Functional Harmony confusion
 

I was reading up on harmony basics and it says that the 1 3 and 6 chords are tonic family and they sound at rest. Well if the key is C major and you play an Em in place of it how would that be at rest? To my ear it sounds like it wants to resolve to C major...a major third (E to C) resolution.

They also say that subdominant chord imply forward motion. To my ear forward motion is a progression such as C major - Dm- Em -F major.....notice the C to D to E to F melody (forward motion)? Also notice the Em chord in what I hear as forward motion...well why is the Em still always referred to as a tonic chord and not forward motion? I just don't understand it.

The iii and vi are referred to as tonic functions because when you look at the voice leading, they don't really have a strong sense of movement to any other chord group.

If you have established C as your key, then any diatonic chord you play will pull towards C, because that's what a key does.

But if you look at the notes, a iii chord (3 5 7) has two of the same notes as the I chord (1 3 5). These notes aren't functioning as tensions. They are already resolved in the sense that 1 3 5 is the key's "home." This chord does have the leading tone in it (7), but it is the fifth of the chord, which is a stable interval from the root.

To give you some context, let's look at the dominant function. In a V7 chord (G7 in this case), you have 5 7 2 and 4. Only one of these notes stays still (5) when resolving to the I chord. The rest move. 7, the leading tone, is the third in the chord, which is the least stable note in the basic triad (1 3 5). This note "pulls" up to the tonic because it is only a half-step away. Likewise, the 4 resolves down to the 3 by a half-step. Now, the 2 (D) isn't as strong of a tension because it resolves by a whole step, to 1 or 3, but it still functions.

I wouldn't worry about the term "forward motion" as it is pretty ambiguous. You're thinking more "upward motion." I think what they mean by the subdominant implying forward motion is that it functions strongly as a predominant (leading to the V). But really, a IV chord will have a plagal function (IV - I) almost as often as it will have a predominant function (IV - V).

Wouldn't the iii want to move to the IV chord ( subdominant group)? The E root of the iii chord is a half step away from the F note of the IV chord. It is a half step pull....just like in a harmonic minor scale from the 7th degree to the root is a strong resolution.

Half-step resolutions individually are strong (such as the leading tone in a dominant chord), but half-step root motion is generally weak. This is because all of the notes move in parallels. Parallel fifths (E and B from the iii chord to F and C from the IV chord, pictured below in the key of C) were strictly prohibited in traditional voice leading. Of course, most music today doesn't follow traditional voice leading, but it is still relevant.

In fact, it is pretty common in most modern music to go from the major III chord (technically a V/vi) to the IV (i.e. E major to F major in the key of C). This is stronger than the minor iii chord because the G# leads to A by a half step.

Another common half-step root motion is the VI to V in a minor key (C major to B major in the key of E minor).

Parallel fifths in C: