A Counterpoint Handbook - sample by David Powell

A Counterpoint Handbook ! ! !

! ! Table of Contents

! Introduction

1. Chords and Progressions 2. Non-chord Notes and Dissonance 3. Features and Techniques of Counterpoint 4. Fugues 5. Invertible Counterpoint 6. Figured Bass 7. Baroque Dances

! !

Preface

This short handbook is an introduction to principles of two-part counterpoint for keyboard in the harmonic language of the Baroque era. It grew out of notes that I created to help me prepare my students for the counterpoint exam of the Royal Conservatory of Music (Toronto), and other similar exams. It is assumed that the reader is already familiar with basic harmony concepts, binary and ternary forms, secondary dominants, and modulation to closely related keys (i.e. one sharp or one flat away).

This handbook contains some homework exercises to help students to learn the material and concepts. To fully master this material, students must also work on practice exams such as those published by the RCM.

Permission is granted to copy homework sections for ease of marking. Otherwise please respect my copyright and refrain from copying this book.

! !

David Powell Vancouver, Canada 2014

Introduction: What is Counterpoint? Counterpoint is simply the art of adding a part* to a given part or parts. The word derives from the Latin words contra (against) and punctum (a note). Any music that has more than one voice is in a sense contrapuntal, even medieval organum, where one voice moves strictly in parallel with another:

& œœ

œœ

The chorales that you learn in your study of harmony are contrapuntal compositions because there are lines of music interacting with other lines:

# 4 œ & 4 œ œ ? # 44 œ

œœ œ œ

œœ # œ œœ œ œ. œ œ œ J

Bach - Jesu meine Freude

˙œ # œ ˙˙ œ œ œ ˙ ˙ œ œ

However, when we use the words 'counterpoint' and 'contrapuntal', these days we are usually referring to a particular style of music where the individual lines are written so as to sound equal to and independent from one another. In this style the parts are like equal partners in a conversation. In this conversation the voices often pass motives back and forth, imitating each other. The dialogue also often features contrary motion and rhythmic variety, which helps the voices stand out from one another. ________________________________________________________________________________________ *In this book I use the words ‘voice’ and ‘part’ interchangeably. The word ‘voice’ in this sense is not necessarily literally a sung part: it could a vocal part or an instrumental part.

There were two golden eras of counterpoint. The first was during the 16th century, which saw the flourishing of the great church polyphony of composers such as Palestrina (the word polyphonic can also be used to mean contrapuntal). This counterpoint was fairly imitative and modal.

b & b bb

? bb b w b

Ó ˙

˙˙

jœ œ ˙ œ . œ œ œ

Palestrina - Sicut Cervus

˙œ ˙œ . œ ˙œ œ œ˙ œ œ Jj œ œ œ . œ œ œ ˙˙ Ó

The second is the Baroque, especially the late Baroque, which was the heyday of instrumental counterpoint. The greatest contrapuntal composer of this era was Johann Sebastian Bach. In Palestrina’s time the music the major/minor tonal system was not yet fully evolved, but by the time Bach came along, it had been for some time. Bach expressed his contrapuntal genius most fully in his fugues and inventions, although you can find contrapuntal writing in almost all his music, even in his chorales.

œ œœœœœœ œ j œ œ œ œj & b 43 ‰ œ œ œ œ œ j œ j œ œ œ ? b 43 œ œ ‰

Bach - Invention 8 BWV 779

It's Baroque counterpoint that we are going to study in this book. If you want models to study, then Bach's fugues and inventions are your best bet. The fugues are really the greatest contrapuntal compositions ever written. The two-part inventions are also good to study because they are in two parts, whereas the fugues are usually in three or four.

Unit 1: Chords and Progressions

The counterpoint of the 18th Century was based on triadic harmony, just like the chorales you write in your harmony studies. Now obviously triads have three notes in them, and 7th chords have four. So how do we create triads and 7th chords in two voices? Well, we can't directly sound a complete triad in two voices, but we can imply one.

Triads We imply a triad in root position by sounding the root and the 3rd, or the root and the 5th. The 1st inversion is implied by the 3rd and the root. The 3rd and the 5th is also possible, except that the root is missing and so the harmony will not be quite so clear. The 2nd inversion is implied using the 5th and the root, or the 5th and the 3rd.

