Trouble understanding resolution direction and general definition of when someone says to "resolve down to the 3rd"

Question

When creating a chord progression, how do you determine whether the notes that make up the chords should resolve downwards or upwards?

For example, a Perfect 4th interval, when it’s formed from the lowest note of a chord along with any of the other upper voicings, gives a "dissonant" sound and results in it’s wanting to be resolved. The way to resolve this, as I've been told, is to resolve it downwards to the 3rd.

1) What exactly does that mean, to resolve "downwards to the 3rd"? Please share examples of a basic chord progressions that shows this movement.

2) Furthermore, I've read that dissonant notes want to resolve downwards, or relax, into its resolution. Why?

3) Are there common, or practical, uses for resolving upwards? Would one direction be more or less effective than the other or provide a totally different "resolving" effect? If so, could you share examples or an explanation, please?

4) In regards to a Perfect 4th again, why, when played on its own, is the upper note (C-F in C Major) perceived as the root? I thought the root is always the first note in the chord or order of notes? How then would the upper note of F be perceived as the root?

Answer 1

The whole thing of Functional Harmony is that some notes are stable (in the most simplistic terms these will be the three notes of the tonic triad of the key, with the actual tonic note - C in C major - being the most stable), the others are to some degree unstable - they'd like to move to the more stable ones. Combine more than one unstable note in a chord, it wants to 'go home' even more!

And that's the harmonic basis of everything from Bach to Tchaikovsky summed up in a couple of sentences! :-) No, of course it isn't. And we mustn't be tempted by glib 'rules' that only apply in certain contexts.

But here's a few things that can happen. You'll discover more, as you encounter more different and varied pieces of music.

Yes, a note can resolve upwards. The classic example of a note that wants to resolve upwards is the leading note of a key, the 7th note of its scale. And a classic example of an interval that needs to resolve is an augmented 4th, where one note resolves up, the other down.

When we think in terms of triad-based harmony, 'Root' does not necessarily mean 'lowest note'. I expect you've come across the idea of chord inversions - Root Position with the root of the chord at the bottom, First Inversion with the 3rd of the chord at the bottom, Second Inversion with the 5th at the bottom.

Sometimes a 'resolution' occurs when one of the notes of a chord is displaced. ('Suspended' is the technical term.) Perhaps the 3rd of a C major chord (that's E) is moved up to F. It wants to go home! Where there should be the interval of a 3rd above the lowest note, there is instead a 4th. It wants to 'resolve downwards to the third'.

Answer 2

You're overthinking it. Notes that are a 1/2 step from notes in the I chord like to move to the notes in the I chord. That's all.

So in an E7 chord: E - G# - B - D

moving to an A chord: A - C# - E

The G# goes up to A, and the D goes down to C#. Change "goes" to "resolves" and you're set. They want to do this because they are close.

Answer 3

This type of rule is based on the observation that most composers (from about 1400 to 1900 and continuing in popular music in the 2000s) have tried to maintain the coherence of musical lines. In the case mentioned (dissonant fourth against the bass), the notes of the dissonant fourth tend to move to the nearest notes that give a resolution.

Let's look at a cadential 6-4 chord: G-C-E moving to G-B-D. The G-C fourth is (in cadences) treated as a dissonant interval and the "shortest" movement is to move a single note by a half-step. The C moves downward to B making a "stable" sounding major third. The E can drop to D making the G-C-E to G-B-D motion sound like the C and E are just "neighbors" to B and D.