what is a key? part iii

Following on the heels of the last post we're going to talk a little bit about dominant 7th chords in this post. And as a way of getting into that let's look at the following common chord progression:

Cmaj | Fmaj | Cmaj | Cmaj |D7 | Gmaj |

To determine the key here we'll go through the same process as we did in the last post. First let's determine all of the notes of all of the chords:

Cmaj = C E G
Fmaj = F A C
D7 = D F# A C
Gmaj = G B D

Now let's put them all side by side:

C E G, F A C, D F# A C, G B D

and get rid of the repititions of notes:

C E G F A D F# B

And now we'll put them in an ascending order:

C D E F F# G A B

Well now we've got a strange situation: there are eight different notes here. All major scales (and minor scales, double harmonic, neapolitan, etc) contain only 7 different notes. If we are to assign this progression to a major key we'll have to get rid of one of these notes. How should we go about this? Let's look at the F, F#, G area. There are no major scales which contain this sequence of half steps, so we might be able to get rid of one of these notes.

If we get rid of the F# we're left with
C D E F G A B
the ol' C major scale. If, on the other hand, we get rid of the F natural, we are left with:
C D E F# G A B.
This has a name, C Lydian. But that is a mode of (or the same group of notes as) G major:
G A B C D E F#

So now if we're only examining the notes of the chord progression we're at somewhat of a stand off: is the key of the progression C major or G major? Or maybe it's both?

Actually it is both, but just not at the same time.

Let's look at the Fmaj and D7 chords. When we come to Fmaj it's safe to say that the note F# is not really being articulated; likewise when we reach D7 the F natural is not part of the chord (look at the notes of the chords above if this doesn't make sense). In other words when we have F in our chord progression we are in the key of C major, and when we have D7 we are in the key of G major.

Notice something else here, too. The D7, as related to G, is V chord (that is the note D is the fifth note up in the key of G major). This is the only place that this happens in the major scale: there is only one dominant 7th chord, and it is built on the 5th scale degree. This is very good information to know, because when we encounter dom7 chords we can check to see if we are in a key where that dom7 chord is the V chord.

When this is the case we say that the dominant seventh chord is functional, i.e. that it has a certain role that it is fulfilling, namely that of pronouncing the key.

Not all dominant seventh chords are funtional! The blues progression is the most famous example of this, but actually this chord (and any chord) might just be used for the sonic atmosphere which it produces. These are cases where the dom7 chord is non-functional.

And even when we have a live, functioning dom7 chord, it may not go to it's I chord. The most famous example is what is known as a deceptive cadence:

Cmaj | Fmaj | G7 | Amin |

Here G7 goes to Amin, the VI of C major, but it's still a part of functional harmony.

And here's a way to hear how dominant 7th chords really push acoustically to a new key.

Let's take a Cmaj triad and go to all the other diatonic chords in that key:

Cmaj | Dmin |
Cmaj | Emin |
Cmaj | Fmaj |
Cmaj | Gmaj |
Cmaj | Amin |
Cmaj | Bdim |

Now in between these chords we'll add a dominant of the second chord -- i.e. the second chord is considered the I and we'll add a V of that right before:

Cmaj | A7 | Dmin |
Cmaj | B7 | Emin |
Cmaj | C7 | Fmaj |
Cmaj | D7 | Gmaj |
Cmaj | E7 | Amin |
Cmaj | F#7 | Bdim |

This isn't really an academic exercise, either. All of these progressions are far from rare, and you're probably familiar with hearing them (with the exception of the last one).

So the main point of this post is that not all progressions are in a single key; and sometimes when this happens dom7 chords can be a helpful signpost in helping us to determine the key(s).

ENDNOTE: There are in fact eight note (octatonic) scales running around out there in the world, the most famous of which are bebop scales and the diminished scale. The reason they weren't considered above is because bebop and diminished scales aren't actual generators of harmonic progressions, they are scales which are used to play over existing harmonies (bebop dominant is used over dominant chords, for example, whereas the diminished scale can be used over diminished chords and dom7b9 chords).