Harmony – First steps

Before we get any further into the world of harmony, it is important that you understand the basics. The following few worksheets will guise you through them. These will tie in with your music theory knowledge, up to grade 5 level.

Exercise One - Chords and triads

Read and complete the following:

• Chords and triads are a number of n _ _ _ _ (three or more) sounded together

• A triad is the simplest form of chord, consisting of t _ _ _ _ notes

• A triad can be based on any degree of a m _ _ _ _ or m _ _ _ _ scale

• A triad consists of: the r _ _ _ - the degree on which it is based

the t _ _ _ _ - major or minor, above the root

the f _ _ _ _ - perfect, diminished or augmented,

above the root

• Triads can be: m _ _ _ _ - consonant

m _ _ _ _ - consonant

d _ _ _ _ _ _ _ _ _ - dissonant

a _ _ _ _ _ _ _ _ - dissonant

Draw the following triads, C is the root in each case:

Major triad Augmented triad Minor triad Diminished triadR, M3, P5 R, M3, A5 R, m3, P5 R, m3, d54,3 4,4 3,4 3,3

• Triads are described by the degree on which they are based, and are referred toby Roman numerals. We use Extended Roman, where the case representsmajor/minor. For example, a major triad on the tonic is I, whereas a minor triadon the tonic is i.

Complete the following:

Degree Name of triad/degree

1st Tonic

2nd S _ _ _ _ _ _ _ _ _

3rd M _ _ _ _ _ _

4th S _ _ _ _ _ _ _ _ _ _

5th D _ _ _ _ _ _ _

6th S _ _ _ _ _ _ _ _ _

7th L _ _ _ _ _ _ N _ _ _

Primary and secondary triads

• Primary Triads are the most important, and are found on the tonic, subdomiantand dominant. Many styles of music are based around these chords.

• Secondary Triads are those found on the other degrees of the scale. These areless important than primary triads, but give harmony movement and colour.

On the following diagram, colour in the primary triads, label them with extended Roman numerals and pop chords, and state whether they are major or minor:

Exercise Two – Triads in a Minor Key

Read and complete the following:

• There is a wider range of triads in minor keys because the s _ _ _ _ _ _ _ _ _ and

l _ _ _ _ _ _ note are different in h _ _ _ _ _ _ _ and m _ _ _ _ _ _ forms of the

minor scale

• In the h _ _ _ _ _ _ _ minor scale the l _ _ _ _ _ _ note is raised by a

s _ _ _ _ _ _ _

• In the ascending m _ _ _ _ _ _ minor scale the s _ _ _ _ _ _ _ _ _ is raised by a

s _ _ _ _ _ _ _ as well.

• In the descending m _ _ _ _ _ _ minor scale the notes follow the key signature.

This is sometimes called the n _ _ _ _ _ _ minor.

Write out F harmonic minor in semibreves, ascending. Label the raised 7th.

Write out F melodic minor in semibreves, ascending and descending. Label the 6ths and 7ths, and explain what has happened to them.

Exercise Two – Triads in a Minor Key

The variation on the submediant and the leading note gives two possible choicesfor triads on each degree of the scale except I.

Complete the following by drawing in the possible triads taken from the harmonic and melodic minors on the given degrees of the scale:

When you have finished, think about which degree each chord is on, whether it is major, minor, diminished or augmented, and which version(s) of the minor scale(s) it belongs to (it could be more than one).

We will mark these together when you’ve finished.

Now, have a look at the following extract:

Label each chord as I, IV or V, then label which versions of the minor scales eachbelongs to. The key is A minor.

Exercise Three – Inversions

• ‘Root position’ describes the arrangement of the notes of a chord when the lowest note is the root of the chord. The 3rd and 5th, if it’s in the chord, will be above it.

• Because the notes are arranged with the 3rd and 5th above the root, it is referred to as a chord. Root position chords are identified by the letter‘a’ after the Roman Numeral, for example Va, but in practice we normallyleave the ‘a’ out.

• Progressions using primary chords (I, IV, V) nearly always give a strong chord progression:

I – V I – IV V – I IV – I IV – V

I – IV – V IV – V – I IV – I – V etc.

One exception to this is V – IV, which is used less

• As long as the root is on the bottom, the other notes can go above in any order

First inversion chords

Read and complete the following:

• A chord is described as an i _ _ _ _ _ _ _ _ when it lowest note is not the r _ _ _ of the chord.

• A chord is in f _ _ _ _ i _ _ _ _ _ _ _ _ when the l _ _ _ _ _ note is the t _ _ _ _ .

• In close position, the chord is arranged with intervals of a 6th and a 3rd above the bass note:

For this reason it is called a chord.

• A first inversion chord is given the letter _ .

• As long as the 3rd is on the bottom, the other notes can go above in any order.

Write out close position first inversions of all the chords in C major:

Label them with the correct Roman Numeral and letter.Label them in pop chords – we use the ‘slash’ to show what’s on the bottom,so C first inversion is written as C/E. These are called slash chords.

