Describing simple or complex chords with an easy shorthand notation is an important part of modern composition, as the composer initially needs a quick way to annotate the harmonic colors he wishes to use in his music, leaving the mechanics of voice-leading to a later stage of the composition process.
A good shorthand notation is one that accurately describes complex chords in their simplest form. The greater the complexity of the chord, the more difficult it is to describe it in simple and unambiguous terms. So, whereas a simple C major triad can be described as 'C', a G dominant 7 with a #9 and b5 would have to be described as G7(#9,b5). Furthermore, neither of these notations specify the distribution of the notes in the chord, a task which is generally left to the discretion of the performer.
One of the fundamental premises of chord notation is that every chord is constructed from the notes in a clearly defined scale. Since most scales have either 7 or 8 notes, we can assume that the most complex chord can have no more than 8 non-repeating notes. If more notes are used, then doubling will be involved.
With this in mind, it becomes possible to describe chords according to their scale of origin and a minimum number of "defining" notes. The "defining" notes of a chord are 4 notes of the scale, stacked at intervals of a 3rd (major or minor) one above the other, with the root of the chord on the bottom. The remaining 3 scale notes (or 4 scale notes, if the scale has 8 notes) are called chord "extensions", and are used to further color and enrich the chord.
Often the defining notes of a specific chord can be found inside a variety of different scales. For example, the Dm7(b5) chord is defined by the notes D, F, Ab and C. But the scale of origin is ambiguous, since this chord exists in the following 4 scales:
1) the VII degree of the Eb major scale;
2) the II degree of the C harmonic minor scale;
3) the VI degree of the F melodic minor scale;
4) the VII degree of the Eb melodic minor scale;
Therefore, the 3 extension notes will differ according to which scale is considered as the parent to the Dm7(b5) chord. So, to fully describe a chord, we must specify its parent scale, as well as the 4 defining notes.
One way to do this is to use a system called Figured Roman. This comprises a Roman numeral and 3 numbers, which represent the intervals of the 3 notes above the root. Using this method, the Dm7(b5) discussed above could be expressed in the following 4 ways:
1) Key = Eb, VII357. The extensions above Dm7(b5) would be b9, 11, b13
2) Key = Cm, II357. The extensions above Dm7(b5) would be b9, 11, 13
3) Key = Fmm, VI357. The extensions above Dm7(b5) would be 9, 11, b13
4) Key = Ebmm, VII357. The extensions above Dm7(b5) would be b9, b11, b13
where m = harmonic minor and mm = melodic minor.
When composers specify the 3 extensions which they may want to employ in a chord, this also determines the functionality of that chord, since each chord function has a unique set of extensions. For example, if the Dm7(b5) chord is being used as a II chord, this implies that the underlying scale is Cm (harmonic), and therefore the possible extensions are b9, 11, 13, as shown in this example:
On the other hand, if the Dm7(b5) chord is being used as a VII chord, then the underlying scale is Eb major, and the 3 extensions are b9, 11, b13, as shown in this example:
The Power of Extensions
Consider first the following chord progression containing just the "defining" notes of each chord:
It sounds fine, but the harmonies are very basic. Extensions can be added to basic chords to make them sound richer, while maintaining the functionality of the chords. The following sequence is the same as the one above, but with added extensions. The parent scales used to determine the extensions are written below the extension notes. Notice the much richer texture for each chord:
The Power of Substitutions
In the next example, some of the basic chords have been substituted with other basic chords. Since dominant 7ths or m7(b5) chords lend themselves to more dissonant extensions, by using them as substitutions we can obtain richer and more diverse harmonies. Taking the above example, let's substitute the Am chord with A7, and change the Dm7 to a Dm7(b5):
We are now ready to add extensions to the above progression. All we need to do is choose the parent scales. As discussed earlier, basic chords can have two or more parent scales. By choosing particular parent scales, we can create extensions that are very rich and dissonant. As shown below, the dominant 7th chords use extensions built from both the VII degree of the melodic minor scale, and the diminished scale (an 8 note scale). The parent scales are indicated below the extension notes.
Notice that whenever a #11 is used as an extension to a basic chord, the 5th is removed from the basic chord, since the resulting dissonance is not very effective.
To summarize, we have seen that complex chords can be annotated in 2 ways:
1) specify the basic chord (say G7) plus the extensions of that chord (say #9,#11,b13);
2) specify the basic chord (say G7) plus the parent scale of that chord (say Abmm).
Both these annotation methods will give the same final result, so the choice is up to the composer/arranger. However, it is generally easier to remember a single scale rather than a set of 3 specific extensions. Furthermore, the scale provides a simpler way to visualize the kind of color that is being used for each basic chord, which, as we said at the beginning if this essay, is an essential component of composing.
