Page 1


FOUR-PART HARMONY Volume One

by David Powell

©Copyright 2013, David Powell www.vancouvermusictheory.com ISBN: 978-0-9918594-2-9


Table of Contents Preface Harmony and Voice Leading 1. Introduction ~ Welcome to the Study of Harmony! 2. Rules for Writing Vocal Music in Four Parts 3. Introduction to Primary Triads 4. Introduction to Secondary Triads 5. The Basics of Chord Progression 6. Consonance and Dissonance 7. Introduction to First Inversion ds 8. Harmony and Rhythm, Part 1 9. Passing and Neighbour Notes 10. V7, Part 1 11. ii7, Part 1 12. Appoggiaturas, Accented Passing Notes and Accented Neighbours 13. Triads in Second Inversion 14. The viio6 triad 15. The iii triad 16. Harmony and Rhythm, Part 2 17. V/V and viio6 /V 18. Introduction to Minor Keys 19. Modulation 20. More Progressions with First Inversion Chords 21. Deceptive and Plagal Cadences 22. Suspensions and Incomplete Neighbours 23. V7 and ii7, part 2 24. The Passing Six-Four 25. Pedals, EchappĂŠes and Anticipations 26. Melodic Considerations in Four Parts 27. Exposed 5ths and Octaves 28. Sequences 29. More about Chord Progressions 30. Summary of Guidelines for Doubling


Forms 31. Binary and Ternary Forms 32. Phrases and Modulation 33. How to Find Cadences 34. The Unexpected

Melody Writing 35. Melody, Part 1: Phrases in Melody Writing 36. Melody, Part 2: Steps and Leaps; Writing in 3/4 37. Melody, Part 3: Shape; Writing in 4/4 t 38. Melody, Part 4: Melodies with Pickups; Implied 39. Melody, Part 5: Melodies in Compound Time; Syncop 40. Melody, Part 6: Minor Keys; Tempo 41. Melody, Part 7: Eight-Bar Melodies 42. Melody, Part 8: Developmen

Appendix 1. 2. 3. 4. 5. 6.

Baroque Dances Common Progressions in Piano Style Structure and Analysis of 7th Chords Non-Chord Note Summary The Leading Note Root/Quality Chord Symbol Summary

Review Sheets


!

Preface

This volume is primarily written for students preparing for harmony exams such as the Introductory and Basic Harmony exams of the Royal Conservatory of Music (Toronto). Volume Two covers the material for the Intermediate and Advanced exams.

!

Studying four-part harmony will be more meaningful for students if they have some awareness of the historical context of this subject. Roughly speaking, four-part harmony texts such as this one teach the harmonic language of the 18th and early 19th Centuries. In broader terms, they teach the principles of tonal harmony and chord progressions. These principles apply not only to classical music, but also to jazz, rock, folk, and other styles.

!

We begin with the simplest of pieces: hymns and chorales for SATB choir. They are the least elaborate music we can write; they have to be easy because they are written to be sung by people with little or no musical training. So, the lines move by step and small leap, and the voices move mostly in the same rhythm.

!

There are exercises for all of the units in the Harmony and Voice Leading and Melody Writing sections. I have not included exercises for analysis of binary and ternary forms nor for chord symbol analysis, because I have always found that commercially available practice exams provide sufficient material for practice in these areas.

!

There are seventeen review sheets. These are simply extra exercises; they are meant to be started about half-way through the course.

! I hope you enjoy using this book, and volume two! ! Copying !

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 revised January 2015


Unit 1 ~ Welcome to the Study of Harmony! In this course we will learn how to compose simple four-part vocal music. That means music for four different voice parts. Imagine a choir in a church. The choir is made up of men and women. Some of the women can sing high notes quite easily. They are called sopranos. Others sing low notes well. They are called altos. Likewise, among the men, some are good at singing higher notes. They are called tenors. The basses are the guys who can sing really low. When we write music for these four voice types, we arrange it on a system of two staves. The music that is sung by the sopranos and altos is written on the top staff, and the men's music is on the bottom staff. To avoid confusion, the stems on the soprano and tenor notes always go up, and the stems on the alto and bass notes always go down. That way, everyone knows which note they should sing and can follow their line. Here's an example of music written for four voices. This is the beginning of a hymn called All through the Night.

Soprano Alto Tenor Bass

&

#

œ . œ œj œ œœ œ

? # œ œ œœ œ œ œ œ

œ . œ œj œœ œ œ œœ œœ œœ œœ

˙˙ ˙œ

j œœ . œœ . J j œ . œœ œ œ

w w w w

You may be wondering why we begin studying harmony using music for singing. This is because vocal music tends, in general, to be a bit simpler than instrumental music. This makes it a good place to start for first time harmony students. One big difference between vocal music and instrumental music is that vocal music tends to move by step (a step is a 2nd), as in a scale. In instrumental music, it is easier to leap around. A leap is any melodic interval of a 3rd or more.