Second inversion chords

Read and complete the following:

• A chord is described as an i _ _ _ _ _ _ _ _ when it lowest note is not the r _ _ _ of the chord.

• A chord is in s _ _ _ _ _ i _ _ _ _ _ _ _ _ when the l _ _ _ _ _ note is the f _ _ _ _ .

• In close position, the chord is arranged with intervals of a 6th and a 4th above the bass note:

For this reason it is called a ____ chord.

• A first inversion chord is given the letter _ .

• As long as the 5th is on the bottom, the other notes can go above in any order.

Write out close position second inversions of all the chords in C major:

Label them with the correct Roman Numeral and letter.Label them in pop chords.

Exercise Three - Cadences

Read and complete the following:

• Tonal music consists of p _ _ _ _ _ _ and s _ _ _ _ _ _ _ _ , built up into longer

s _ _ _ _ _ _ _ . These all help to define the s _ _ _ _ _ _ _ _ .

• Certain chord p _ _ _ _ _ _ _ _ _ _ _ are used during or at the end of p _ _ _ _ _ _,

to indicate points of rest. In this they are similar to p _ _ _ _ _ _ _ _ _ _ marks.

• These chord progressions are called c _ _ _ _ _ _ _ , and each consists of two

chords.

• There are four types of cadence:

p _ _ _ _ _ _ - full stop (strong final cadence) - V is followed by I

p _ _ _ _ _ - full stop (strong final cadence) - _ is followed by _

i _ _ _ _ _ _ _ _ - comma (weaker) - _ / _ / _ followed by _

i _ _ _ _ _ _ _ _ _ _ - comma (weaker) - _ followed by _

Chord V7 (dominant 7th)

• Write out chord V in C major, and label the root, third and fifth:

• Now, put the seventh on top (or, thinking of it another way, add another third on top). Label the 7th.

This is chord V7, which can be used in cadences instead of chord V

• QUESTION: Why does adding the 7th work?HINT: think about leading notes and tritones…

ANSWER:

Draw a diagram of how chord V7 resolves:

So, it follows that chord V7 goes to I or vi at cadence points, thesame as chord V.

IF USING CHORD V7, THE LEADING NOTE RISES AND THE 7th FALLS

Learning to Modulate

• ‘Modulation’ is the term given to the process of changing key(s)in a piece of music. It shouldn’t be confused with the term ‘key-change’, which tells us nothing about the process.Think of key change as start point/destination and modulationas the whole journey.

• One of the easiest places to modulate is at a cadence. The easiest keys to modulate to are the closely related ones (one more or one less accidental in the key signature)

Finding closely related keys

• You can find closely related keys easily on a cycle of fifths. Theyare the relative major/minor (opposite), the dominant andsubdominant (either side) and the relative majors/minors ofthese (opposite either side)

Draw a ring round the closely related keys to D major

Notice how the keys you’ve ringed correspond to chords I-vi:

I D major D F# Aii E minor E G Biii F# minor F# A C#IV G major G B DV A major A C# Evi B minor B D F#

This is another way of finding closely related keys, but it only works in major keys. (In natural minors you need I then iii – vii)

Modulation Tables

If you’re planning a journey, it’s a good idea to have a map A modulation table gives you a map of chords I, ii, IV, V and vi(the cadence chords) in the closely related keys so that you can planpossible pathways through them.

Fill out the following in D major (use harmonic minors)

I ii IV V(7) vi

D major D F# A E G B G B D A C# E (G) B D F#

G major

A major

b minor

e minor

f# minor

You should have ended up with the following:

I ii IV V(7) vi

D major D F# A E G B G B D A C# E (G) B D F#

G major G B D A C E C E G D F# A (C) E G B

A major A C# E B D F# D F# A E G# B (D) F# A C#

b minor B D F# C# E G E G B F# A# C# (E) G B D

e minor E G B F# A C A C E B D# F# (A) C E G

f# minor F# A C# G# B D B D F# C# E# G# (B) D F# A

Take a minute to check and correct yours. Did you remember raised sevenths in your minor keys?

Using the modulation table

Consider a piece in D major with the notes F# - B at a cadence point. Try to find a cadence in D major that works. What do you notice?

So, the piece must have modulated. To find out what might work,look elsewhere in the table for an F# - B that forms a cadence (not just any F# to any B). Make sure it is F# - B, not B – F#

Ring them and use an arrow to connect them

You should now have lots of possible ways of harmonising an F# - Bmelody at a cadence. Make sure you have them all ringed. Which one you use is up to you, but always consider how it will sound in context:

• Is it too early for a modulation that involves accidentals• What will happen after it?• What happens before it?• Can you save the more complex modulations for the same

cadence if it repeats later on?

Some of the possibilities, ranging from simple to more complex:

Melody F# B F# B F# B F# B

BA D F# B C# D C# G#F# B D G# A# B A E#D G B E F# G F# C#

Key/chords/ G:V I A:ii V b:V vi f#:i V7Cadence Perfect Imperfect Interrupted Imperfect

Remember – just because it fits doesn’t mean you should use it!