& ˙˙ C: I

˙˙ I

˙ ˙ I6

˙˙ I6 (or iii?)

˙˙ I6 4

˙ ˙ I6 (iii6?) 4

Seventh chords A seventh chord such as V7 can be satisfactorily implied using either the root and the 7th together, or the 3rd and the 7th. Study the examples below:

w & w

ww V6 5

˙˙

V4 2

˙˙

Arpeggiation Another way to imply a triad in one voice is by using an arpeggio. We'll talk more about this in unit 3.

Ambiguity As you can see there's sometimes some ambiguity when you only have two voices. In the 2nd bar on the previous page, is that a I6 chord or a iii chord? Well, most likely the context will show you. Consider the following. What is the chord on the 3rd beat? It looks like ii, but if you play it and add in the extra notes to complete the chords you'll hear it sounds more like vii6 even though there's no B. Our ears interpret according to what we're used to hearing (also, passages in parallel 3rds sound nice, in moderation).

& œ˙ œ œœ œœ ii?

Chord Progressions The rules governing chords progressions are really the same rules that you learned in harmony. The chart below is actually borrowed from the four-part harmony text I wrote. It offers a general guide to chord progressions that applies equally to two-part counterpoint. Pieces of tonal music generally begin on the tonic chord, leave it for a while, and come back to it by way of the dominant. We put the tonic chord, I, at the top of the chart. It's a "Level 1" chord. The I chord can go to any other chord. All the other chords tend to move up one level. So • Level 2 chords are dominant chords: V and vii. These chords like to go to level 1, to I. • Level 3 chords are pre-dominant chords. This means they like to go to the Level 2 chords V or vii. • The lonely iii chord on level 4 likes to go up to level 3, either to vi or I

level 1: level 2:

level 3:

level 4: 4

I vii IV iii

2nd inversions Triads Implied 2nd inversion chords are OK in 2 parts but limit yourself to the standard types: cadential, passing, and arpeggio. Also, it's better use the 5th in the bass and the 3rd above it. If you use the root you'll have a bare perfect 4th.

œœœœœœœ & œ œ œ œ œ œœ

œ œœœœ œ œœ œ œ I6

I64

œ œ

Consecutives and Direct 5ths and 8ves. You guessed it, all the rules that you learned about consecutives in 4 parts still apply. In fact, they are even more important. You might get away with a consecutive 5th in a 4-part texture, but it'll be very noticeable in two voice, and will sound bad. Bad

& ˙˙

˙˙

˙ ˙

Similarly, direct (a.k.a. exposed) 5ths and 8ves sound very bad in 2 parts: Bad

& œœ œœ ˙˙

Better

œœ œœ ˙ ˙

Range This book is focused on keyboard counterpoint, not vocal. You are therefore less bound by range restrictions than you were when writing four-part harmony for actual singers. Having said that, there is still a limit to how high and low you can go. As a very rough rule you generally don't see notes more than one ledger line above the treble staff (B or C) or below the bass staff (E or D).

Complete these chord progressions in two parts. It's possible to write these without any empty perfect 5ths and 4ths. Use only 3rds, 6ths, 2nds, 7ths and tritones; you can also use an octave at the end of exercises 6 and 7 (next page). Use quarter or half notes in 4/4 time. 1. I - V6 - I

in G and F

2. I - V6 - vi

in A and B b

3. I - IV6 - V6 - I 5 4. I - V6 - IV6 - iii6 - ii6 - V - I6

in B and D

# & 44 œ œ ˙ 1.

? # 44 œ œ ˙ &

? 6

(4. cont.)

in C, E, and F # 2.

b b 4.