1


Types of voice movement There are some other terms and concepts with which you should be familiar before we begin: 1. Contrary motion: When two voices are moving in opposite directions, we say that they are moving in contrary motion.

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œ # œœ n œœ œœ

˙˙

2. Similar motion: When 2 parts are moving in the same direction, we say that they are moving in similar motion.

˙˙

œœ

& œœ

3. Parallel motion: When 2 parts move in similar motion and stay exactly the same distance apart, we say that they are moving in parallel motion.

& œœ

œœ

œœ

œœ

4. Oblique motion: When one voice moves and another stays on the same note, this is called 'oblique motion'.

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œœ

œœ

œ œ 2


Triads You will remember triads from your rudiments studies. They are formed by adding a 3rd and a 5th to each note of a major or minor scale. There are four different kinds of triads: Major, Minor, Diminished and Augmented. Major triads contain a major 3rd and a perfect 5th Minor triads contain a minor 3rd and a perfect 5th Diminished triads contain a minor 3rd and a diminished 5th Augmented triads contain a major 3rd and an augmented 5th Here are the 7 triads found in C major:

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www

www

www

www

www

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In major keys, the tonic, subdominant and dominant triads are major The supertonic, mediant and submediant triads are minor The leading note triad is diminished There is no augmented triad in major keys Labelling chords When we analyse music we use systems of notation to label the chords. There are two systems we will learn about: Functional Chord Symbols and Root/Quality Chord Symbols. Functional Chord Symbols use Roman numerals to label the chords:

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C: I

www

ii

www

iii

www IV

www V

www vi

www viio

3


This system is called Functional Chord Symbols because it tells us the function of each chord in a particular key. You will notice that some of these triad symbols are written in capital numerals, and others in small numerals. The rule is that triads containing a major 3rd are written in capital numerals, and those triads with minor thirds are written in small numerals. The vii triad is diminished and the convention is to put a small circle next to diminished triads. The Root/Quality system The Root/Quality system labels each chord with its root and quality (i.e. major, minor, diminished or augmented). Major triads are simply designated by the root. So a C major triad is just labelled "C" Minor triads are labelled by the root, followed by 'm' for 'minor', e.g. a D minor triad is "Dm" Diminished triads are labelled by the root and a small circle: Bo

Here are the triads of C major labelled using the Root/Quality system:

C

Dm

Em

www

www

& www

F

www

G

Bo

www

Am

www

www

Minor Keys Here are the triads derived from C minor harmonic scale. (you can create more triads if you use the melodic minor - we will look at these later on)

b & b b www

Cm

C-

i

Do

www

iio

E baug

n www

IIIx

Ab

www

n www

www

iv

V

VI

Fm

G

n www

Bo

viio

4


Homework for Unit 1 ~ Introduction

1. Name the 4 voice parts, starting with the highest and going down. 2. Which 2 parts are written in the bass clef.? 3. Which 2 parts are written in the treble clef ? 4. Which 2 parts have their stems always going up? 5. Which 2 always have their stems going down? 6. How many triads can you make using the notes of a major scale? 7. What is contrary motion?

8. What is similar motion?

9. What is parallel motion?

10. What is oblique motion?

11. Name one difference between music written for voices and music written for instruments.

5


Unit 2 ~ Rules for Writing Vocal Music in Four Parts When you are writing, you must remember that there are limits to how high and low people can sing. Here are the highest and lowest notes of the four voices:

Soprano

& w ?

Alto

w

w

Tenor

w

w

Bass

w

w

w

Distance between parts: The soprano and the alto parts should never get more than an octave apart from each other. Nor should the alto and tenor. However, the tenor and bass may be separated by as much as a perfect 12th.

OK

& ˙˙ ?

Incorrect

˙ ˙

OK

Incorrect

˙

˙

˙

˙

OK

˙ ˙

Incorrect

˙ ˙

6


Overlapping

&

? ˙˙

˙˙

Look at the bass and tenor parts in the above example. Notice how the tenor part in the second chord is lower than the bass part in the first. This is called overlapping. Overlaps should be avoided in all parts. For example, the alto should never sing a note that is higher than the previous soprano note. The soprano should never sing a note that is lower than the previous alto note, and so on.

Crossing

& ˙˙ ?

˙˙

Here, the soprano and alto are actually trading places, and the alto is singing higher than the soprano. This is called crossing and should also be avoided.

7


Consecutives We learned in Unit 1 about parallel motion. This is when two voices move in the same direction and stay the same distance apart. Sometimes this is OK. For example, it's fine for two voices to move in parallel motion a third apart. However, it is not permitted for two voices to move in parallel motion a 5th apart, or an octave apart, or to move together on the same notes (parallel unisons). See the examples below:

& ˙˙ ?

˙˙

& ˙ ? ˙

˙ ˙

&

? ˙˙ & ˙ ? ˙

Consecutive perfect 5ths between the soprano and alto voices (some people use the word 'parallel' instead of consecutive, as in 'parallel 5ths').

