MT08 Scheme KS5 Dominant Sevenths

7/30/2019 MT08 Scheme KS5 Dominant Sevenths

1/16Music Teacher August 20111

KS5KS5 D i 7 s, di i is ed 7 s dBee e s s by Richard Knight

IntroDuctIonAt AQA its time or a change o set work at AS level no more Jupiter Symphony. Instead, we have to grapplewith Beethoven, and the rst and second movements o his rst symphony.

You may think that this is quite a burden. Just when you have the measure o Mozarts Jupiter symphony, trustan exam board to cause you more hard work preparing your teaching o Beethovens First: why cant they justleave things alone or once? Its not as though this is a radical change its swapping one classical periodsymphony or another.

Understandable as this response may be, this change o set work presents an opportunity to review your ap-proach to teaching AS level. The obligation to steer your pupils through Beethovens harmonic vocabulary is awonder ul invitation to develop your pupils own harmonic palettes when they come to compose.

It can be very di cult to nd the time to develop your pupils compositional techniques. By the time you havescheduled the 20 hours o Controlled Time or the Unit 2 work, there can be a serious pressure on class time

or teaching the Unit 1 topics (listening, set work and the Area o Study 2 topic) and the skills that will move yourpupils compositional work orwards rom GCSE. The aim o this resource is to show how these two aspects canbe tackled simultaneously. Moreover, not only will analysis o Beethovens harmonic language in orm composi-tion work, by exploring the theory in practice, understanding should be rein orced.

DomInant 7 th chorDSOne cannot go very ar with a study o Beethovens First Symphony without understanding the signi cance odominant 7th. A ter all, here is the opening bar:

The important thing about dominant 7th chords (such as the rst chord o Beethovens symphony above) is thatthey have an inherent impetus to move to the tonic chord o which they are the dominant.

This is not the case with standard triads chords o three notes, ormed by superimposing two intervals o a3rd. Take the ollowing chord, or instance:

The change o setwork a ects yournew Year 12 pupils the Unit 1 exam inMay 2012 will haveSection B questionson the Beethoven.Rhinegold Educationhave produced anew edition o theirAS Study Guide torefect this change,which is now avail-able to buy

O ten it is harmonicvocabulary thatlimits an AS com-position. Melodicinterest, rhythmiccharacter andre nement o texturehave to be strongto overcome a har-monic palette thatis purely diatonic,moving at an un-varying one-chord-per bar harmonicrhythm.

Richard Knight isa composer witha wide range oworks to his name,especially chambermusic. He has beendirector o music attwo leading indepen-dent schools and isa senior examiner

or music at A level.He also examines orABRSM.


2/16Music Teacher August 2011 2

This chord can appear in a lot o di erent roles:

t e i d c j

t e edi d a i t e s bd i d G j t e d i F j t e s b edi E i

Isolated, with no visual or aural clues as to its context, we have no way o knowing which o these roles ourC major triad is ul lling, and there ore we can have no expectation o what chord comes next. It could quitereasonably be ollowed by an F major chord (IV in C major), E major (V in A minor), D major (V in G major), Bmajor (IV in F major) or B major (V in E minor). Yet you will struggle to nd a key in which both the chords o Dmajor and B major appear, or or that matter the chords o F major and B major.

Triads only begin to orm a sense o tonal context in combination; isolated they are a neutral, harmonic sound.

The dominant 7 th, however, is di erent. Instead o three notes, we now have our. That ourth note comes romthe harmonic series, where it is seen to be the next upper partial a ter the octave, 5 th and 3 rd:

The extra note creates a mild dissonance in this case C against B and this creates a need or resolution.

That resolution needs to be to F major: the tonic o the only (major) key that has both B and E in it (notes inthe dominant 7 th chord).

The pull to this destination is so strong that to leave the dominant 7 th chord hanging in the air or any time issomewhere between irritating and pain ul. In much the same way, playing this sequence o notes as a melodycries out or someone to complete it by playing one more note

so this short snippet desperately needs someone to complete it by playing a tonic chord:

Try these out on your pupils: i they get that eeling o something le t undone that needs completing, then theyget the magical orce o the dominant 7 th chord.

