Making Your Own Tools: Harmony


Harmony is a very complex subject that I can only briefly touch on. As with the previous essays, my goal is to convince the starting-out composer to explore harmony rather than read about it in books, and to try to overcome preconceived ideas. Harmony, in its crudest form, is simply playing two or more notes at the same time. Some intervals can be quiescent, some can be sharp, some uneasy, some relaxing. Some of the uneasy-sounding intervals can be quite pleasant when combined with other intervals. But, rather than write a textbook on what harmony "should" or "should not" be, I invite you to sit at a keyboard and play any two notes simultaneously out of context. Play them loudly and softly. After doing this for a while can you honestly say that certain intervals should be avoided? I certainly hope not.

Every combination of sounds can have a role to play in the development of a musical work. However, anarchy (ie., random intervals) doesn't really mean anything, any more than playing random notes does. Your harmony needs a structure, much the same as tonally-centred music needs scales. Certain combinations of intervals seem to point to certain subsequent intervals. You can let them move the way they apparently want to, or you can thwart that movement. For example, a G7 chord seems to want to turn into a C major chord, but, it doesn't have to. The same holds true for the potentially thousands of chords at a composer's disposal. Some seem to force a direction; some have a resolved air about them. Simply put, a harmonic structure contains within it a sense of movement or rest; that is, if it is structured. Key word that.

Chords can be structured in many ways. By the number of distinct pitches (excluding octaves), for example: two-, three-, four-, five-note chords, etc. They can be structured by the intervals contained within them. I limit that to 2nds, 3rds, and 4ths because other intervals are octave displacements or are inversions (7ths, 6ths, and 5ths). And, they can be structured by primary cycles. Cycles are the relationship of chords to each other. We all know about the cycle of fifths—which defines the relative aural distance between harmonic structures. A cycle of fifths goes through all twelve pitches, a perfect fifth apart, until it returns to its origin. The two closest chords to the root are on either side of it on the cycle (F and G to a root of C). But there are also cycles of thirds and cycles of seconds. The two most important chords to a root in a cycle of thirds are based the third and sixth steps of the scale (E and A to a root of C). Similarly, a cycle of seconds places the important chords on the second and seventh step of the scale (D and B to a root of C). Some scales are best utilized with the primary chords based on the root and on an interval or pitch unique to that scale (such as the root, 2nd, and 4th of a Dorian scale). These structures of: number of pitches; kinds of intervals; and primary cycles can be applied to any scale structure.

Scale structure brings up a point in relation to harmonies. Are the notes of the chord contained within the scale, or do they exist outside of it? For example, suppose you are using a Lydian scale (C D E F# G A B) and you have a passage of: F# G B C. You decide to harmonize it with the open sounds of 5ths. Does that make your pairs: F#-C#, G-D, B-F#, C-G or does it make them: F#-C, G-D, B-F#, C-G? The question is: is that first interval outside the scale (perfect 5th), or inside of it (diminished 5th)? What makes the most sense in the passage?

Another consideration: are your harmonies going to be based primarily on one type of interval? For example, the 2nd (secundal harmony)—which would tend to give you clusters of sound. The most common 3rd (tertial harmony)? Or the 4th (quartal harmony)? Any can be sustained for short periods. Below is a short example where the intervals are only 4ths and 5ths.


Finally, a series of harmonies needs a sense of direction; otherwise, it is just a meaningless meander. What general direction is the music travelling towards? Upwards or downwards? Brightening or darkening? Tightening or opening? Thinning or thickening? Tensing or relaxing? Slowing or speeding up? Only the composer can answer these questions, but the listener must hear the answers in the harmony.

Before we leave harmony, you should also be aware that you can play differently structured chords simultaneously. Polychords as usually constructed of a pair of triads set in different registers. They can share the same root and scale; or, they can use different roots or different scales.

Here is a sample of a short piece showing harmonic structure: Click for PDF file



It is in a basic AABA format. "A" is a descending theme, generally going from more complex to less. Along with the "more complex to less" idea, the first appearance of "A" uses quartal harmony. "A1" has a mixed bag of harmonic types, and "A2," the final appearance, is based on tertial harmony— and that simplifies further into the coda by becoming simple thirds, ending on a unison. The "B" theme is a contrast in scale, tonal centre, tone cycle, rhythm, and harmonic type. The primary beats in the "B" section are polychords, while the off-beats are openly spaced harmonic intervals. "B" is also a contrast by maintaining an even direction—neither ascending nor descending, until it finally falls back into the main theme. Note how sections are resolved by their relationship to the tonic on C. There's not a single dominant 7th resolution in the piece, yet C persists as the tone centre for the entire work. And, the primary tonal direction driven by the bass line indicates a cycle of seconds at work. One more thing to point out: at each repetition of the "A" theme, the harmony varied.

I hope that gives you some idea of how you can use harmonies as an integral part of a work. To study harmony in detail, this site cannot be beat: Alan Belkin, Composer General Principles of Harmony.