Consecutive unisons between tenor and alto.

Consecutive octaves between tenor and bass.

˙ ˙ OK

˙ ˙

OK

˙

˙

˙

˙

Note: it is not a mistake to have two consecutive fifths or octaves or unisons if the parts are not moving to different notes.

8


Finally, try to make the voices move as smoothly as you can. This means using mostly stepwise motion, and keeping leaps to a minimum (the bass part tends to have more leaps than the other voices - this is fine). Usually, you should always try to move each part to the next nearest note. This example is poor. Look how many leaps there are:

˙ & ˙ ? ˙˙

˙˙ ˙ ˙

˙˙ ˙˙

˙˙ ˙˙

Here is an improved version of the same progression. Most of the leaps have been removed simply by re-arranging the parts.

˙ & ˙ ? ˙˙

˙˙ ˙˙

˙˙ ˙˙

˙ ˙ ˙ ˙

Summary: 1. Each voice has a limited range within which it must sing. 2. The soprano and alto may be as much as an octave apart. 3. The alto and tenor may be as much as an octave apart. 4. The bass and tenor may be as much as a 12th apart. 5. No two voices may cross or overlap. 6. No two voices may move in consecutive unisons, 5ths, or octaves. 7. Parts should move, as much as possible, by step or small leap.

9


Homework for Unit 2 ~ Rules for Writing Vocal Music in Four Parts

In this line, find and circle any notes that are too high or too low. Refer to page 1 of unit 2.

˙ & ˙ ˙ ? ˙

˙˙

˙˙

˙ ˙

˙˙

˙ ˙ ˙ ˙

˙ ˙ ˙˙

˙˙

˙˙ ˙ ˙

˙ ˙

˙˙

˙ ˙

In this line, find and circle the parts that are too far apart - see page 1 of unit 2

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˙˙

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˙

˙˙

˙

˙ ˙ ˙ ˙

˙ ˙

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˙ ˙

˙˙

˙ ˙

˙˙

˙ ˙

˙ ˙

In this line, find and circle the note that is overlapping. Sometimes there are 2 notes that overlap see page 2 of unit 2

& ˙˙ ˙˙ ˙ ˙ ? ˙ ˙

˙˙ ˙ ˙ ˙˙ ˙˙

˙˙ ˙ ˙ ˙ ˙˙ ˙

˙˙ ˙˙ ˙ ˙˙ ˙

˙˙ ˙˙ ˙˙ ˙ ˙

˙˙ ˙ ˙

˙˙ ˙˙ 10


In this line, find and circle the 2 parts which have crossed - see page 2 of unit 2

& ˙˙ ˙˙ ˙ ? ˙ ˙˙

˙ ˙

˙ ˙

˙ ˙˙ ˙

˙˙ ˙˙ ˙˙ ˙˙

˙˙ ˙ ˙ ˙ ˙ ˙ ˙

˙ ˙ ˙ ˙

˙˙ ˙˙

˙˙ ˙ ˙ ˙˙ ˙˙

In the next 2 lines, find the consecutive 5ths, octaves and unisons - see page 3 of unit 2

& ˙˙ ˙˙ ? ˙ ˙ ˙ ˙

& ˙˙ ˙˙ ? ˙˙ ˙˙

˙˙ ˙˙ ˙ ˙ ˙ ˙

˙˙ ˙˙ ˙ ˙˙ ˙

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11


Practise writing triads in 4 parts in root position using the given notes as bass notes. Arrange the 3 upper voices differently in each one. Double the root of each one. Make sure each voice is in its proper range and that there is not too much space between the voices. I've done the first 4 as an example:

& ˙ ˙ ? ˙˙

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˙˙

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˙

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Homework for Unit 2 - page 3 of 4 12


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Unit 3 ~ Introduction to Primary Triads The first triads we will learn about are the tonic, subdominant and dominant triads. These triads are called the primary triads. To begin with, we will look at the primary triads only in root position.

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www

C+: I

www

www

IV

V

As you know, there are three notes in a triad. Since we are writing music for 4 voices, one of the notes must be sung by 2 of the voices. We call this 'doubling'. The best note to double in a primary triad is the root. The 5th is an acceptable second choice. The 3rd of V is the leading note of the key. It is a very strong note and we only need one of them at a time, so never double the leading note. Note that in minor keys you must raise the leading note with an accidental.

Phrases and Cadences Pieces of tonal music are made up of phrases, which are a bit like sentences in speech. In the kind of music we will be studying and writing, phrases are very often four bars long. You will also see short phrases that are two bars long. As you probably already know, phrases are separated from each other by cadences. A cadence is a pair of chords that creates a sense of partial or full closure or rest, rather like commas and periods in spoken and written language. There are four kinds of cadence: perfect, imperfect, plagal, and deceptive. Perfect and imperfect cadences are the most common. We'll learn about them today, and save plagal and deceptive cadences for later.