5. I6 - ii6 - V - I6

in G and A

6. I - I6 - IV - V4 - I6 - V - I 2 7. I6 - I - V6 - vi - ii6 - V - I

in A b and E b in C and D in E, F and B b

8. V - I6 - IV - viio6 - vi - V6 - I

? &

? 7

Unit 2: Non-Chord Notes and Dissonance As we write in two part counterpoint, we must be very aware of the harmonic, or vertical, intervals that are created by the two parts. Intervals may be divided into two categories: consonant and dissonant. Consonances are either perfect or imperfect. In general, you want to keep perfect intervals to a minimum. This is because they sound bare and empty. The exception to this is at the beginning and end of the piece: the piece needs to end on an octave or unison, and sometimes also begins with a perfect interval (although bare, these intervals sound strong). The imperfect intervals, the 3rd and 6th, are your 'bread and butter' intervals, the ones you will be using most of the time to construct chords. Dissonances Dissonances are very important in counterpoint and add a lot of richness and interest to the music. If the perfect intervals are your bread and butter, it's the dissonant intervals that add spice. Dissonant intervals are 2nds, 7ths, tritones, and perfect 4ths. Generally, dissonant intervals arise because of the use of non-chord notes or 7th chords. Let's begin by reviewing non-chord notes.

Non-chord Notes in Two Voices The non-chord notes that you have learned about in your harmony studies are all possible in two-part counterpoint:

Passing notes When a note fills in a gap between two chord notes and is sounded on a weak beat or weak part of a beat, we call it a passing note or passing tone. Note that in the 2nd example below, the notes begin a 10th, not a 3rd, apart. If they start only a 3rd apart, as in the 3rd example, the music is congested and too awkward to play. The passing notes in these examples create a passing dissonance of a 2nd (9th).

& œ˙ œ 8

œ ˙

too congested

˙œ

Neighbour notes When we decorate a note by sounding the note above or below it on a weak beat, and then return to the original note, we call it a neighbour note, or an auxiliary note. In these examples the neighbours create a dissonant perfect 4th, a dissonant 9th, and a perfect 5th (not dissonant): nn

& œœ

œ œ

œ ˙

œ œ

œœ

Echappées These notes are found on weak beats. They are approached by step and then resolve by leap of a 3rd in the opposite direction. It's a common keyboard idiom to string a few of them together. A dissonant perfect 4th is created by the echappée.

œœ &

ech.

œœ

ech.

œœ œ œœ œ œœ œ œœ

Anticipations Anticipations occur only on weak beats or the weak part of a beat. The best way to think of an anticipation is that it's a note that arrives early. Most often you'll find an anticipation anticipating the final tonic of a phrase at a cadence in the top part. In this scenario an anticipation creates a dissonant 4th with the bass.

œœ &

ant.

œœ œ ˙ ˙

œ œ

œ œ œœ . œ

j œ

ant.

w w 9

Accented Passing Notes Like their weaker brethren the accented passing notes fill in gaps of a 3rd between chord notes. The difference is that they occur on the strong part of the beat. The apn in the first example makes a dissonant 7th with the bass. In the 2nd example it makes a dissonant 9th (2nd).

œ & œ

apn

œ œ

œ ˙

apn

Suspensions I like to think of suspensions as being the opposite of anticipations: instead of a note arriving early, a note stays late, and then has to catch up with the other voice. Suspensions occur on strong beats and are often tied from the previous note, but not always. In the 1st example below, the C in the upper voice 'stays late', creating a dissonant 2nd. This is the suspension. It must resolve down a step to B. In the 2nd example the parts have been inverted and the suspension is in the upper part, causing a dissonant 7th, which must also resolve down a step to B. The 3rd example shows a dissonant perfect 4th. When it appears on a strong beat the top note of the 4th must resolve down by step. Here the C is resolving down a step to B. Play it on a keyboard. See how bare and empty it sounds? If you have a choice, try to avoid accented perfect 4ths altogether for this reason. The 3rd example is not incorrect but it doesn't sound very good either.