You may like to askpupils to compile asimilar list o pos-sible roles or an Aminor chord


3/163 Music Teacher August 2011

thE FIrSt Duty oF thE DomInant 7 th chorDThe theory

This inherent property o the dominant 7 th chord makes it the easiest way to announce and establish the key oa piece o music. This well-known opening rom Mozart shows the dominant 7 th very clearly doing this job. Bybar 5 there is no doubt at all; we are going to be in G major or this piece:

By now it should be apparent that this dominant 7th

chord acts like a musical signpost in real time. It highlightsthe ollowing chord as being signi cant: the tonic. It is as though our ears hear the chord pointing to the onethat ollows; at the same time the ollowing chord gains in importance by having that signpost o its dominant7 th in ront o it. A visual equivalent might be:

Another very common way o announcing the key is to have a pair o phrases, the rst o which is based on I V7, with the answering phrase reversing this or a V7 I progression. Mozart provides a clear example at thestart o his Piano Concerto k.467. A ter these opening our bars there can be no doubt what key the concertois going to be in, and its all done by the relationship o the dominant 7th chord to its tonic:

Composing exercise 1

Now would be a good moment to get composing and show that this undamental understanding o how thedominant 7th relates to its tonic has been grasped. Ask pupils to write the opening our bars to two new pieceso music. The ollowing choices are theirs:

t e ke ( b b bes se j ) t e i e sig e

d o

m i n a n t 7 t h

c

h o r d ~

Thenext chord

should be the tonico this chord

EXPECT IT!



t e e e (ei e e d , be i es, e d e si e d i e , bea be i s e)

For the rst exercise they should write a two bar phrase to t chord I in their key, ollowed by a two bar answer-ing phrase that ts chord V7. For example:

For the second exercise they should write a two bar phrase that ts a I V7 progression, ollowed by an an-swering phrase that ts the reverse pattern (V7 I). For instance:

Advise pupils that so ar as the melody is concerned, answering phrases usually work best when they have the

same rhythm as the opening phrase. Its contour can be di erent.

You might also try out your pupils instinct or being able to improvise suitable answering phrases by playingopening two bar phrases that ollow one or other pattern and challenging them to sing (or play) a respondinganswer immediately (and in time). I they can, it will mean they have thoroughly tapped into the tonic / dominant7 th relationship.

BEEthovEnS thrEE-carD trIcKThe theory

We have already seen the opening bar o Beethovens 1 st Symphony. It starts with a dominant 7 th chord. Butwait: this symphony is billed as being in C major, yet that opening chord isnt the dominant 7 th of C major(thereby pointing to C major as the tonic - instead it is a dominant 7 th on C (there ore pointing to F major). Whatis going on here?

Well, in the course o the opening our bars, Beethoven actually presents three di erent dominant 7 th chords:



This may at rst seem con using: just what key is Beethoven wanting to establish here as the tonic o his rstsymphony? Yet there is method here. The three dominant 7 th chords have pointed to three keys, moving sharp-wards around the circle o 5ths:

This is the tension inducing direction o travel round the circle and sets up an expectation to all back in theopposite, relaxation inducing direction (i.e. anticlockwise) at some point.

Ask your pupils which o the three dominant 7 th chords is given the most prominence. The answer is the thirdone (V 7 o G), because:

I is ei e ed I s s e e i e b (i.e. wi e s g s e e i s w ) I s es i is ked b e s e e s d i i I s es i s b e ig es (1s f e) d wes (d b e b sses) es e d s

So the three dominant 7 th chords each point to a di erent tonic chord, but the one that points to the dominanto the home key is the weightiest o the three. And or the remainder o the slow introduction we wait or anF natural the dominant 7 th note to be introduced to that G chord so that the tonic key can be released orthe main Allegro section. Beethoven duly obliges at the very end o b.12 as the strings scurry down their de-misemiquaver run.

