There are three basic harmonic functions upon which the jazz player must be able to improvise: the tonic function, the dominant function, and the traveling function. Chord extensions and alterations result from the need to intensify a specific harmonic function. A triad can be extended to its 7th, 9th, 11th, and 13th (which together contain all the notes of the scale from which the chord pitches are chosen.) Alterations of chord pitches thus imply new, altered scales by which the tension of the music is increased.
A chord which functions as a tonic represents closure and is typically built on the 1st degree of the scale. The level of tension/relaxation in the surrounding material is very important, however. If one is harmonizing a folk song in the key of C major, for example, the tonic chord might be a simple C triad . On the other hand, if the composition requires a higher tension level, the C tonic function might require further extensions of the chord, even with some altered tones. Example A shows the C Major chord which can function as a tonic in any of the versions listed, depending on the surrounding harmonic context, from triad to 13th chord.
Example B shows the increased tension as the original tonic triad at 1. is both altered and extended from 2. to 5. The alterations shown below alter the extended chord by implying an additional major or augmented triad within the original tonic. For example, no.2. changes G to G#, thus building an E Major triad from the original C M7 chord. Note also that the original C Major triad becomes an augmented triad. In No. 3., by raising the 9th, an augmented triad results beginning on the 5th of the chord, G. Two different major triads are heard in no. 4.The original C triad is heard along with a B Major triad as the 9th and 11th are both raised. Finally, another new Major triad, D Major, is heard above the CM7th chord in no. 5.
These examples are not the only possibilities for tonic alterations and do not account for pitch omission and pitch doubling. Nonetheless, it appears that, by stacking an additional major or augmented triad quality onto the original tonic, the tension level increases but the C major tonic function can still be heard.
Example D below depicts some of the alterations one can add to provide more tension to the dominant chord quality. No. 2. shows a C7 with a b5. No.3. is a C7 with a #5 and #9. No. 4. is a C9 with an added #11 and No. 5. is a C7 with a b13, and b9. Note that the altered pitches can either raised or lowered (i.e. the 5th in nos. 2 and 3, and the 9th in 3 and 5) depending on the surrounding material. Also, as in the description of the tonic function above, each of the chords below might contain doublings of some of the pitches or others of them might be omitted.
As stated above, a tonic chord represents closure and a dominant chord represents tension. "Traveling" chords are the means by which harmonies move between relaxation and tension and are often represented by the iii, vi, and especially the ii chords in a major scale. The example below depicts the unaltered extensions of the C minor triad, the ii chord in the key of Bb major.
Typically the 5th of a ii chord might be lowered to bring a diminished quality to the minor 7th chord. However, traveling chords are altered in accordance with the surrounding tension level. Some of the possibilities are given below.
Traveling, dominant, and tonic chords are placed in appropriate parts of the phrase to regulate the direction of the music and the relationships between tension and relaxation. Familiar chord progressions such as I, vi, ii, V, I show the progression from the tonic, traveling through the vi and ii toward the dominant, ultimately ending again with the tonic. Play this progression, using many combinations of the chord alterations discussed above, after which it will be highly beneficial to play the progression in all keys!