˙˙ & I

˙œ œ

˙ œ œ ˙ ˙

vii6

A suspension could also resolve by step upwards. It may seem odd to see a 7th resolving up, but it makes sense when you look at the harmony. Upward-rising suspensions are sometimes called 'retardations'. 10

w w I

˙ œ œ˙ œ œ. J

œ œ œ œ & œ œ

I64

œ ˙

w w I

On an exam question, whenever a given part has a note tied over from a weak beat to a strong beat and then the note resolves down a step, you can be pretty sure that you are expected to treat that given note as a suspension: Given part:

œ œœœ œ &

Solution with suspension:

œ œ œ

œ œ œ œ œœ œ œ

œ œœ œ œ œœœ

Appoggiaturas Appoggiaturas are accented notes that are approached by leap and resolve by step. Most often they are approached from below and resolve down a step, but the reverse is possible too. The 1st example below creates a dissonant 7th that resolves down a step (the B below it is the chord note). In the 2nd example the B also creates a 7th but this one goes up because it's decorating the C above it. app app app

& œœ œ œœ œ œœ

œ œ œ ˙˙ ˙

œœ œœ œ œ œ œ œ œ

Incomplete Neighbours These notes are unaccented. They are approached by leap and then resolve by step in the other direction. This one creates a dissonant 7th which resolves up because it's decorating the C above it.

œ œ œ & œ œ

7th chords and Tritones As in four part harmony, the 7th of a 7th chord is a dissonant note and generally resolves down by step into the next chord, whether it's on a weak beat or a strong beat. As noted in unit 1, 7th chords can be implied using 7ths, 2nds or tritones. In the 1st example, the F in the top part is the 7th and falls a step. The 2nd example is the inversion of the 1st example, so the 7th is in the bottom part and also falls a step.

œ & œ V7

œœ I

œœ V4 2

œ œ

œœ V4 2

œ œ

œœ

V6 (vii) I 5

Tritones and 7ths must resolve in the standard way, but we can make the resolutions more interesting by using what is known as an ornamental resolution. For example we can leap from the 7th to another note of the chord (on a weak beat most likely) before letting it resolve to the correct note. Below I have taken the progressions on the previous line and added ornamental resolutions:

œ œ œœ & œ

œœ œ œœ

Resolve these tritones as in the example example:

& ˙˙ ˙˙

# ˙˙

b ˙˙

# ˙˙

b ˙˙

& # ˙˙

b ˙˙

# ˙˙

& ˙ #˙

b ˙˙

# ˙˙

˙˙

# ˙˙

Write the example passage in 4 major keys: -6 -7

-7 +3

& œ œ ˙˙ œœœœ V6

V6 5

###

And now in 4 minor keys (don't forget to raise the leading note)

###

These two examples show suspensions. Complete the exercises below using the examples.

& ˙˙

œ œ ˙

-6

-7

˙˙

w w -6

˙œ œ

-3

ww P1

Add a bottom part

# ˙

œ œ

˙ b &

œ œ

Add a top part

b b & & ˙

˙ ˙

œ œ

Redo the exercises from the previous unit, adding non-chord notes where possible. Label the non-chord notes and show all intervals (see the first example). 1. I - V6 - I

5. I - V6 - IV6 - iii6 - ii6 - V - I6

2. I - V6 - vi

6. I - I6 - IV - V4 - I6 - V - I 2 6 6 7. I - I - V - vi - ii6 - V - I

3. I - IV6 - V6 - I 5 4. I6 - ii6 - V - I6

8. V - I6 - IV - viio6 - vi - V6 - I

# œ pn œ œ ˙ & ? # +3œ

œ +3˙

P4 -6

? &

? ~ Always play your homework at the keyboard after you've finished it! ~ 15

Unit 3: Features and Techniques of Counterpoint One of the main features of contrapuntal music is independence of the voices. In a fugue, for example, each voice is equally important, unlike in a hymn or chorale, where one voice, the soprano, is usually the most important. In counterpoint we want equal voices in dialogue with each other. There are a few ways to achieve this: Rhythmic Independence in our harmony exercises the 4 parts very often move in the same rhythm as each other. For example, it is quite possible for all parts to move in quarter notes for several bars. In counterpoint we want to avoid this as much as possible. Instead, we want the parts to move in mostly different rhythms, so that we hear them as separate from each other. Which of these two is bettter?