One nal and important aspect o the opening our bars: we were correct in plotting the three dominant 7 th chords taking us around the circle o 5ths. However, the second one, which is V 7 o C major, takes a sidestepwhen it resolves, and instead o moving to a C chord (its chord I), goes to an A minor chord (its chord VI), just

like might happen in an interrupted cadence. This enables Beethoven to keep us waiting or the categorical Cmajor is the tonic moment, which is care ully placed as adagio molto gives way to allegro con brio.


Ludwig is not the only one who can use alse dominant 7ths to keep a sense o suspense at the start o a pieceas the listener is kept waiting or the real tonic to be revealed. Consider the ollowing opening:

CG

D

A

E

B

G /F

D

A

E

B

F



Here there are two alse dominant 7ths: in bar 1, there is A 7, which suggests we might be in D minor, and in bar2 there is E 7, which suggests that, no, we are not in D, we might be in A minor. However, all is made clear inbars 3-4 when G 7 takes the music to C. We can tell that this third dominant 7 th is the real one, because:

I is de I s s wi e s g ( e is e e i g Bee e s s ) t e e is sse i e isi g e d s e e i e d w be e e b

Challenge your pupils to compose the opening to a piece that uses one, two or even thee alse dominant 7thsbe ore clearly establishing the real tonic. In order to make it clear which dominant 7 th has the most signi cance,encourage them to consider:

D i s a i i D i te e regis e

ti b e

BEEthovEnS nExt DomInant 7 th

The theory

Once the allegro is reached, Beethoven presents his main 1 st subject idea, a rather quirky melody that is builtrom a three note moti (G B C) played ve times:

There is precious little accompaniment: just a ew detached C major chords in the lower strings.

On the good composing basis that i an idea is worth doing, you should do it twice Beethoven immediatelyrepeats his theme, but he chooses to do so a tone higher. This could be a rather clumsy juxtaposition o chords lots o chord I ollowed by lots o chord II but Beethoven eases the move by a simple chord progressionthat moves rom C major to D minor via the dominant o D minor: an A 7 chord. This is a cunning move because:

I s e s e ge D i , si e e we e sig s a7 d, we e e e i g e D d I i d es, fee i g , ide e c i w i e e ie ed se s w ge

ed e di i e e d i k d i g

Beethoven hasnt modulated here: the big cadence at the end o the rst subject (b.22-23) is emphatically stillin C major, but there is a sense o sophistication about the music at this point due to the chromatic infectionin the harmony.



compoSInG ExErcISE 3Here are three opening phrases ollowed by an instruction to repeat in a related key in a manner similar to theopening o Beethovens Allegro. In the rst one the linking dominant 7 th is given and you only have to work atthe transposition o the opening phrase; the other two you will need to work out which dominant 7 th is required.

In this nal one, i t should prove help ul to think about the melodic minor scale when working out the transposi-tion o the melody into the mediant minor.

For each exercise, once the repeated phrase is created in its transposed version, suggest to pupils that theycontinue the opening or a urther 8 bars, bringing the musical sentence to a close with a per ect cadence

back in C major. Pupils can then try a similar procedure having devised their own opening our bar phrase.

SEconDary 7thSThe theory

The example rom the Beethoven symphony that we have just studied precedes the supertonic chord (Dminor) with its dominant 7 th in order to ease the progression rom C to D minor. This is at a moment o somesigni cance: the end o one phrase to the start o the next. In act, dominant 7ths can be used more reely

than this; wherever one is going to use a diatonic chord, it is possible to precede it with the dominant 7th

othat chord.

