what is a key? part iv -- caveat i

So up to this point we've been analyzing keys by looking at the group(s) of notes that we've found in pieces of music and giving the group(s) a name, so far basically a major key name. There are two caveats we need to be aware of now, and in this post we're going to look at the first one of them.

CAVEAT NUMBER ONE

Let's look now at the following progression:

Amin | Dmin | Emin| Amin |

Let's go through all the steps we did before to find the key of this progression. We'll look at the notes of the chords:

Amin = A, C, E

Dmin = D, F, A

Emin = E, G, B

Putting them all side by side gives us

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

And if we only leave the first instance of a note (and throw out the repetitions) we are left with

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

Finally while we put these notes in ascending order we might notice that there are no sharps or flats, which means that we have the notes of a C major scale:

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

And this is true. From an improvisational standpoint you could take your C major scale and blow away over these chords and you would be on firm ground. 

BUT if we had to describe the key of this piece to someone it might seem strange to say that it's in the key of C major. Perhaps they ask well, shouldn't there be a C major chord in the key of C?

That seems like a good point, and it's really true. When we want to describe the key of a piece as accurately as possible we should take note of the harmony. For instance a piece in the key of C major should probably somehow articulate "C-ness". In the progression above it seems most likely that the A minor chord is the tonic, or the harmonic base. If A is the harmonic base we could organize all of the notes above as

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

This is commonly referred to as the A natural minor scale, and it is also known as A aeolian, The above progression is best seen as being in A minor because that is the most pronounced chord. 

The A minor-ness of this progression could even be more pronounced. Let's switch Emin to E7:

Amin | Dmin | E7 | Amin |

The only difference from before is that E7 (and you could just go ahead and use plain ol' E maj) has  a G# where E minor had a G natural. 

E7 = E, G#, B, D

The scale then looks like this:

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

This, too, has a name: the A harmonic minor scale.

The point of all of the foregoing is that simply identifying a group of notes is not really enough to determine a key: we really have to take into account the chords and see (actually hear) what the harmonic focal point is. 

And by the way this is why I think a lot of people get tripped up on modes. Simply telling someone that ABCDEFG is A aeolian is not enough information to make something sound like it's centered around A. You could play those group of notes over 

Cmaj | Fmaj | G7 | Cmaj |

and the result will never be that the progression sounds like A aeolian. It will sound in C major because of the chords.