& œ œ œ œ &

œ œ œ œ

‰ j œ œ œ œ œ œ œ

˙ ˙

It's the second one, because the different rhythms help us to hear the two parts as independent and separate parts. Independence of Motion: parts that move in contrary motion will sound more independent than parts that move in similar motion, so try to use it most of the time; if the given part is going up then make your counterpoint go down. If the given part is going down, make your counterpoint go up! Here are two different counterpoints to the same melody. The first is OK but moves mostly in similar motion with the top part. The second is much more interesting (thank you J.S. Bach), partly because it features more contrary motion. OK

& œ! œ œœ 16

œ œœ

œ œ

Much better

œ œœ œ œœ œ œœ œ œ

Imitation: Imitation is a very important part of contrapuntal music. Sometimes the imitation is immediate, as in the beginning of a fugue or invention. Or a binary dance might feature a motive in the top part that is heard in a later phrase in the bass. If you use imitation in this way you can present the motive as is, or modify it in some way. For example, you could invert it, or modify the intervals slightly. Here's the opening of a two-part invention by Bach, showing imitation. Notice also how the voices move in different rhythms from one another: when one has 8ths, the other has 16ths.

œ œ œ œ œ œ œ œ œ & !œœœœœœœœ œœœ œœœ œ œœœ œ œ œ œ ? Ó œ !œœœ œœœ ! œ Œ Sometimes if you look carefully you'll see that a given phrase or passage contains its own counterpoint. In other words, the question itself will contain one possible answer. In the following example, you'll notice that motive B will fit under motive A, and A will go under B which will give a nice imitation between the voices: A

œœœœœ & œœœ œœœ ?

œœœœœ œœœ œ œ œ œ œ œ œ œœœœœ B

Use of Dissonance: although the underlying harmonic progressions must be clear, good counterpoint contains plenty of dissonance. Let's look at that fragment of Bach from the previous page again:

& œœ

œ œ

The main notes in this fragment are as follows ...

& œœ

œ œ

and these main notes alone form an acceptable counterpoint, but Bach's version is more interesting because the of the added non-chord notes, which mean the parts move in different rhythms. And the magic touch is the C on the 2nd beat, an accented passing note, that creates a momentary clash against the B above it. Brilliant! This bit of Bach is actually from the first fugue in C major in the Well-Tempered Clavier, Book I. Here are the first 2.5 bars:

j œ œ œ .# œœ œ œœ ‰ Ó ‰ j œ œ & œ œ œ œ . œ œ œ œ œ œ œ œ œ œ œœ œ œ œ œ œ œ This passage illustrates everything mentioned in this unit so far: • Imitation

• Rhythmic variety

• Contrary motion

• Use of dissonance.

Some Other Basic Techniques Voice exchange Voice exchange is a technique where the two parts trade notes. Take a look at these example. Parts a 10th apart move in contrary motion to a 6th apart, or vice-versa:

œ & œ

œ œ

In a voice exchange the parts are moving in contrary motion, which is great, but in the above examples the parts are moving in the same rhythm. We can make it more interesting by adding a passing note to one part.

œ & œ

œ œ

Parallelism When parts move in parallel motion, they have very little independence. They may be singing different notes, but they are going in the same direction in the same rhythm. This is the opposite of what I have been telling you to do so far in this chapter, but it can be effective occasionally to provide a moment of contrast to the rest of the piece.

œ œ œ œ œ œ œ œ œ œ œ n œ œ œ œb œ œ œ # œ œ œ œ œ œ œ œ œœ œœœœœœœœ & œ œ œœ œœ œ œ œ œ œ œ œ œ œ œ œœœœœœœ œ ! ?# œ !œœœ œ œ entirely in parallel 6ths

WTC I Fugue 10

The above is a passage in parallel 6ths from a Bach fugue. The passage is 4 beats long, after which Bach returns to a more independent texture.

Consonant Skips The components of melody are scales and arpeggios (that's why we practise them so much). In an arpeggio we skip from one note of a chord to another. In two part counterpoint we are constantly doing this. Consider this simple example. Let's start with a basic progression:

This implies V7 - I in C. It has contrary motion but isn't very interesting apart from that.