Take this passage or instance:

This is a rather innocuous passage with only diatonic chords in use. However, in each quaver rest in the LH, itis possible to use the dominant 7the o the next downbeat chord to signpost the chords that is about to ollow:



I e b w , c7 d the d i 7 e ke is ie e wi i e e e ed Fd i b 2

I b s w d ee, a7 d wi i e i g D i ds I b , F7 d wi i e B d i b 5 I b e, G7 d wi i e c d i b 6

Put these harmonic infections into the music and the passage picks up more character:

The enhanced character is due to the chromatic notes C , E , B that do not appear in diatonic F majorharmony, and also orm the livelier harmonic rhythm which now has two chords per bar. But there is a morepro ound actor: the listener picks up on a greater sense o momentum through the passage because at the

end o every bar they hear the dominant 7th

signpost or the chord that is coming next.

The use o all these additional dominant 7 th chords dominant 7ths not in terms o the key we are in (the musicnever leaves F major here), but in relationship to each ollowing chord are known as secondary 7ths . Theyare guaranteed to make your music sound harmonically more sophisticated, and will probably impress anexaminer

Put this harmonic basis into the hands o a creative genius such as Herr Beethoven, who can think to pick upon the melodys dotted rhythm and refect it in the accompaniment, and emphasise the secondary 7ths in hisinimitable way with heavy sf markings, and you achieve this

which can be ound in the 2 nd movement at bar 147.


Using secondary 7 th chords is a great way o increasing the harmonic vocabulary o your music somethingthat should be in the minds o AS composers. Like all these things, at rst it will take a little conscious brain-power and mental struggle, but a ter a while it will be more spontaneous and part o their musical imaginationand instinct.

As an exercise take the ollowing steps or eight bars:

c se j ke Se e di i d seq e e, e d e b (e di g wi s g de e) W k e d i 7 e d d i se i i e se d e e i s b Se e i e si s e d e si g b ss i e

De e e d s wi d e

Inversions are an important aspect o writing good harmony, and care should be taken with the bass line.Remember that a dominant 7 th chord has our di erent notes, so can appear in our di erent inversions: the



root can be in the bass (V 7), the 3 rd can be in the bass (V 7b), the 5 th can be in the bass (V 7c), or the 7 th can bein the bass (V 7d).

The ollowing chart is an illustration o how the thinking might go. This is or the opening o a piece in G major:

b 1 2 3 4 5

Di id

I vI IIb v I

c d i Gj

G E i a i D G

D . 7e d B7 E7 a 7 D7

n es id

G B D B DF a

E B G E GB D

a c E a cE G

D F a D Fa c

G B D

c i e e b ss

i e

G F E D c c D F G

I e si d . 7

dv 7 v 7d v 7b v 7b

Notice how smooth a bass line is possible with care ul selection o bass notes: it is almost entirely conjunct.

From this planning phase, something like the ollowing could be possible:

Chords marked Ic* are cadential places where the expected chord V is delayed by the use o chord I. I youview the six our ve three pattern o Ic V as a double appoggiatura, then it is really a chord V masquerad-ing as Ic or a beat or so, and thus it is not strange that these chords are preceded by V7 o V. The dominantnote is, a ter all, very prominent in the bass o the Ic chord.

Are you wonderingabout the title? Tryplaying, rhythmically,just the downbeat oeach bar



So by using lots o secondary 7th chords we turn a slightly staid, diatonic chord sequence into something armore sophisticated and stylish, with plenty o chromatic nuance.

When your pupils work at this exercise, make sure they write out the original diatonic chord sequence rst, sothat they and you can hear the basis or the more elaborate music that they compose therea ter. One optionis to choose a couple o phrases rom a church hymn book (traditional tunes recommended).

DomInant 7 th aS a portal BEtWEEn tonalWorlDS

The theory

So, whether you are in the major or minor mode o a key, the dominant 7 th is going to be in common. Thismakes it the per ect harmonic warp to slip through i you ancy changing or a touch o the other side (that is,switching to major or minor) and is also the per ect way back again when you eel the need to return home.

This move between tonic major and tonic minor was a hallmark modulation o the classical period composersand shows just how instinctively they understood the tonic dominant axis at the heart o tonal music. Thereare several excellent examples in Mozarts Jupiter Symphony (which, o course, you have now care ully putback in its place on your shelves).

