should move in the direction opposite the leap. c. You should not leap by a tritone (diminished fifth or augmented fourth) or by a minor sixth.

d. Use accidentals only to avoid augmented seconds or at the cadence. e. All dissonances must be approached and left by step, never by skip or leap.

These rules are meant to help you write in a vocal style. Music is easily singable when it follows the above guidelines.

7. New: Include as many suspensions as possible in your new melody.

a. Use chains of 4-3 or 7-6 suspensions in a melody above a cantus firmus that moves down by step. b. Use chains of 2-3 suspensions in a melody below a cantus firmus that moves down by step. c. Use individual 9-8 suspensions as possible.

d. When no suspension is possible, revert to the rules for second-species counterpoint.

e. If a single 6-5 or 5-6 figure will allow you to move into a new chain of suspension without breaking the rhythm of the exercise, you should write it, but a chain of 6-5s or 5-6s implies parallel fifths and is forbidden.

8. Revised: You must use parallel motion very carefully because it obscures the independence of the voices. a. You may write as many thirds or sixths in a row as possible if they are all resolutions of suspensions. b. Parallel fifths and octaves are forbidden in this style. Always. Forever. Period.

This means that chains of 9-8 suspensions and 6-5 figures are forbidden as well. c. A perfect fifth may move to a diminished fifth, but not the other way.

This rule also seems arbitrary but it has a musical justification. The diminished fifth (or tritone) must always be left by contrary motion, creating a third (the voices will move inward). To do otherwise confuses our sense of mode or key.

d. A corollary to rule 7b: Fifths should be moved into by contrary or oblique motion, not similar motion.

This is true in the 16th-century style, but not in all later or earlier styles. This is referred to as “hidden fifths,” because the voice that moves further could be filled in with passing tones and the result would be parallel fifths.

9. Revised: Repetition between notes in your new line is not permitted, unless the first note is a suspension and the second note is its resolution.

Other types of repetition in fourth-species breaks down the flow and momentum of the line.

10. Revised: The overall shape of your melody should have a single high-point, preferably in the second half of the line, but it is more important to write as many suspensions as possible.

This rule can be best justified on aesthetic grounds—it is interesting to have the high point closer to the end, but a long chain of suspensions is even more interesting.

Fourth species is fun to write, because suspensions sound really cool. You will probably have one type that becomes your favorite (mine is 2-3), and the rhythm of tension and release is very effective. Composers have written chains of suspensions ever since the 16th century to create an effect of motion unfettered by rhythm.

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Again, we begin with a cantus firmus. On investigating it, we should see that there are two places with consecutive descending steps, measures 2-6 and measures 8-10. We should try to put chains of suspensions in these places.

Write the first note (unison or octave) and a cadence. I am choosing a half-note for my next-to-last note because I am anticipating a 7-6 suspension in that measure.

I’ll begin with the end. To have a proper cadence, I need a sixth between the voices on the next-to-last note, which means that if there is going to be a suspension in measure 9, it will have to be a 7-6 suspension. Since the cantus in measure 8 is a step above measure 9, I can easily extend my chain backward one measure, giving me two suspensions in a row. It is customary to tie the preparation to the suspension, but not required—you can simply repeat the note. I need to make sure that I remember to prepare my suspension in measure 8, so the second beat of measure 7 must also be E5. I could have a 9-8 suspension in measure 7 by writing F5 on the downbeat, but in looking at measures 2-6, I see an opportunity for another chain. I will need measures 6 and 7 to link the two chains together, so maybe the 9-8 will work out. I’ll keep it in mind as a possibility as I move on.

For measures 2-6, I have also chosen a chain of 7-6 suspensions. I can’t have G5 on the downbeat of measure 2 because it would be a dissonance that I wouldn’t be able to prepare—it would form a fourth with the first note of the cantus firmus. Now all I have left are a few linking notes. As you can see, the 9-8 suspension I had considered for measure 7 won’t work—the F5 I would need at the end of measure 6 would mean that the suspension in measure 6 wouldn’t resolve correctly. (in a three-voice texture, however, I could put that suspension in another voice).

At the beginning, I have F5 as the last note of the first measure, with E5 as the downbeat of measure 2. Notice that this part of the music that does not involve suspensions follows the rules of second-species counterpoint exactly.

To connect my two chains of suspensions, I chose a note for the downbeat of measure 7, C5, that would be completely in line with the rules of second species counterpoint.

My line doesn’t have the ideal arch-shaped contour that I might wish it had. On the other hand, in fourth-species, the point is more to write as many suspensions as possible, and in ten measures, I have six suspensions.

Other Examples

Even though the cadence at the end required 7-6 suspensions, I didn’t have to choose them for my big chain in measures 2-6. Here is an alternate answer, just as correct, that uses a chain of 4-3 suspensions instead:

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Notice that I chose to have a half-rest at the beginning of my line. This is because to get the D5 I needed on the downbeat of measure 2, I needed to tie that note in from the previous bar. I could have written a whole note instead of half-rest followed by half-note as well, but this is more interesting. With my chain of 4-3 suspensions, I end up a fourth lower in measure 6, and I can connect with measure 7 using parallel thirds. I moved my second chain of suspensions (measures 7-9) down an octave to avoid a bad leap up to E5. This means that my line ends an octave lower than where it begins, but in fourth species, this is permissible.

Which version is better? The first version has the advantage of a more compact range—everything happens in the tritone between B4 and F5. But the constant 7-6 suspensions may get monotonous. The second version is more spread out—the range of a ninth is fairly wide by 16th-century standards, and it doesn’t end where it begins, which is a disappointment. But—it uses two kinds of suspensions instead of one.

Here is a version that is written below the same cantus firmus. Remember that a suspension below the cantus must be a 2-3 suspension, so that’s all you will see:

Once again, I am able to take full advantage of the descending stepwise cantus firmus, and again, my notes that aren’t suspensions follow the rules of second species. Another way to think of fourth-species is as a first-species line in which one of the lines has been delayed by a half-note. It means a lot of parallel imperfect consonances (sixths and thirds), but other than that, should follow the rules for first-species.

This is where we will stop for counterpoint for now. Traditionally, composers studying counterpoint would also study fifth-species writing, in which you are still given a

cantus firmus, but you are free to write any rhythm against it, including whole notes, half notes, quarter notes and a few eighth notes. If you would like to try some of this, I

guarantee you will enjoy the challenge. It is more expressive and creative than the first four species and combines all of their possibilities and limitations. After mastering the five species in two parts, students of counterpoint then begin to work in three parts, writing two parts against one cantus firmus, and then four parts. Depending on your teacher, you might even move from there to five or six parts, which are truly difficult, but by this time you would also be writing actual pieces of music, at first in the style of Palestrina and in the style prevalent in your time. Eventually, if you were very good, you would develop your own voice within your contemporary style, in the way that Mozart’s music is thoroughly classical, but in his best pieces, you can’t mistake them for the work of anyone else. A very few composers take this even one step further and step out of any established style to create something completely new. It was Monteverdi’s doing just this that signaled the end of the 16th century style, and Beethoven’s work ushered in the Romantic style.

For us, however, for now, I think by stopping at fourth-species, we have experienced enough counterpoint to help our study of harmony. OPSU offers a course in counterpoint that will come around again before you graduate, and I recommend it to all of you.

Email:

matthew@martiandances.com

All Rights Reserved, © 2008 by Matthew C. Saunders

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