14


The Perfect Cadence A perfect cadence consists of the dominant chord, V, going to the tonic chord, I. This is like a full stop in speech. There is a feeling that the idea is complete. Figure 3.2 shows a four-bar phrase, with a perfect cadence at the end. fig. 3.2

# 3 & 4 œ œ ? # 34 œ œ

œœ œ œ

œœ œœ œ œœ œ

˙ ˙ ˙

œ œ œœ

œœ œœ œœ œœ œ œ œ œ

William Croft

˙˙ ˙ ˙

Perfect cadence: V - I When writing this progression, there are a couple of things to remember. One is that the part that has the leading note of the scale in the V triad should sing the tonic note in the I triad (there are exceptions that we'll learn about later). In figure 3.2, the soprano has the leading note, F #, which then rises to G. In figure 3.3, the soprano has the leading note B, which then rises to C.

fig. 3.3

& c ˙˙ ?c ˙ ˙

C+: V

˙ ˙ ˙˙

There's another thing to notice about these examples. Notice in figure 3 that both triads contain the note G. This is referred to as a 'common tone'. Whenever possible, try to keep the common tone in the same voice. In figure 3.3, the G is in the tenor in both chords. In figure 3.2, the common tone is the D, and is in the alto in both chords.

I

________________________________________________________________________ 3-2 15


The Imperfect Cadence Sometimes a phrase comes to rest on the dominant chord. This is known as an imperfect cadence. Why is it called imperfect? Because although V is a good place to rest for a moment, it doesn't quite feel like home. The piece only really feels finished when we return to our starting place, the tonic triad. The imperfect cadence consists of a V chord, and a chord before it. Here's a phrase that ends with an impefect cadence.

& b 34 ˙˙ ? b 34 ˙œ œ

œœ œœ

jœ œ˙ . œ œ jœ œ˙ . œ œ

˙˙ œœ œ œ œ œ œ œ Imperfect cadence:

Rowland Prichard

œœ œ œ

œœ œœ œœ œ œ

vi

V

There is a family of chords that go well before the V chord. We can call them dominant approach chords. The first one of these we will look at is IV ("iv" in minor keys), the subdominant triad. IV goes very well to V. fig. 3.5

& c ˙˙ ?c ˙ ˙ IV

˙ ˙ ˙ ˙

Figure 3.5 shows you IV going to V. In this progression there are no common tones, but the voices are moving quite smoothly - by step or small leap.

V

You must always be on the lookout to avoid consecutive octaves and 5ths. It's surprisingly easy to let them slip into your work. One trick you can use with the progression IV - V is to have the upper three parts descend while the bass rises. Two of the voices descend by step, and one leaps down a third. This is what happens in figure 3.5. ________________________________________________________________________ 3-3 16


Leaps: Avoid leaps bigger than a 4th in the soprano, alto and tenor. The bass may leap as much as a 5th or 6th (you can even leap an octave in the bass, but not a 7th - more about leaps later). If you find yourself making leaps larger than these, there's usually a way to rearrange the voices to reduce the leaps. Now that we've seen I and V together, and IV and V together, let's put the 3 of them together to make a phrase, starting and ending with I: fig. 3.6

& b ˙˙ ?b ˙ ˙

˙ ˙ ˙˙

˙˙ ˙˙

˙ ˙ ˙ ˙

F+: I

IV

V

I

17


Homework for Unit 3 ~ Primary Triads 1. Complete these exercises by adding the alto and tenor. voices All the triads in these exercises are in root position. Write the functional chord symbols beneath the exercises and root/quality symbols above. Name the keys of the exercises. Double the root of each triad and hold common notes in the same part. G

C

& c ˙˙ ˙˙ ?c

˙˙ ˙˙

C: V

I

# ˙ &

˙ ˙

?# ˙

& ˙ ? ˙

˙ ˙

## ˙ ## ˙

bb ˙

# # # 23 ˙

˙ ˙

˙

bbbb ˙

˙

bb ˙

### 3 ˙ 2

bbbb ˙

˙

˙

b ˙

˙

b

˙

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bb ˙

˙

bb ˙

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˙ 18


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bbb ˙ ## ˙ ## ˙

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2. In the following blank bars, write these progressions: a. I - IV in C, G, D, and B b. IV - V in E, C, A b and C # Let the top 3 voices come down as the bass rises. c. V - I in A b, E b, B b and C Do them exactly in exactly the same way as they're done in this unit: write each one in root position and double the root of each. Keep common notes in the same voice where possible, and make sure that when V goes to I, whoever has the leading note in V gets the tonic in I. a.

&c ?c b.

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? c.

&

? 20


Unit 4 ~ Introduction to Secondary Triads In the last unit, we met the primary triads, I, IV, and V. The remaining triads - ii, vi, and vii - are known as secondary triads. In this unit we'll look at vi and ii. You'll learn about iii and vii in a later unit. Both ii and vi like to go to V. Let's have a look at each in turn.