Simple Complex

Using your modulation table, write out some possible cadences for the following pairs of melody notes:

C# - D 1) D: V(7) – I 4)

2) 5)

3)

E – A 1) 5)

2) 6)

3) 7)

4)

D – E 1) 5)

2) 6)

3) 7)

4)

Discuss and check your answers with your peers

Pivot chords

Look again at the modulation table. Notice how some chords appear in more than one key. I’ve underlined all the B minor (B D F#) chords, find some others:

I ii IV V(7) vi

D major D F# A E G B G B D A C# E (G) B D F#

G major G B D A C E C E G D F# A (C) E G B

A major A C# E B D F# D F# A E G# B (D) F# A C#

b minor B D F# C# E G E G B F# A# C# (E) G B D

e minor E G B F# A C A C E B D# F# (A) C E G

f# minor F# A C# G# B D B D F# C# E# G# (B) D F# A

We can use these chords to connect different keys and make ourjourney between them smoother. They are called pivot chords.

Think of them like the middle of a seesaw….

D

f#

BDF#(vi in D/iv in f#)

Imagine you chose to harmonise our F# - B melody with an imperfectcadence in A:

Melody F# B

F# BD G#B E

Key/chords/ D:vicadence A:ii V (imperfect in A)

This will work smoothly because b minor (B D F#) is an importantchord in both keys. The pivot chord is part of the cadence. We showthe pivot in our labeling by labeling it in both keys.

Sometimes you have to put your pivot chord before the cadence,often on the chord directly before (known as the approach chord).Imagine our melody extended slightly, and with our chosen cadencean interrupted in b minor. The pivot is now on the chord before:

Melody F# F# B

F# C# DD A# BB F# G

Key/chords/ D:vicadence b: i V vi (interrupted in b)

Pivots are easy to find in closely related keys because they share a lot of chords.

Triads in a minor key

Lesson prep / revision:

Write out and label the triads in E harmonic minor, from the bottom up, in order. The first one is done for you:

PrimaryMinor

Underneath each chord, label whether it is primary or secondary, andwhether it is major, minor, diminished or augmented.

Resolutions that we already know from a major key:

Fill in the following:

V7 V7 goes to ____ or ____

iii chord iii is used in ______ inversion and goesto _____ or ______

vii° chord vii° is used in ______ inversion and goesto _____ or ______

BGE

I

Rules we have learnt so far:

Complete the following:

Leading notes ________

Sevenths _______

Exposed intervals occur when the melody ______ and the bass part moves in the same direction, landing on a ____ or an ________

To determine whether you have parallels, you ask three questions.What are they?

1)

2)

3)

The best voicings for triads in three parts are ____ and _____

The best voicing for a 7th chord in three parts is ____

If you double leading notes you will get ___________________

If you double sevenths you will get __________________

Good partwriting occurs when you avoid ___________ intervalsand make sure that leading notes _____ and sevenths ______

The primary triads

We are going to use the HARMONIC minor for our purposes

Chord i and chord iv

The only real difference with chord i and chord iv in a minor key is that they are minor. Compare I(i) and IV(iv) in E major/E minor here:

Chord V(7) (dominant 7th)

Chord V(7) in a minor key works in the same way as in a major key -it’s goes to i and VI, it’s just that VI is major. Chord V(7) is still major because of the raised 7th in a harmonic minor.

Draw a diagram of how chord V7 in E minor can resolve:

IF USING CHORD V7, THE LEADING NOTE RISES AND THE 7th FALLS

The secondary triads

Chord ii°b (two diminished in first inversion)

Chord ii°b, because it is diminished, is used in first inversion tominimise the dissonance (like vii°b), and resolves to V(7).

Draw a diagram of how ii°b resolves in E minor here:

Chord VI

Chord VI is different in a minor key because it is major.Compare VI(vi) in E major/E minor here:

Chord vii°b (seven diminished in first inversion)

Chord vii° is the same in both major and minor keys, so is treated the same.

Because the root to the fifth is a tritone, we use chord vii° in first inversion to lessen the dissonance. The minor 3rd at the bottom stabalises it.

Draw a diagram of how chord vii°b resolves to i in E minor:

IF USING CHORD vii°b, THE LEADING NOTE RISES AND THE 5th FALLS

Often a further diminished 7th is added above the root (or to think of it another way another minor 3rd is added on top) to increase the dissonance, making the resolution even better. Redraw your diagram from above to make the progression viidim7b - i

Chord III+b (three augmented in first inversion)

In a minor key chord III is augmented. We haven’t had one of these yet. Augmented chords need treating with care.

When using the harmonic minor, III+ is used in first inversion andresolves to ic (then often to V-I for a cadential 6/4)

Draw a diagram of that resolution here:

IF USING CHORD III+b, THE LEADING NOTE RISES