Chord Relations

Any song or tune constructs its melody on top of a chord progression. The chord progression profoundly affects your perception of how the song 'moves around' even if you are not conciously aware of it. When one chord changes into another, there is effectively a jump, or discontinuity, in the harmony. Depending on the chord sequence, the jumps can be small, or large. The point of this section is to show quantitatively how 'far away' two chords are from each other. For example, it turns out that C major and A minor are very similar whereas C major and Gb major are radically different. If the material at the bottom of this page comes across as overly technical I recommend you leave it for now and return to it after making yourself familiar with the basic scales.

Parallel chords

Consider the relationship between C major and A minor. The root note of the minor chord is three semitones below the root note of the major chord. Such major-minor chord pairs three semitones apart are said to form parallel chords. At first it might not seem that the members of such a pair have much in common but it is a remarkable fact that there is a pool of six 'safe' notes that sound good on both of them. Taking this property to the extreme, we can essentially eliminate either major or minor chords completely by consistently substituting one for the other. For example, if you are soloing on C major and F major you could just as well be soloing on A minor and D minor. So what is your poison? Major or minor? Pat Martino is addicted to minor, and everything he plays in a major key he thinks of as being in the parallel minor key. The conversion is trivial, you just need to get used to it. As usual the clock notation is far superior to the letter notation but for your reference I have listed the parallel chord pairs in a table. The pairs of parallel chords are so important that you should be able to recite them in your sleep. Efficient use of the pentatonic and hexatonic scales -- two out of three of the essential symmetric scales -- requires that you can switch effortlessly between the parallel modes of major and minor.

Major C Db D Eb E F Gb G Ab A Bb B
Minor A Bb B C Db D Eb E F Gb G Ab

Chord distances

We are now going to do a bit of analysis of chords and scales without looking too closely at where the individual notes go when the key changes (until at the end where we will single out an important case in dominant). We will consider pairs of parallel chords to be 'identical' in the sense that the distance between them is zero. The reason such pairs can be grouped together is that the same pool of six safe notes can be used on both chords (for the record that pool of six notes is the hexatonic scale which contains, in major, the major scale without the fourth, and in minor the dorian scale without the sixth). For dominant chords we will use a pool of six safe notes obtained by taking a major scale with a flattened seventh (mixolydian) but without the fourth. For reference we are also going to include the conventional major scale which in C consists of the seven white keys on the piano. The table below contains a lot of information so give yourself some time to digest it.

Root distance 0 5 2 3 4 1 6
Major (7 notes) 0 1 2 3 4 5 5
Hexatonic (6 notes) 0 1 2 3 4 5 6
Dominant (6 notes) 0 2 2 3 4 5 4

The first row gives the interval, in semitones, between the root notes of two chords. The intervals are ordered according to the cycle of fifths without considering intervals greater than six semitones. For example, whether you consider the interval between C and F to be five or seven semitones is a matter of choice, and we always choose the number that is no greater than six. The sequence 0-5-2-3-4-1-6 is easy to remember since the numbers are in order except 1 and 5 have swapped places. Rows 2, 3, and 4 gives the distance (defined as the number of notes NOT in common) between chords displaced by the intervals in row 1. Thus, the distance between C major and F major is 1 (the two scales differ by only one note) as indicated in second row below a root interval of five. For the hexatonic scale we immediately notice that since the numbers in the third row are in order the distance between two chords is the same as the root interval except that 1 and 5 are swapped. So for adjacent root notes the two chords are very far apart with a distance of 5 (only one note in common) whereas for a root interval of 5 the two chords are actually very similar with a distance of 1 (five notes in common). For all other pairs of hexatonic scales the root note interval is the same as the distance between the scales, as we would expect intuitively. For the dominant in row 4 we see that compared to the hexatonic there are two differences: for a root note interval of 5 the distance is 2 rather than 1, and for a root note interval of 6 the distance is 4 rather than 6. This is significant, not least because the two notes in common between two dominant chords six semitones apart are the 3rd and the b7th -- the two notes that determines whether the quality of a chord is major, minor, or dominant. It is equally remarkable that the only two notes NOT in common between two dominant chords five semitones apart are the 3rd and the b7th. Consequently, we can summarise two properties that set the group of dominant sounds apart from the group of major and minor sounds as follows.

We finish this section with a beautifully simple visual demonstration of the distance between the hexatonic scales that fit major and minor chords. The drawing shows the cycle of fifths combined with parallel chords (although there are twelve fields on a circle do not confuse this representation with the clock notation!). You find the distance between two chords by counting the steps you have to walk around the circle. This is a good time to see how the statements made above work in practice. As mentioned, 'the distance between two chords is the same as the root interval except for 1 and 5'. So let us take a chord and move around the circle in jumps of, say, two steps. Start anywhere, and you find that the number of fields covered (distance between chords) corresponds exactly to the change in the root note. For example, going round clockwise in steps of two fields from the top with A minor gives you the sequence G minor, F minor, ... until you get back to A minor. You can do the same thing with three, four, or six steps at a time. Now try to move in steps of one field. You then find that adjacent root notes are five semitones apart. The field just to the right of A minor is D minor, five semitones above, and the field just to the left is E minor, five semitones below. Finally, try to jump in steps of five fields. Clockwise from the top you get A minor, Bb minor, B minor, ... until you get back to A minor in twelve steps.