Approaching V with vi fig. 4.1

C

Am

˙ ˙ ˙ ˙

G

˙˙ ˙ ˙

˙ ˙ ˙ ˙

I

vi

V

I

& c ˙˙ ? c ˙˙

C

The submediant triad is a minor triad in major keys. Figure 4.1 shows the vi triad approaching the dominant. When it comes right before or right after V, the best note to double is the 3rd. The root can also be doubled. Notice the common notes. The tonic and submediant triads share two common notes. In figure 4.1 I have kept them in the same voice, which makes the movement of the voices between the chords (known as 'voice leading') very smooth.

21


Approaching V using ii fig. 4.3

˙ c & ˙ ? c ˙˙

˙ ˙ ˙˙

˙ ˙ ˙

˙ ˙ ˙˙

I

ii

V

I

Figure 4.3 shows V being approached using ii, the supertonic triad. Like vi, ii is a minor triad. Also like vi, the best notes to double are the root and the 3rd. ii goes realy well to V, but this progression usually doesn't work well in reverse, so don't go from V to ii.

22


Homework for Unit 4 ~ Introduction to Secondary Triads Use the blank bars for questions 1 - 3. Use one bar per progression. Write functional chord symbols below the staff and root/quality symbols above. 1. Write the progression vi - V in G, A, B b, D and F. Double the 3rd of vi and the root of V. Em

# c ˙ & ˙ ? # c ˙˙ G:

vi

D

˙ ˙ ˙˙ V

2. Write the progression ii - V in C, G, D, E,and C #. Let the soprano have the supertonic going to the leading note (2-7). Double the root of ii and of V.

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? 3. Write the progression I - vi - ii - V - I in F and G. Use quarter notes for the first four chords and a whole note for the last one

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?

23


4. Add the inner voices to the following. Use I, IV, ii, vi, and V. Write the chord symbols and name the keys. Let the leading note rise to the tonic when V goes to I. Double the 3rd of vi. These are all in major keys. Example:

& ˙˙ ? ˙˙ C+:

&

I

˙˙ ˙˙

˙ ˙ ˙

˙ ˙ ˙˙

IV

V

I

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w w

25


Unit 5 ~ The Basics of Chord Progression In this course you will learn how to handle each chord in detail. First however, let's take a look at general principles of chord progression. Where does each chord like to go? 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 IV.

level 1:

I

level 2:

V

level 3:

vi

level 4:

vii IV

ii

iii

I have used major key triads in the chart, but this principle applies equally to minor key triads, which you will learn all about later on. Now you have a basic grasp of the principle of chord progression in tonal music. There is more for you to learn about this but this is the basic principle. If you can remember the information on this page you already know most of what you need to know to write good progressions!

26


Common Progressions There are many progressions that are frequently found in tonal music, and these progressions often use a particular soprano line. For example, IV - V - I is a common progression in many styles of music. In classical music we might use the melody 4 - 2 - 1, which means that the soprano sings the subdominant in IV, the supertonic in V, and the tonic in I, like this:

œ & œ ? œœ

œ œ œœ IV

4

œœ œœ V

2

œ œ œ œ

1

I

There are actually a couple of different melody lines that could be used with this progression, but there are some progressions that tend to use only one specific melody line. Throughout this book you will periodically see summaries of the common progressions you should know so far, and they will look like this: Progression IV - V - I

Soprano 4-2-1

It's very important to memorize these progressions, as knowing them will really help you on your exams.

27


Unit 6 ~ Consonance and Dissonance Some notes sound stable together. They are restful to hear. They sound as if they 'agree' with each other. We say these intervals are 'consonant'. The consonant intervals are:

&

ww

P1

b ww

n ww

-3

bw w

ww

+3

P5

-6

nw w

+6

w w

P8

Other pairs of notes sound like they disagree. Instead of sounding restful and relaxed, they sound tense and restless, and want to resolve or release their tension. These are dissonances. Although they create tension, dissonances can be very beautiful. In fact, it is the resolution of dissonance into consonance that gives music much of its power. The dissonant intervals are:

-2&

b ww

n ww

-2

+2

ww

# ww

b ww

bw w

nw w

P4*

X4

o5

-7

+7

There are special guidelines that you must follow when you use dissonances. We will begin to learn about this in later units. *The Perfect 4th is a special case. It is considered dissonant only when the lowest note of the 4th is in the bass part.

28


Homework for Unit 6 ~ Consonance and Dissonance Name these intervals, and state whether each is consonant or dissonant.

&

&

#w # w

b ww

ww

bw w

ww

#w w

ww

bw w

bw bw

#w #w

ww

b b ww

w bw

# ww

bw w

# ww

+3 Consonant

&

b ww

ww

&

# ww

&

w w

29


Unit 7 ~ Introduction to First Inversion Triads So far we have only looked at triads in root position. These triads sound strong and solid. Usually cadences use root position chords. Away from cadences we can add more variety and interest to our music by using chords in first inversion as well as root position. In 1st inversion, the bass note is the third of the triad. Root position triads contain a 3rd and a 5th from the bass. 1st inversion triads contain a 3rd and a 6th:

&

ww w

www 5 3

6 3

In the Functional Chord Symbol system we omit the '3' and just write a '6' after the symbol. So, a 'ii' chord in 1st inversion is written "ii6" In the Root/Quality system, we write the root, then the quality, then a forward slash, then the bass note. So, a 1st inversion D minor triad is written "Dm/F"

&

?