In the exposition o the rst movement o his rst symphony, Beethoven has ollowed sonata orm principlesand ound himsel in the dominant key (G major) ready or the 2 nd subject. He presents a lovely lyrical melodythat is very sunny in character, and shared by the oboe and fute:

Notice how the new key is categorically stated through the chord progression at this point.

Around bar 76 it would seem that this second subject is about to conclude with a weighty per ect cadence.But or Beethoven, the dominant 7 th that this cadence involves reminds him that it is the gateway to G minor aswell as G major. He takes the plunge, moves the melody rom the high, bright winds, to the deeper register othe cellos and basses, as the music moves rom major to minor, and immediately it is as though a dark cloudhas gone in ront o the sun.

Q. What is the dominant 7 th chord of G major?

A. D7

Q. What is the dominant 7 th chord of G minor?

A. D7

Anyone not sure of this should be reminded that we are talking about harmony here, so the harmonicversion of the minor scale pertains.



From bars 77 to 85, there is no doubt that the music is now in G minor. Bar 85 is, however, a dominant 7 th chord(D7) once again, and provides the per ect moment to slip back into G major. Since this is coupled with the bassmelody rising rom its gloomy depths at the start o the minor section to a much brighter register, one and a haloctaves higher, the sense o the sunny breaking through the dark cloud is vivid:

(Note the use o a secondary 7 th chord in the second hal o bar 84. This signposts the ollowing chord as

signi cant, and indeed it is: it is going to be the V 7 moment where Beethoven can slip back into the major key.)

This use o the dominant 7 th opens up a range o di erent chords that can be used without ever changing thesense o where the tonic lies. Many o the chords take on a di erent character, as can be seen in the ollowingchart (where G is the tonic):

m j mi

t i G j G i

S e i a i a di i is ed

medi B i B j

S bd i c j c iD i D j D j

S b edi E i E j

le di g e F di i is ed F j or F di i is ed

Composing project 5

Ask your pupils to write a 16 bar piece that ollows this plan:

B s 1-4: i ses wi g e I v: v I e , s ised i si g je 1 B s 5-8: ge b se kee s i e j d e ds v7 B s 9-12: ge se i e i i s d se e s e ds III, i vI; i s d s

e d v7



B s 13-16: e e j de e d wi e e or g de e

All other actors: tonic note, metre, instrumentation, etc. can be the pupils own choice.

The ollowing piece is one example o what these instructions might lead to:

BEyonD DomInant 7thS: DImInIShED 7thSThe theory

Early on in this article we looked at how the three notes o a triad, heard in isolation, are tonally neutral, whereasthe our notes o a dominant 7th chord have a strong tonal implication. Is it possible to go urther through ex-ploring ve note chords?

Well, yes it is. To the root, 3rd, 5th and 7th o the dominant 7th chord, we can add a 9th. This is most likely to

be a minor 9th, making the ull chord one major 3rd at the bottom, and three minor 3rds on top. This makes achord that has a erce dissonance: a semitone between the root (the dominant note o the key) and the minor9th one octave above. As a result, this o ten leads composers to omit the root when using a dominant minor9th chord. This leaves a collection o our notes that orm something most developing musicians rst meet asa diminished 7th arpeggio at higher instrumental grades:



The extraordinary thing here is that, once the root is omitted the dominant note the remaining chord de-

pends on context or its impact: like a basic triad, heard in isolation, i t is not obvious which key i t is signpost-ing. Look again at chords 4 and 9 above: both contain B, D and F; one then has an A , and the other a G . Tothe ear, these chords are the same. Yet in context, one works as a dominant chord in C major (and needs tobe spelled as having an A , it being a 9 th above G), and the other works as a dominant chord in A minor (andneeds to be spelled as having a G , it being the major 3 rd o an E chord).

