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Outlining chords with a scale sequence.
Here's a good hand workout—Bach's Invention #4 in D minor.
There's a lot of scale work going on here, but there are some pretty cool melodic sequences that are outlining chords.
Bach was a master of harmony in the Baroque era. He'd have two or more voicings moving independently in a horizontal direction. In other words, when single-note lines are stacked on top of one another, they create chords that we can see vertically. This is why even hearing just two independent voices playing a scale sequence, whether by 3rds or other groupings. You can hear an underlying harmony of chords. You can also hear this even with a single voice playing single notes that outline a chord sequence.
The being of this piece is outlining two chords. Dm and C#°(diminish), he then points it out to us as he ascends to the octave to repeat the same motif. F A D is an inversion of Dm, G C# E is an inversion of C#°.
Let's back up and look at the first two measures. We have a D harmonic minor scale ascending and descending.
D E F G A Bb C#
1 2 b3 4 5 b6 7
However, he's not going up to the 7th degree; instead, he "pivots" the (C#) note down an octave.
This is a saxophone technique. By pivoting a note up or down an octave, we can repeat a sequence, phrase, or line. So if we were playing a phrase that is out of range, we could pivot to a note an octave below and keep the phrase going.
He then plays the two chords Dm and C#° to move up an octave, then repeats the motif from the first two measures.
He then descends this pivot pattern down, they're moving in 4ths. Each note is moving in 4ths of some kind. F Bb E A, etc. Bb to E is an augmented 4th, a tritone interval. Which can lead us down another rabbit hole, but we'll skip that one for now.
Each of those starting notes acts as a 3rd of a chord. F is the minor 3rd of Dm, Bb is the minor 3rd of Gm, E is a major 3rd of C, and A is the major 3rd of F. He's outlining Dm, Gm, C, and F.
We could take this same idea with a typical scale sequence and pivot a note down an octave to outline chords. For example, a scale sequence in A major. By pivoting the 6th note in a scale down an octave, we'll be outlining some chords.
This is already becoming a rabbit hole, but just as we have these "pivots" to move to another note, either an octave down or up, we also have "Pivot" chords. In the context of a "Pivot chord," it simply means a chord can exist in other keys with different functions. This piece starts in Dm, but we can see and hear it modulate to F major, which is the relative major of Dm.
How many keys have a Dm chord in it? It's the ii of C, it's the iii of Bb, and the vi of F. We could take this even further and look at some other functions, but that alone is enough to make us approach harmony differently.
Looking at the sheet music for this piece. Our Dm chord by the 7th measure no longer functions as our tonic chord, but rather the relative minor chord to F, it's acting as a vi chord. We see this again when he outlines a Bb chord, in the key of F, that chord functions as a IV chord, in Dm it functions as a bVI chord. Again, these are pivot chords that can lead the harmony into a different direction.
This is Bach we're talking about, so there are a lot of little gems of harmony we could explore and learn to use. For another time, we could revisit using pivot chords as a way to modulate to different keys to create a wide scope of harmony. But I think this is enough theory exploration for a Saturday afternoon.
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Outlining chords with a scale sequence.
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