Why does the dominant lead to the tonic?

Question

Going from a dominant to the chord to which it is a dominant always sounds good to the ear. It feels like the chord leads to the next one. And if the composition or movement is written in a specific key, then when the harmony reaches a dominant chord, you feel a sense of unease and instability. Moreover, if the 7th key is added to the chord, the effect is increased.

I've heard that the reason for this has to do with half steps. For instance, if we consider the key to be C-major, then in order to form a C-major chord from a G-major chord, you only need to change the B to a C (minor second difference) and the D to an E (major second up). However, this also applies to the subdominant F-major, but the effect is completely different. And of course, you can go the other way - from the dominant to the tonic - and the steps are the same but reversed. So, it seems to me that just saying that the steps cause this effect isn't the full truth.

Basically, is there any known explanation as to why the dominant sounds like it leads to the tonic? When we listen to music, why does it sound so natural when chords follow in sequence through different dominants?

Answer 1

You've done a nice job of describing the V-I progression, and you've identified the resolution through half steps and whole steps. All of this is important to understanding why the V-I sounds so good, but it's not the whole story. There is something else that a V-I progression possesses which is not present in a I-V progression or a IV-I progression. In a V-I progression, the V chord contains a chord tone that resolves to the root of the I chord. This is a crucial distinction which allows the V chord to resolve strongly to the I chord.

For example, here's a V⁷-I resolution in C maj, taken from Beethoven's Fifth Symphony:

The V⁷ chord contains a B which resolves to the root of the I chord, C.

By contrast, playing | F maj | C maj | (a IV-I progression) would not be the same. The notes of the F maj chord are F A C, and the notes of the C maj chord are C E G. We can set up our chords so that:

• the F resolves down a half step to the E
• the A resolves down a whole step to the G
• the C remains a C

As this shows, there are no notes from the IV chord (F maj) which resolve up or down a step to the root of the I chord (C maj). Rather, in this progression (with this particular voice leading), the tones of the IV chord only lead in to the 3rd and 5th tones of the I chord. To our ear, this IV-I resolution is weaker as the IV's chord tones provide no movement toward the root of the I chord. That movement toward the root of the I is present, though, in a V-I progression; in fact, our ear anticipates that movement/resolution of the chord tones, making the V-I progression even more natural sounding.

The instability of the V⁷ chord, as you've described, is largely due to the presence of a tritone (diminished fifth) interval in the V⁷ chord. In particular, the V⁷ chord contains both an F (the seventh of the V⁷ chord) and a B (the third of the V⁷ chord), and these two notes are 6 half notes apart. That particular interval has a quality of instability and dissonance that further drives the ear to desire resolution. This is part of why a I-V progression would not sound like a resolution.

When analyzing a progression, a key thing to look for is the particular chord tones involved in the resolution. For example, resolving to the root of the tonic creates stronger movement to the tonic than resolving to the fifth of the tonic.

Answer 2

Yes, it's about the minor second ("half step") movement.

The progression can be generalized in terms of root progression and voice leading: root progression by descending perfect fifth, and voice leading of one voice held and two voices moving by step.

In the diatonic gamut that only happens in two places: Vb I and Ib IV. (b means first inversion.) There is a sort of equivalence in those two progressions in terms of root progression and voice leading. In a purely diatonic context the two can be distinguished by making V a dominant seventh chord, like V7b I. You cannot do the same diatonically moving to IV and the added seventh in V7b provides two minor-second motions resolving to I in TI DO and FA MI.

It's interesting to compare these progressions with some other progressions that also have the voice leading of one voice held and two moving by step:

• ivc I the borrowed minor iv
• IIIc I a chromatic mediant relationship
• Fr+6 V an imperfect cadence progression (Fr means the French sixth)

While those chords are all chromatic it's important to note the chord roots are diatonic. So while they are chromatic, they are also quite "at home" in a key.

Technically Fr+6 V is root progression by descending P5 and it has two minor-second resolutions, with one of those moving to the chord root of V. That is quite strong.

ivc I is root progression by descending P4 a bit "less strong" than descending P5, and the non-movement to the root of I as a held note provides some theoretical explanation of why it's "less strong."

IIIc I is interesting, because while the root progression would be considered a "weaker" roots by descending third it does have a minor-second motion to the root of I. This is a chromatic mediant relationship. And while the root progression may be "weak" the chromatic mediant is unique and very identifiable. They are "strong" in chromatic color and expressive potential.

To some degree I'm simply saying an important, unique distinction for V7 I, in addition to the minor-second movements, is that it's a diatonic progression. But some other chromatic progressions share similar characteristics. It's good to be aware of those progressions. And they also reinforce the notion that minor-second motions do indeed create "strong" progressions.

Finally, I think it needs to be stated that the "strength" of the dominant leading to the tonic, the strength of the leading-note moving up to the tonic, is a matter of convention. It's perceived as strong, because that is how the major/minor system treats it. However, in modal style, in the Phrygian mode, this convention is literally turned upside down. In Phrygian the "leading note" is a minor-second above the tonic. Final cadences might look like vii I or viib I, a minor subtonic chord moving to a tonic with a tierce de Picardie (two voices moving by a minor second, but root progression by a major second). (In the Phrygian mode, the seventh degree --- the root of the chord vii --- is a major second below the tonic.) That progression totally reinforces the theory that minor-second movements make strong progressions, but allows for tonalities other than only major and minor keys.