Okay, it occurred to me that I would probably have regular recourse to a couple more music-theoretical ideas, so I should just go ahead and get them out of the way now.
Relative and parallel minor
I mentioned in my last post that the natural-minor scale is a permutation of the major scale -- the major scale begun on the sixth scale degree and wrapped around on itself. That means that for any given major key -- C, E, B-flat -- there is a minor key that uses all the same notes. On the piano, the C-major scale uses all white keys; so does the natural A-minor scale. The E-major scale uses black keys at F-sharp, G-sharp, C-sharp, and D-sharp; so does the natural C#-minor scale. Etc.
If you read the section on whole and half-steps carefully, you will have noticed that the minor scale that shares all its notes with a given major scale begins a minor third down from the first note of the major scale. A is a minor third down from C; C# is a minor third down from E. The minor scale that shares all its notes with a given major scale is called the relative minor of the major scale; the major scale, naturally, is the relative major of the minor.
But of course, you can build a minor scale on any note, just as you can build a major scale on any note. You just have to make sure to follow the pattern of whole and half-steps we established last time:
So you can build a minor scale that starts on C or E, too. But those scales will use different notes than the major scales starting on the same notes and, perforce, different notes than the major scales' relative minors, too. On the piano, the minor scale built on C uses black keys at E-flat, A-flat, and B-flat; the minor scale built on E uses only one black key -- at F#. What are the relative majors of C-minor and E-minor? Count up a minor third from the first note of each scale (C and E); answer below.
The minor scale that begins on the same note as a given major scale is called the parallel minor. The major scale that begins on the same note as a minor scale is, of course, the parallel major.
I want to say at least a little about harmony (chords). As I mentioned in my first post on music theory, a chord is a set of notes played simultaneously. Any set of notes can constitute a chord, but in classical music of the classical period (not the pleonasm it seems, pending some better term than “classical music”), and in the vast majority of pop music, the chords that predominate are what used to be called “common chords” -- the major and minor triads. Technically, any chord with three notes is a triad, but musicians generally use the word to denote three-note chords constructed from stacked thirds.
By “stacked thirds” I mean that the triad’s second note is a third above its first note, and its third note is a third above its second note. If you were paying attention to my discussion of intervals, however, you’ll recall that a third can be either major or minor, i.e., it spans either four or three half-steps. Two types of thirds give you four types of stacked-third triads, named as follows:
major third on major third: augmented triad
minor third on major third: major triad
major third on minor third: minor triad
minor third on minor third: diminished triad
Of these four types of triad, however, the major and the minor are by far the most common. If you’ve ever sat down to learn a couple chords on the guitar, you were probably learning to play major triads, with possibly a few minor triads thrown in. If you can play “Heart and Soul” on the piano, you can play a few major triads. Etc.
Qualitatively, major triads partake of the brightness of the major scale; minor triads partake of the melancholy or ominousness of the minor scale. If you know any pop songs that have a kind of spooky or gloomy feel to them, they probably feature a lot of minor triads.
There are seven notes in the major scale, so there are seven natural triads in any major key. (For instance, the natural triad built on the first scale degree would consist of the notes 1, 3, and 5; the triad built on the third scale degree would consist of the notes 3, 5, and 7.) Of the seven natural triads in a major key, three are major triads, three are minor triads, and one is a diminished triad.
The three natural major triads are the ones built on the 1st, 4th, and 5th scale degrees. The triad built on the first scale degree is known as the tonic, and it’s kind of the “home base” for the key: most pop songs that are written in a single key probably start on the tonic, and almost all of them end on the tonic. The chords built on the 4th and 5th scale degrees are called the subdominant and dominant, respectively. As their names imply, they are very closely related to the tonic. If you’ve ever heard the term “three-chord pop song”, the three chords in question are the tonic, dominant, and subdominant.
The natural triads built on the 2nd, 3rd, and 6th scale degrees are minor triads. That means that a major triad built on one of those scale degrees perforce takes you into a different key (or at least into a different mode).
Finally, I’ll just mention that the next most common chords after the major and minor triads also consist of stacked thirds; it’s just that the stacks keep getting higher. A seventh chord, for instance, consists of a triad with another third stacked on top of it. (The second note of the chord is a third above the first note; the third note is a fifth above the first note; and the fourth note is a seventh above the first note, hence the chord’s name.) A ninth chord consists of a seventh with another third stacked on top of it. Etc. Sevenths are very common: in any given key, the seventh chord built on the fifth scale degree -- the dominant seventh -- is almost as common as the natural major chords. Again, if you’ve ever fooled around with the basic chord shapes on a guitar, you probably learned a couple dominant sevenths.
Answer key: the relative major of C minor is E-flat major; the relative major of E minor is G major.