Beethoven uses both these dominant minor 9 th chords in close proximity in the rst movement o his symphony.At bar 65, midway through the second subject, he writes the ollowing:

Lets analyse these chords:

a W, e e is di i is ed 7 d is de i ed d i d G ( s be 4 b e) a x, es i is d i d is ie ed c j d, w i G is e d i a y, e e is di i is ed 7 d is de i ed d i d E ( s be 9 b e) a Z , es i is d i d is ie ed a i d, w i E is e d i

So why use these dominant minor 9th

chords (probably without their roots, so as diminished 7th

chords)?

Key:

1 = Dominant triad in C major

2 = The same chord with the 7 th added (V 7)

3 = The same chord with the minor 9 th added (V 9)

4 = Root omitted due to the semitone clash with the minor 9 th

5 = Resolution to the tonic chord of C major

6 = Dominant triad in A minor

7 = The same chord with the 7 th added (V 7)

8 = The same chord with the minor 9 th added (V 9)

9 = Root omitted due to the semitone clash with the minor 9 th

10 = Resolution to the tonic chord of A minor

Why do the timpanihave to be silent in226?

G in 96 becomesviolins bottom noteG in 291 (not theexpected F ).



Well, rstly, they increase the amount o chromatic colour that your harmonic vocabulary will have. Considerthe ollowing chords or C major:

One can see here that the dominant minor 9 th option never has ewer, and in our cases has more accidentals,than the dominant 7 th option. Moreover, on this stave there are notes that are never ound on the stave above:

A , D , and E .

Secondly, there is an ambiguity to these diminished 7 th chords that the dominant 7 th chords lack. This maysound like a disadvantage, but it means each can be a portal or taking the harmony (and tonality) o a pas-sage into unexpected areas. Here we are on the brink o very advanced harmony that AS candidates areunlikely to need, but a ew may wish to explore. So, just to li t the lid on this area, some may like to experimentwith the ollowing instructions:

p di i is ed 7 d l we e e es b se i e d see w e e e es i g d w s es e re e igi di i is ed 7 e d d se di e e e we b se i e re e e ed e wi e e i i g w es n w e e be e e d i 7 d es e i i s we s j i d

e e e e e ise

This short experiment shows how any given diminished 7 th chord can resolve in one o eight directions:

In each case one can go direct rom the diminished 7 th to the destination chord.



Composing project 6

Those wanting to explore the chromatic favour o diminished 7 th chords in their composing need to revisitcomposing project our, and or each secondary 7 th chord involved, work out the dominant minor 9 th option.This would make the chart in my version look like this:

b 1 2 3 4 5

Di id

I vI IIb v I

c d i Gj

G E i a i D G

D . i 9 e d B-9 E -9 a -9 D-9

n es id

i ( )G B D

(B)D Fa c

E B G(E)G BD F

a c E(a)c E GB

D F a(D)F# ac E

G B D

c i e e b ss

i eG F E D c c D F G

I e si d . 7

dv -9 v-9d v -9b v -9b

Here is a possible opening or developing this chart into music:

The original, purely diatonic tune can still be traced here, i not heard.


16/16

laSt WorDDominant 7 th, secondary 7 th and diminished 7 th chords can seem complex at rst. Like so much o music,however, they comprise an area where there is a dual beauty at work: the patterns to some minds have a nearmathematical ascination in this area o elaborate harmony, whilst at the same time carrying with them a strongemotional potential or those drawn to music more as an aesthetic pursuit.

By teaching the theory o these chords in context, as part o the set work study o Beethovens rst symphony,at the same time as encouraging exploration o the same harmonic vocabulary in compositional work, wecan maximise the chances that our pupils will delight in both these types o musical beauty. Ideally those witha mathematical mind, who revel in the mental agility to analyse the chordal patterns, will eel the emotionalweight o Beethovens musical language and discover the joy in using the theory or their own expressiveintent; meanwhile, those o an aesthetic mind, eager to make creative use o the expressive power they instinc-tively hear in Beethoven can, by learning and applying the theory learned in set work study, ul l their mostinstinctive aspirations.

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MT08 Scheme KS5 Dominant Sevenths

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