Harmonising cadences given the bass line. When and when not to use inversions?
I've been completing practice exams online for Grade 5 theory and I'm struggling with some of the cadence questions. I feel that, without the use of inversions, you reach a dead end. The questions normally take the form:
"In four-part vocal style, harmonise the notes under each of the four brackets with a cadence and an approach chord. The passage includes modulation to related keys. Show one examle of each of the four principal cadences."
An example of a question looks something like this:
This isn't the full question, but it would be helpful to know how to harmonise the second cadence. Because there is an E natural, I know that it must be in either D minor or F major (modulation is to related keys, tonic major is Bb major). So first I tried D minor. In D minor, E natural is only present in in chord ii and chord vii (chord vii can't be used in a principal cadence). But, I'm not allowed to use ii in a minor key, so I can't use chord ii as E natural is the bass note. The D (the next note) is present in I and and vi, none of which can be used to make a principal cadence following a ii chord. Next I tried F major. For F major, E natural is only present in chord V and vii (chord vii can't be used in a principal cadence). For chord V, E natural as a bass note would make it an inversion. The next note, D, is in the vi chord.
My question is, does a movement from Vb-vi count as a cadence? Also, is there something I haven't thought of, which is just glaringly obvious!
Thanks so much!
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When and when not to use inversions?
A natural E in Bb major in root position could only be the root of (VIIdim7) a leading tone resolving to F. But as it steps downwards to D it obviously has to be an inversion.
Also, is there something I haven't thought of
G minor is also a related key, unless the rules of your exam board prohibit using notes from the melodic minor scale in harmony exercises (it's 50+ years since I passed ABRSM grade 5 theory, so I don't remember that level of detail!) That would gives you a nice IVb-V imperfect cadence (the first inversion subdominant is conveniently arranged to sidestep any problems with parallel 5ths and octaves) and the dominant chord resolves nicely onto the tonic G minor in the next bar.
"In D minor, E natural is only present in in chord ii and chord vii..."
The glaringly obvious point you may have missed is that in D minor, E nat is also part of A, the dominant! You have Vc - i in D minor.
Yes, you would use C major in first inversion leading to D minor. You would probably handle the upbeat in the previous bar as G minor in root position, so the progression is ii/V - V6/V - vi/V, which is a classic deceptive cadence. As ttw notes, inversions are frequently used in phrases where a strong authentic cadence isn't required.
A first inversion dominant chord is fine in a non-final cadence. Some texts class these as "imperfect cadences." The root movement is V-I (or V-i) but one or both chords are not in root position. The final cadence in a piece (or section of a piece) almost always has both chords in root position.
Often first inversion chords are used to produce a more melodic bass line.
Natural E is the 4th note augmented. Thus, it is a Domonant.Dominant (the fifth chord of your fifth chord) in first inversion. For example in C major scale the D.D is D-F#-A. A D.D resolves to the V of the current scale. You can also have a D.DVII chord in first inversion.
I wonder how this person did on their exam? :-)
@JDaly probably won't be coming back here to select an answer, but it may be helpful to an something for future visitors.
One approach is to identify the final chord of the cadence and then work backward.
Here the given bass notes are F and D.
Common cadences end on the I, V, or vi chords in major keys, and i, V, or VI in minor keys. Those chords would normally be in root position except for I6 or i6 for imperfect cadences.
Second inversion chords can be used in cadences, but normally they are cadential 6/4 chords which decorate a dominant in the bass with a fourth and a sixth above as a kind of double appoggriatura: I6/4 V or i6/4 V. For this example we won't consider cadential 6/4 chords.
For the F bass it could support chords I6/4, iii6, or V. When aren't using 6/4 chords and we don't have a common cadence on a iii so V is our target chord.
For the D bass it could support chords I6, iii, or vi6/4. We aren't using 6/4 chords and so rule out vi6/4. Possibly it's an imperfect cadence on I6, but notice that the D is preceded by an E natural a tone foreign to the key of B flat. If this were an imperfect cadence to I6, the E would need to be in the key and have a flat. That rules out I6. We only have iii left, but that isn't a common cadence chord... in B flat. We can temporarily say the iii becomes the tonic and the key is D minor. Now E natural is in the key and we temporarily consider that Dm chord is i our target chord.
Quick recap. our two target chords are: F as V and Dm as i.
Now we need to determine the preceding chords.
We can keep things simple by looking for options by root progression by descending 5th V to I or descending 4th from I to V.
The bass movements from the preceding tones are D to F and E natural to D.
For D to F in the bass we can use I6 to V in B flat major.
For E natural to D in the bass we can use V4/3 to i in D minor.
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