Dm/F

w w ww

C+: ii

6

The doubling rules are the same for 1st inversion and root position triads. Being inverted doesn't usually change a chord's level. So just as 'ii' is a level 3 chord, so is ii6, and ii6 likes to go to level 2 just as much as ii.

30


C

& c ˙˙ ? c ˙˙ C+: I

Dm/F

G

˙ ˙ ˙˙

ii6

˙ ˙ ˙ ˙

V

I

˙ ˙ ˙ ˙

C

Another common technique involving 1st inversions is to go from a root position chord to its 1st inversion, or vice versa. In this example, a ii chord goes to ii6 before going to V:

˙ c & ˙ ˙ ?c ˙

˙˙ ˙ ˙

˙˙ ˙˙

C+: ii

ii6

V

˙˙ ˙ ˙ I

Notice in the first bar how the soprano and bass trade notes: the soprano goes from F to D while the bass goes from D to F. This is called voice exchange and is very effective.

31


Finally, here is a progression with IV6, V6, and I6. Just like IV in root position, IV6 goes very well to V:

& œœ

œœ

œ œ

œœ

C+ : I

V6

I

IV6

œ ? œ

œ œ

œ œ

œœ

œ œ œœ

œœ œ œ

œœ

œœ

ww

V

I6

ii6

V

I

œ œ

œœ

w w

Common Progressions you should know so far: Progression

Soprano

IV - V - I

4-2-1

ii6 - V - I

2-7-1

32


Homework for Unit 7 ~ First Inversion Triads 1. Write these progressions: a. I - I6 b. V6 - I c. IV6 - V

in A and F in C and E in A and F

d. I - IV e. IV - I6

in F and D in G and B

Write the chords in half-notes, in 4/4 time

&c

c.

b.

a.

?c d.

&

e.

? f. I - I6 - ii6 - V - I in C and F. Let the soprano have the melody 3 - 1 - 2 - 7 - 1. Make the first 4 chords a quarter note long each, and the last one a whole note..

&

f.

?

33


2. Complete these in 4 parts. Name the keys and write the functional and root/quality chord symbols. Name the keys of each one. Remember, a double bar line does not cancel a key signature. A key signature made up of naturals only is C major.

˙

˙

? ˙

˙

&

bb ˙ ˙ b b

b &bb ˙ ? bb &

b ˙

###

? ˙

˙

˙

˙

˙

## ˙

˙

˙

## ˙

˙

˙

˙

˙

˙

˙

˙

˙

˙

˙

˙

˙

˙

w

˙

w

˙

˙

bbb ˙ ˙

nn ˙

˙

˙

bbb ˙

˙

nn ˙

˙

˙

˙

? ### ˙ &

˙

w 34


3. Complete these progression. Show all chord symbols. Double the roots or fifths of the primary triads (preferably roots if they're in root position). Double the 3rd of vi when it comes before or after V. Write I - IV - V - I in C and G

& ˙˙ ? ˙˙

˙˙ ˙˙

˙ ˙ ˙

˙ ˙ ˙˙

# #

Write I - vi - V - I in D and A

&

? Write I - ii -V - I

in F and B b

&

? I - ii6 - V - I in C and B b (use the soprano 1-2-7-1)

&

? 35


Write I - V6 - I - I6 - ii6 - V - I in A b and B b (soprano 1-2-3-1-2-7-1)

&

? &

? Write I - IV6 - V - I in C and F (soprano 3-4-5-5)

&

?

36


Unit 8 ~ Harmony & Rhythm, part 1 As you know, there are strong beats and weak beats in every bar of music. In duple time (2/4, 6/8, etc.) the first beat is strong and the second is weak.

& 24

strong

œ

weak

œ

In triple time (3/4, 9/8, etc.) the first beat is strongest: strong

& 34 œ

weak

weak

œ

œ

In quadruple time (4/4, 12/8, etc) the strongest beat is the first. The third beat is weaker than the 1st, but stronger than 2 or 4, which are weak.

strong

&c œ

weak

œ

medium

œ

weak

œ

Also, if you subdivide a beat , the first note will feel more accented than the second:

strong

& œ

weak

œ 37


In our exercises, we are usually given a time signature at the beginning. We must make sure that the chords we choose will 'fit' the time signature. Basically all this means is that we must make sure that there is a change of chord on the strong beats of the piece. It is OK to repeat a chord from a strong beat to a weak one, but not from a weak one to a strong one. The example in figure 1 is fine because the repeated chords are on weak beats. Figure 2, however, is poor because the V triad is being repeated from a weak beat to a strong beat. It may make the music suddenly sound like it's in 3/4, not 2/4 fig. 1

fig. 2 s

& 24 œœ ? 24 œœ C+:

w

œ œ œœ

I ________

s

œ œ œ

w

V ______

œ œ œ

s

œ œ œœ I

w

œ œ œ

s

œ œ œ

V___________

w

œ œ œœ I

38


Homework for Unit 8 ~ Harmony and Rhythm, part 1 1. Write these progressions twice each. Put each one in a different key. Use quarter notes.

