When writing complex harmonies for only four voices, many times there will be more notes in the chord than horns to play them with. If a horn section is playing with a rhythm section, you can rely on the bass and keyboard or guitar to provide the harmonic framework to help the ear of the listener hear the chord as intended.
However, when writing for only a sax quartet, or other small wind ensemble, with no accompanying rhythm section, all of the harmonic framework will have to be provided by only these instruments. Voice leading takes on a much greater role for the listener. When writing more complex harmonies, 9th chords, 11th chords, etc, there are more than just four notes. Something has to be left out, or provided in another way.
The human brain is a marvelous device. We can visualize though our "mind's eye" things we do not actually see. We can easily recognize a person from a simple line drawing, a meager sketch. Japanese art is a good example… it shows what is actually needed to be shown, and nothing else… the mind sees the rest.
Similarly, the importance of voice leading cannot be stressed enough. With good voice leading the "mind's ear" is seduced into hearing what is not really there. I will demonstrate with a simple two-part excerpt taken from my sax quartet arrangement of "Amazing Grace":
In measure 6, there is a D in the soprano, with the alto holding an Eb. If you were to simply play these two notes in isolation, the notes would seem to clash… but in the context of what came before, the voice leading implies to the "mind's ear" that the instruments are coming to rest on the dominant 7th chord, F7. The brain hears what it is expecting to hear, and fills in the missing pieces.
We can use these "implied harmonies" to fill out music and take advantage of this in our writing in three, four, or more parts. I call this "the Mulligan Method" of arranging. Listen to Gerry Mulligan with his quartet from the 50's… bari sax, trumpet, string bass, drums… and nothing else! Yet you can clearly hear the complex harmonies implied by the motion of the bass, and the simple harmonization of the trumpet and bari sax. The "mind's ear" fills in the blanks and the listener hears the vast palette of jazz chords.
For a major or minor based chord, where the fifth is a perfect fifth, and especially when the root of the chord is in the bass, or one of the other lower voices, the fifth can be left out. The fifth will still be "heard" as a strong overtone of the root note. So a 9th chord is easily played effectively by providing the root, the third (which identifies it major or minor to the listener), the seventh, and the ninth.
Other chord members may be "implied" by a moving line in one of the inner voices. A note played in the first part of the measure is sustained in the mind of the listener throughout the measure. Thus, a moving bass line, or a moving line in an inner voice, can "imply" a more complicated harmony.
In the following Example 3, we will see the three upper voices in close harmony, with a moving bass line in the bari sax. The chord root on count one of the measure is heard throughout the measure by the mind. It was not necessary to have another sax or two to fill in all the chord notes in the upper soli section-the mind fills in for us. Yet the AAT soli line sounds like a big band sax section! The walking bass line in measure three outlines the augmented dominant chord.
Example 4 is the same as Example 3, but the parts are transposed for each instrument. I encourage you to play this with your sax quartet. First, play it without the bari sax. Then add the bari sax and hear how it adds much more than just one voice… it provides a mental framework for the upper three voices.