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Introduction to Counterpoint by Matthew C. Saunders, DMA
Contents:
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:
Contrary motion: The two voices move in opposite
directions. If the top voice moves
up, the bottom voice moves down. If
the top voice moves down, the bottom voice moves up.
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)
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 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.
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
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
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
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
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
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.
Consonant skip:
(CS) 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 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.
Again, we begin with a cantus firmus.
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
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
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
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
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
Consider the final result:
The cantus firmus has its
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.
So I tried again, even changing my
bottom staff to alto clef to help me think of going up instead of down:
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.
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.
- 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.
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.
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.
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.
It would also be permissible for
the next-to-last note of my melody to be a half-note.
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
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
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
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:
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
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
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!
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.
Suspensions: For
the first time, we will have dissonances sounding on the downbeats of measures,
but as usual, only in a very controlled manner.
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.
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.
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:
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.
