Here we have a map for harmony. It shows the chords of the diatonic system, the flat majors, and the secondary dominants in Roman Numerals.
On the next tab, we take a look at the same harmonic map using the example A Major.
These maps are great songwriting tools. The inside box is the diatonic system, the next box out is the flat majors, and the outer box is the secondary dominants. We explore these terms below.
The Diatonic system is composed of the tonic chords in the center (I, vi, and iii), dominant chords (V, viio and iii), and the subdominant chords (IV and ii).
The tonic is actually the I chord proper, yet the vi chord functions as a tonic chord. Above the tonic is the dominant (V), sharing its function space with the viio chord. The iii chord has a split function depending on where it is placed in a harmonic rhythm (a stream of chords).
The iii chord (mediant) is most commonly grouped with the tonic chord, yet the mediant contains the leading tone of the scale and can be grouped as a dominant (plus when it is moving to the vi - the iii is the vi's minor dominant).
The subdominant (IV) shares its function space with the ii chord.
The ii chord is called a supertonic, the vi chord is called the submediant, and the viio chord is the leading tone chord. The vii is called a subtonic when it is lowered (flatted). These names also apply to the single pitch (the root or member of the scale). And to be thorough, the I chord is the tonic, the IV chord is the subdominant, and V chord is the dominant, proper.
Subdominant means dominant below the tonic, not one number below the dominant. The subdominant is the five below the tonic.
The flat Majors are very common in rock music. They are simply the lowered (flatted) version of the corresponding diatonic chord. They don't have to be Major, yet they work very well as Majors. Keep in mind, that the map is a guideline for harmonic possibilities, yet there are always other options. Your ear dictates the landscape. A great example of the use of flat majors is Linkin Park.
The secondary dominants are used as passing chords and points for modulation to new keys. They are the dominants of diatonic chord members. So, the five of two, the five of three, the five of four, the five of five, and the five of six. The five of seven has been left out because it is a special case, where its implications aren't as useful as the others. Use these chords before moving to the diatonic chord member (i.e. in the key of A, use F# before moving to Bm in a stream of changing chords).
To apply what is presented above, let's take a look at an example in A Major [see the next tab on this page]. The idea is to expand our harmonic landscape, while creating interest through tension and contrast. Knowing how things are related/named does not hinder flow, but expands our potentials. This is a palette.
Here we have the map applied to A Major. Understand that the flat majors don't necessarily have flat names. Flat names appear where the chords have naturals for roots. If a chord is a sharp, then flatting it will actually create a natural root. When the flat seven is created it is called the subtonic chord. The subtonic tone to A is G. The leading tone to A is G#.
The five of viio doesn't function as a secondary dominant in the way the others do. The V of viio for the key of A Major would be E flat Major (D sharp), which is already functioning as the flat V Major in A's harmonic space.
In progressive harmony (in our ear), tonics like to move to subdominants, subdominants like to move to dominants, and dominants like to move to tonics.
Regressive harmony is when chords move in the reverse order of progressive harmony. Both are progressive and regressive are completely acceptable. We go where our ear leads us. Harmonic rhythm [changing chords] is often determined by melodic rhythm and contour.
Next, play some progressions. And, write progressions using your best artistic sensibilities. Listen for how chords interact with each other in their harmonic environment. When we experiment for long enough, we will identify known songs and progressions.