a. I - IV - V - I b. I - vi - V - I c. I - ii6 - V - I d. I - vi - IV - V

e. I - I6 - IV - V f. I - IV6 - V - I g. I - V6 - I - IV h. I - vi - ii - V

Above each beat, write S or W, according to whether the beat is strong or weak

&

a.

b.

? &

c.

d.

e.

f.

? &

?

39


&

g.

h.

? 2. Add the inner voices to the following 8 exercises. Write root/quality symbols above each chord.

œ œ ˙ & ? œ œ ˙ & œ œ ˙ ? œ œ ˙

b œ œ ˙ b

œ œ ˙

# œ œ ˙ # œ œ ˙

n ˙

˙

bb œ œ ˙

n ˙

˙

bb œ œ œ œ

##

### œ œ ˙

œ œ ˙

###

## œ œ ˙

œ œ ˙

3. The following passage is full of consecutive 5ths and 8ves. Search for them part by part and mark them..

& œœ œ ? œ

œœ œ œ

œœ œ œ

œœ œ œ

œ œ ˙ œ œ ˙ œ œ ˙ ˙ ˙

œœ œœ œœ œœœ œœœ

œ œ œ œ

œ œ œ œ

œ œ œ œ

˙˙ ˙˙

˙˙

œœ œœ w w ˙œ œ ˙œ œ w w 40


Unit 9 ~ Passing and Neighbour Notes So far in the course, all the notes we have written have belonged to triads. However, music is often decorated with notes that don't belong to the chord they're in. These notes are known as 'non-chord notes' and are divided into different categories. In addition, some of them always occur on the strong part of the beat, while others always occur on the weak part. Passing Notes The first type we will look at are known as passing notes. Passing notes are very simple. They always occur on the weak part of the beat, and always fill in a gap between two chord notes. Usually one passing note will fill in a gap of a third, although it is possible to have two passing notes in a row filling in a gap of a 4th.

& œœ œ ? œ 6 C+: ii

& œœ œ ? œ C+: I

œ œ œ œ

œ

The E in the soprano does not belong to the ii6 chord. It fills a gap between the F and the D. Passing notes are labelled "pn".

ii

œ œ œœ œ œ

Here, the A and B in the soprano don't belong to the I triad. They fill in a gap of a 4th between G and C. Sometimes these are called 'double passing notes'.

6 I

41


Passing notes may also occur simultaneously in different voices, creating passages in parallel thirds or sixths.

bb œ œœ b & œ œ ? bb

œœ œ œœ b

In this example, the bass and alto have passing notes on the 'and 'of the first beat (D and F).

i6

C-: i

Sometimes a passing note fills in the gap between two notes only a major second apart. This passing note has an accidental next to it, and is known as a 'chromatic passing note'.

& œœ # œ ? œœ

œ œ œœ ii6

C+: I

Neighbour Notes The next type of non-chord note we will study is the neighbour note. They are simple decorations of a single chord note. They work like this: we hear the chord note, then the note either a step above or a step below it, and then hear the chord note again. The note above or below is the auxiliary note. They are also known as auxiliary notes.

& œœ œ ? œ C+: I

œ

œœ œ œ I

Here, the soprano C is decorated by an upper auxiliary, D. The D doesn't belong to the I triad. Neighbour notes are labelled "nn".

6

42


& œœ œ ? œ

œ

C+: I

œœ œ œ

In this one, the C is decorated by a lower auxiliary, B.

I6

Just as we have chromatic passing notes, we may also have chromatic neighbours. The example below shows chromatic neighbour notes in both soprano and alto voices.

œ #œ & œ #œ œ ? œ

œ œ œ œ

C+: I ___________

43


Homework for Unit 9 ~ Passing and Neighbour Notes Find the passing notes and the neighbour notes in the following and circle them. Add functional chord symbols.