We can make is more interesting by doing a consonant skip from the B (the 3rd of the chord) to G (the root)

˙˙ & ˙œ &

If it fits the style of our piece we could go a step further and add a neighbour note

˙œ &

You could even use an arpeggio, which is several consonant skips in a row:

˙ œ &

˙˙ ˙˙

˙˙

˙ ˙

Octave Leaps Sometimes you want to stay on a note for a few beats because it's the perfect note, but you don't want to just sit on a long note and do nothing with it. Adding a neighbour note, as in the last example on the previous page, is a good way to add interest to longer note. That B lasts for 2 beats but we don't just have a boring half note. Another way to stay on the same note but add interest is by using an octave leap. This can be very effective. Here's a given bass:

? œ

C would be a great note to have against both notes:

But an octave leap makes the part much more lively:

& ˙ ? œ

œ œ

Even better: now we have different rhythms and a bit of dissonance

œ œ

Sequences Parts often imitate each other in sequences, which can modulate, as in the following example. Notice that the voices move in different rhythms and in contrary motion. Often you'll see a modulating sequence like this in the codetta of a fugue (see unit 4) or the 3rd phrase of a 6-bar binary form dance. Note well the structure of this very useful cliché. Motive A appears on top of motive B, and then immediately they are inverted, just like in the earlier example in this unit under the heading 'Imitation'. You should be able to play this at the keyboard and continue it all the way around the circle of 5ths. A

œ & # œ œ œœ œ œœ œ n œœ œ B

œ b œ œœ œ œ œ œ œ œ œ bœ

bœ œ

A 21

Continue these modulating sequences. Continue writing the chord symbols in the same way.

& œœ œ b œœ œ œœ œ bœœ œ b œœ œ b œ œ bœ V7/F

V7/B b

bw bw

V7/E b

œœœœœœœ bœ œ œ œ œ œ œ b & J œ œ bœ ?b œ J œœœœœœ J V7/B b

# œ & œ n œœ œ V7/C

b˙ .

V7/E b

œ bœ œ œ œ

b ˙˙

V7/F

# œœœœœ & œ ? # œ œ œ œ œ nœ V7/G

˙.

V7/C

œ œ œ bœ œ œ V7/F

bw w

Write a lower counterpoint to these two-bar phrases. Each one ends on the tonic. Try to apply what you learned in this unit about contrary motion and using different rhythms. Supply all chord symbols and all intervals. I've begun the first one for you. These are all in major keys. If a note is tied from weak to strong and then goes down a step on the next weak beat, treat it as a dissonance such as a suspension or a 7th (e.g. beat 3 of the 2nd exercise on this page)

# œ œ œ ˙ & ˙ œ œ œ +3 +2 +3 P4 -6

œ œ œ œ

œ œ ˙

bb œ œ œ œ

œ œ ˙

bbb œ œ ˙

œ œ ˙

b œ œ ˙

œ œ ˙

# œ œ œ œ &

& œ œ œ ˙

œ œ œ ˙

b &b ˙

&b ˙

œ œ

œ œ ˙

œ œ œ œ

Write an upper counterpoint to these basslines. These are also all major.

& b ˙.

œ œ œ œ

use susp. here

& b œ œ œ œ. œ J &b ˙ &

œ.

˙ ˙

œ œ

&b œ œ œ œ œ 24

œ J ˙

œ œ ˙

œ œ œ œ

œ œ ˙

bbb ˙

œ œ œ

###

œ œ ˙

œ œ œ ˙

bbb ˙

œœœ ˙

bbb ˙

˙ ˙

œ œ ˙ ˙

œ œ ˙ œœœœ˙

This page contains minor key exercises. Write a counterpoint below these melodies:

b &b b ˙ bbb b &

nœ nœ ˙

œ œ œ œ œ

bb œ œ œ œ œ œ

œœœ˙

b œ #œ œ œ

œ œ œ ˙

j b . œ œ œ œ œ œ #œ ˙ b œ

# œ œ œ œ œ. j œ œ œœœ˙ & ... and above these:

œ. œ ˙ J

œ œ œ œ ˙

œ #œ

nn #

œ œ ˙

& œ œ œ œ œ œ œ

#œ ˙

œ œ œ œ

œ œœ œœ œ ###

œ œ ˙

#œ œ #œ œ ˙

œ œ œ œ

œ #œ ˙ 25