The main concerns for polyphonic instruments, or instruments that can easily play more than one note at time, such as piano, organ, guitar, and the various mallet instruments, are voicing chords, reharmonizing, and playing rhythms.
In jazz, when the music calls for a Cmaj7 chord, this almost never implies a pianist should play “C E G B”. Usually, the pianist will choose some other way of playing the chord, even if it is simply an inversion of the basic root position chord. There have been entire books written on the subject of chord voicings. The discussion here only scratches at the surface of the possibilities. I have loosely categorized the voicings described here as 3/7 voicings, quartal voicings, polychord voicings, close position and drop voicings, and other scale based voicings.
An accompanist may occasionally reharmonize a chord progression to sustain interest, introduce contrast, or create tension. This involves replacing some of the written or expected chords with other unexpected chords. Substitutions such as the tritone substitution are one type of reharmonization.
Some musicians spend a lot of time trying different reharmonizations when working on a tune. However, unless they tell the soloist what they doing beforehand, many of the reharmonizations they may come up with are not suitable for use in accompanying, since the soloist will be playing from a different set of changes. There are some simple reharmonizations that can be used without disturbing the soloist too much. The tritone substitutionis one example; at any time a dominant seventh chord is called for, the accompanist may substitute the dominant seventh chord a tritone away. This creates exactly the same type of tension that is created when the soloist performs the substitution. Another simple reharmonization is to change the chord quality. That is, play a D7alt in place of a Dm, and so forth.
Another common reharmonization is to replace a dominant chord with a ii-V progression. This was already demonstrated when discussing the blues progression; one of the progressions replaced the F7 chord in bar 4 with a Cm7 – F7. This is especially common at the end of a phrase, leading to the tonic at the start of the next phrase. Most of the scale choices the soloist may have been using over the F7 chord will also work over the Cm7 chord, so this reharmonization doesn’t usually create too much tension. This technique can be combined with the tritone substitution to create a more complex reharmonization. Rather than replace the V with a ii-V, first replace the V with its tritone substitution, and then replace that with a ii-V. For example, in bar 4 of the F blues, first replace the F7 with B7, and then replace that with F#m7 – B7.
Another type of reharmonization involves the use of alternation. Rather than play several measures of a given chord, the accompanist may alternate between it and the chord a half step above or below, or a dominant chord a fifth below. For instance, on a G7 chord, you might alternate between G7 and Ab7, or between G7 and F#7, or between G7 and D7. This is especially common in rock based styles, where the alternation is performed in rhythm. If the alternation is performed regularly, such as throughout an entire chorus, or even the whole tune, the soloist should be able to pick up on it and control the amount of tension produced by playing along with the reharmonization or by playing against it. That is, the soloist can lessen the tension by changing scales as you change chords, or increase tension by keeping to the original scale.
Once you have decided what notes you want to play, you must decide when to play them. You do not want to simply play whole notes or half notes; your accompanying generally should be rhythmically interesting, although not distracting to the soloist or listener.
There are few guidelines that can be given for playing comping rhythms. Because there is very little theory to fall back on, the first piece of advice I can give is to listen to other accompanists. Too often we tend to ignore everyone but the soloist anyhow. Be sure to choose albums that have solo instrumentalists other than the accompanist on them. Pianists to listen to include Bud Powell, Thelonious Monk, Horace Silver, Bill Evans, Wynton Kelly, Herbie Hancock, and McCoy Tyner. Pianists should also listen to guitarists and mallet players; often the constraints of those instruments can lead to ideas you might not have thought of otherwise.
Guitarists should listen to pianists, but also to guitarists such as Herb Ellis, Joe Pass, and Wes Montgomery. Often, guitarists work in tandem with pianists, and their style when there is a pianist in the group may differ from how they play when they are the only chordal accompanists. For instance, some guitarists play only short chords on every beat if there is a pianist providing most of the rhythmic interest. Others will lay out (stop playing) entirely. For this reason, it is especially important to listen to guitarists in several different types of settings.
You should also listen to recordings that do not have any chordal accompaniment, such as any of several Gerry Mulligan, Chet Baker, or even Ornette Coleman quartet albums. Try to play along with these. This will often be difficult, since the music was recorded with the knowledge that there was no chordal accompaniment, so the soloist and other accompanists generally left little room for a piano or guitar. Practicing accompanying in this type of situation can help you avoid over-playing. Most beginning accompanists, like many beginning soloists, tend to play too much. Just as space can be an effective tool while soloing, it can be even more so when accompanying. Let the soloist work with only the bassist and drummer for a few measures, or longer, every so often. Laying out and leaving the soloist with no chordal accompaniment is sometimes called strolling. McCoy Tyner, Herbie Hancock, and Thelonious Monk often laid out for entire solos.
Sometimes it helps to imagine yourself as a background part in a big band arrangement. When you are comfortable with a particular chord progression, and no longer are having to concentrate fully just on playing the “right” notes, you can concentrate on the rhythmic and even melodic content of your comping. Listen to the horn backings in some big band recordings, such as those of Count Basie, to see how melodic accompaniment can be.
Certain styles of music call for particular rhythmic patterns. For instance, many forms of music before the bebop era used the stride left hand pattern, which consists of alternating a bass note on one and three with a chord voicing on two and four. Many rock based styles also depend on rhythmic patterns, often specific to the individual song. While the Brazilian derived styles such as the bossa nova and samba, as played by most jazz musicians, do not have well-defined comping patterns, other Latin jazz styles, particularly the Afro-Cuban forms sometimes collectively referred to as salsa, use a two measure repeating motif called a montuno. A typical rhythmic pattern is “and-of-one, and-of-two, and-of-three, and-of-four; one, two, and-of-two, and-of-three, and-of-four”. These two measures may be reversed if the underlying drum pattern (see below) is reversed as well. A full description of the role of the piano in Latin jazz and other styles is beyond the scope of this primer. A good discussion can be found in Mark Levine’s The Jazz Piano Book.
The most important aspect of accompanying in most styles is to communicate with the soloist. There are several forms this communication can take. For instance, there is call and response, in which you essentially try to echo back or answer what the soloist has played. This is particularly effective if the soloist seems to be playing short, simple phrases, with pauses between them. If the soloist is working on a repeated rhythmic motif, you can often anticipate the echo and actually play right along with the soloist. Sometimes you can also lead the soloist in directions he might not have tried otherwise. For instance, you might start a repeated rhythmic motif, which might encourage the soloist to echo you. Some soloists like this type of aggressive comping, and others do not. You will have to work out with each soloist how far you may take him.