Any chord can be substituted for another which has the same tonic, dominant or traveling function. A substitute chord, or series of substitute chords, can provide alternate harmonic paths while maintaining its original function. (Two different V7 chords can provide the same dominant function with different harmonic conclusions, for example.) Or, the substitution can imply two functions simultaneously. (As will be seen below, with the help of an altered pitch, a chord can be heard as having both a traveling and dominant function.) Three types of substitutions which occur frequently are the tritone substitutions, the omitted/added root substitutions, and circle progression additions.
The tritone substitution is a dominant 7th chord whose root is a tritone (3 whole steps) away from the original dominant 7th chord. The chords are interchangeable because the tritone interval pitches are identical in each.
Chord substitution often results from an attempt to provide smooth voice leading. Using the tritone substitution, the roots of the ii-V-I progression move down by half-steps, instead of ascending 4ths. For example, in the key of C the progression becomes Dm7, Db7, CM rather than Dm7, G7, CM.
The omitted/added root substitution exchanges the root of the given chord for a root a third or fifth higher (occasionally lower.) The substituted chord still retains several pitches of the original, implying the same harmony, but can also point toward different directions--both in key and function.
Example B depicts a G7 chord with various omitted-root substitutions. The B dim. 7 chord, with 3 pitches in common with the original, retains the dominant quality, as it contains two tritone intervals. At first glance it seems to share an identical function with a G7 (b9) chord, yet, because G is omitted as the root, the diminished 7th chord offers additional possibilities of resolution. In short, unlike G7 (b9), B dim 7 is as likely to resolve to A Major or Eb Major as C Major.
The G7 and Bb7 chords have two pitches in common and, along with their dominant 7th constructions, generate enough similarity to share a dominant function but also enough diversity to provide pathways in different directions. (The obvious resolution of Bb7 is in the key of Eb and the G7 is the dominant of C.)
Because of common pitches and the presence of a tritone, D-7 (b5) can also be a dominant substitute for G7. At the same time, however, its root, a fifth higher, also has a traveling function. As the ii chord in the key of C, the D-7 (with its altered 5th) allows the progression to extend itself before progressing toward a dominant and eventual tonic.
Circle progressions, as well as being fundamental to the structure of many traditional jazz compositions, are often inserted as turnarounds (discussed above) or used as a series of substitute chords in specific parts of a composition. Example C, below, shows both a basic 12-bar blues progression (in black letters) and several circle progression substitutions (in red letters), which are used to amplify the structure. Not only do the added substitutions provide tension by their harmonic direction, but also by the quicker harmonic rhythm. You can note the effect of this by pushing the "play" button to see how the progression occurs in real time. Can you decide how the specific substitutions might be chosen?
I wrote a blues called, "Wildwoman Blues" for my students some years back which was used as a sight-singing exercise. It seems appropriate to bring it back for your analysis (be able to discuss in class) and, oh yes! as a sight singing exercise (to be sung in class). Many different dominant 7th chords here--some have tonic function, others dominant function. There are example of tritone substitutions, and many instances of circle progressions. Find out what you can. You can hear a synth version in the example below by pushing the "play" button.
The singing exercise should be in three stages: first sing the roots of the chords as they occur in the form, then sing the melody. Finally, improvise over the progression (use only chord tones!) while someone else sings the bass line!