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Figured Bass Lesson 3: 7th Chords

Grade 7 Music Theory, Q1, Adding a Figured Bass. Lesson 3 - Added 7th Chords

The Dominant 7th Chord

The most important chord in any key is the tonic. The second most important chord is the dominant. In the key of C major, for example, the chord of G major is the dominant chord. These two chords work together to fix the key of a piece of music. In tonal music, the tonic-dominant relationship is absolutely the most important relationship that there is, and therefore we find many V-I or I-V progressions throughout any piece of music (in the period we are studying, which is late Baroque to Classical).

In a V-I progression, it is the magnetism of the semitone pull from the leading note to the tonic which creates the power of the progression. We feel that the leading note has to be followed by the tonic, to release the tension which has built up. Here, the leading note B has a strong pull towards the tonic C:

V-I

 

The magnetism of the semitone can be increased, by adding a 7th to the dominant chord. The 7th is calculated from the root of the triad. In this case, it's a G major chord, so the 7th is F. The result is two semitones with magnetic pulls. The 7th (F here) falls to the mediant of the tonic chord.

V7-I

 

 

• Dominant 7th chords occur frequently within a piece of music, but are less common at important cadences, where the basic V-I progression is often preferred.

• Dominant 7th chords occur very frequently when music is modulating. When music changes key, it is necessary to use chords which fix the new key without any ambiguity. The only chords able to do this are V and I (in the new key). V7-I allows a richer harmony.

• V7 chords are nearly always followed by a chord I, but V7-VI is also used.

This example starts in C major (chord I). The next chord (D7-shaded) is V7 in G major – the music is modulating to the dominant key. The final G major chord is chord I (in G major).

v7 modulating 2

 

Secondary 7ths

You can add a 7th on to any chord. The dominant 7th has such an important place in the way that harmony functions, that it is the only "primary" 7th chord. If you add a 7th on to any other chord, it is known as a "secondary 7th".

The most common secondary 7th found in this grade 7 question is ii7. It is no coincidence that chord ii is actually the "dominant of the dominant", being a fifth higher!

dominant-of-dominant

Chord ii7 leads very nicely on to chord V, so you can often find a ii7-V-I progression. The supertonic 7th chord is found in both the minor and major versions. In the example below, the bass note can be F or F#.

secondary 7ths

 

The supertonic 7th chord is found in both the minor and major versions. In the example above, the bass note is just as likely to be F#, for example.

 

Notating 7ths in Figured Bass

Since there are four notes in added 7th chords, it should come as no surprise that there are four ways you can write them: root position, plus 1st, 2nd and 3rd inversions. (3rd inversion is notated as "d" in Roman numerals). The abbreviated figures are normally used:

• Root position (a): 7 (short for 7-5-3)

• 1st inversion (b): 6-5 (short for 6-5-3)

• 2nd inversion (c): 4-3 (short for 6-4-3)

• 3rd inversion (d): 4-2 (short for 6-4-2)

You can learn these figures in less than a minute. Notice the pattern:

7 – 65 – 43 – 2

All you need to remember is that you should add a "4" to the last figure to make "4-2". The other numbers are just the descending numbers from 7!

You will see some of the "missed out numbers" reappear if they need accidentals added to them, or if they cannot be omitted from the chord. (There's an example later in this lesson).

Here are the four inversions of the dominant 7th chord in C major:

seventh-inversions

 

As with any figures, accidentals can be added. An accidental which appears without a number applies to the third above the bass. Because 7th chords are often added when music is changing key, you can expect lots of accidentals thrown in!

Here's an example for you to play. Starting in C major, the music quickly modulates through D minor then E minor:

sevenths progression

 

 

Here's the same music with the bass figured:

sevenths progression figured

The second chord has a "floating" sharp which means the third above the bass (C) must be sharpened.

The fourth chord has a 5#, meaning the fifth above the bass (F) must be sharpened, and a "floating" sharp, which means the third, D, is also sharpened. This is an example of the "missed out" 5 reappearing in the figure, because it's been altered chromatically. Both of these 7th chords are root position.

 

Voice Leading

Each note of a chord should move gracefully to the next note in the same part. You will have studied some rules of voice-leading during the Grade 6 course.

For example, the soprano often moves by step, the alto and tenor parts should move as little as possible or not at all, and the bass often has a fall of a 4th or leap of a 5th.

In the first example below, the voice-leading is good. The soprano part moves by a second (a "step"), as does the tenor part. The alto part repeats the same note, and the bass falls by a 4th. In the second example, the alto and tenor parts have poor voice-leading.

good-voiceleading

 

The rules of voice-leading tell us that if two notes are a semitone apart, they should normally be kept in the same part. The two semitones created by a V7 chord need to be treated carefully!

The 7th in an added 7th chord should always fall by step.

This is important to know, because it means that V and V7 chords are not necessarily interchangeable. In the grade 7 theory exam figured bass question, you are given a bass line and melody line and are asked to suggest figures for the bass. Sometimes you might consider V or V7, thinking they are more or less the same. The voice-leading, however, can cause problems. You need to check the melody line to make sure a V7 chord would work. Here's an example.

V7-wont-work

 

The G# and E in chord 1 might fit with Vb (E major) or V7b (E7), and chord 2 is Ia (A major).

To check if the V7 chord would work, sketch in the missing notes and work out where they should move to, according the rules of voice-leading:

test-the-v7-chord

 

The added 7th in chord 1 would be D. D would have to fall to C#, because it's a semitone pull. This would create two C#s in the A major chord, but doubling the third in a major chord (and also, doubling the leading note) is not allowed. Therefore, chord V7 won't work here. Chord V is fine though.

 

The Clue's in the Question

An easy way to spot where a 7th chord is intended is to identify a bass note and melody note which are a 2nd (compound) apart. Here's an example – look at the chord marked 1:

2nd-in-question

The bass note is G and the melody note is A – they are a compound 2nd apart. You need to figure out which chord contains both of these notes – only a 7th chord can contain two notes which are a compound 2nd apart. In this case it is Am7 – or ii7d. The chord notes are A-C-E-G. (Remember that in a 7th chord, there are four notes which are a third apart from each other, and the lowest of these is the chord root.)

This is how you could figure the above progression (alto and tenor parts also added for reference):

clue-figured

 

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