œ œ ˙ & ˙ ˙ ˙ ˙ ? ˙ ˙ # œ œ & w w ?# ˙

˙ œ œ ˙ ˙

˙ ˙

˙ ˙ ˙ ˙œ œ ˙ ˙ ˙

œ˙ # œ ˙˙

œ œ ˙˙ ˙ œ œ ˙ ˙ ˙

˙ ˙ ˙ ˙

œ œœ ˙ ˙ ˙ œ . œj ˙ ˙ ˙

˙˙ ˙ ˙

& b œ˙ œ ˙˙ ˙˙ ?b ˙ ˙

œw # œ ˙ ˙ ˙˙ ˙

œ œ ˙˙ ˙

## œ œ œ œ ˙ & ˙ ˙

œ œ ˙ ˙ ˙ œ œœ˙ œœœ

œœ œ œ œ œ œœ œ œ œ œ ˙ œ œœœ œ

? # # ˙˙

˙

˙˙

˙˙

œ #œ ˙ œ #œ ˙ ˙ ˙ œ œ ˙ ˙ ˙ ˙ ˙ ˙ ˙ œ œœ œœ œ œ œ œ œœœœœ

œ œ

œ œœ 44


Unit 10 ~ V7, part 1 If we add a seventh to the V triad, we get what is called the dominant seventh chord (figure 1). In root position it is labelled "V7".

www w

fig. 1

&

= V7

As V7 is a level 2 chord, the usual place for it to go is I. The dominant 7th in root position contains the following intervals: +3, P5, -7. The root/quality symbol is the root plus "7", so a dominant 7th whose root is G would be labelled "G7" V7 contains two notes that we call 'active notes' or 'active tones'. This means that they have a particular job to do. One of these notes is the leading note, and the other is the 7th (remember to raise the leading note in minor keys) As we have seen, the leading note tends to rise a step to the tonic. The new rule to learn here is that the 7th must fall a step. When V7 goes to I, that means the seventh will fall a step to the 3rd of I. fig. 2

&

?

G7

˙˙ ˙ ˙

C+: V7

C

˙ ˙ ˙ ˙

fig. 3

˙ ˙ ˙ ˙

˙ ˙ ˙˙

fig. 4

˙˙ ˙ ˙

˙ ˙ ˙˙

I

Notice that in figure 2 the I chord is missing the 5th (there is no G). If you follow all the rules, i.e. if your leading note rises to the tonic and your 7th falls a step, it's impossible to get the 5th into the I chord without having consecutive 5ths. However, fig. 3 shows a dodge you can use to get the 5th into that I chord: if the leading note is in either the alto or tenor voice, it may fall a 3rd to sing the 5th of I. It's allowed in the alto or tenor because it's not so noticeable. When the soprano has the leading note, it must rise, which is why the I triad in figure 2 has no 5th. You could also leave the 5th out of the V7 chord instead, as in figure 4. This will be less noticeable than a 5th missing from I.

45


Now, let's talk about the inversions of V7. Here they are in C major:

&

1st

wwww 6 5 3

www w

2nd

3rd

www w

6 4 3

6 4 2

As you might have guessed, we abbreviate the symbols for these chords: The 1st inversion is labelled V6 , the 2nd is V4 and the 3rd is V4 5 3 2 The root/quality symbol for the inversions consist of the root plus "7", then a slash, then the bass note. The rules are the same as for V7: the leading note rises and the seventh falls. Note: If we are using inversions of V7, there is never any need to leave the 5th out of I and there is never any need to use the 'dodge': the leading note can always rise to the tonic. fig. 5

G7/B

&

˙ ˙

fig. 6

G7/D

&

˙˙

?

?

˙ ˙

˙˙

˙ ˙ ˙˙ ˙ ˙ ˙˙

Figure 5 shows the 1st inversion. The first inversion of V7 always goes to I in root position, because the leading note is sung by the bass, who must then sing the tonic note.

Figure 6 shows the second inversion, V4 3

46


Figure 6 shows the 3rd inversion of V7. The symbol for this chord isV42 It follows the same rules. The seventh of the chord is in the bass. Because the seventh always falls, V4 always goes to I6 2

fig. 6

&

?

G7/F

˙ ˙

˙˙

C/E

˙ ˙ ˙˙

Summary 1. V likes to go to I. We can make this tendency even stronger by adding a 7th to V. 2. When resolving V7 to I, the part which has the leading note in V7must rise a step to sing the tonic note of I, unless it is an inner voice, where it may fall to the 5th of I. 3. The part which sings the 7th in V7 must fall a step to sing the 3rd of I. 4. V7 may also go to vi or IV6. We'll talk about this more in a later unit.

47


Homework for Unit 10 ~ V7, part 1 Write these progressions using the empty bars on this and the next pages. Write functional chord symbols under your answers and root/quality above. Write each one twice each, arranging the voices differently the second time. See my example below. For exercise 1, use the voice leading found in unit 10, figures 3 and 4. 1. V7 - I

in F , B b, E b, A b

2. V6 - I 5

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

3. V4 - I 3

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

4. V4 - I6 2

Don't forget to write the proper key signature for each exercise.

C7

F

C7

F

& b c ˙˙

˙ ˙

˙˙ ˙ ˙

˙˙ ˙ ˙

1.

? b c ˙˙ F+: V7

˙ I

48


&

?

2.

&

? &

?

3.

&

?

49


&

? 4.

&

?

&

?

50

Four-Part Harmony Volume One - sample  

These books cover the material for harmony exams such as those set by the RCM in Toronto. Vol. One covers the material for Introductory and...

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