Jazz is used in its widest sense throughout the guide to include its myriad sub genres and its historic development from traditional (trad) jazz through modern jazz to free jazz and on to contemporary jazz.
There is a small body of jazz harmony theory. It is an eclectic mix of functional harmony, pop harmony, modal harmony, pentatonic harmony and quartal harmony with a few new bits of its own thrown in for good measure.
Improvisation is one area in which jazz harmony is said to differ from other approaches to harmony. Composition in jazz harmony is as much a performance issue as it is a writing issue. Jazz harmony can be written in detail but it can also have a much looser framework. All that is needed is a chord progression, and maybe a short melody as well, and the details can be worked out later during actual performance when the musicians and singers improvise variants on the basic melodic and harmonic framework. This is a boon to jazz writers because it means that a jazz piece can be quickly sketched out in lead sheet format.
This theme of improvisation is evident in jazz harmonisation and melodisation, the processes of adding a new harmony or melody to an old jazz standard. The Great American Songbook is a good source of material for jazz standards.
Improvisation and harmonisation are important features of jazz harmony. They are not, though, exclusive to jazz, they also feature in pop. Many a pop song consists of just a lead sheet, performers of pop music regularly improvise, and many pop songs are reharmonised oldies but goldies.
The guide focusses instead on those aspects of jazz harmony that distinguish it from pop harmony and functional harmony and all the other approaches to harmony. Two features in particular are deemed important:
The twin themes of dissonance and atonality create the structure of this part of the guide.
Dissonance is tackled first. Jazz harmony embraces dissonance to a much greater extent than functional and pop harmony. Dissonance is, in many ways, THE feature of jazz harmony. It gives jazz music its distinctive sound. This is evident in the use of the seventh chord. The seventh chord is a dissonant chord and it is the chord of choice in jazz harmony rather than the consonant triad used in functional harmony and much of pop harmony. Jazz voicing uses complete and incomplete seventh chords to form a jazz progression which is often based on the extensive use of secondary dominant chords. A seventh chord can be extended to make it even bigger and more dissonant until all the notes in a scale have been used up.
At the same time as jazz harmony becomes more dissonant it also becomes more atonal. It starts innocuously enough with chord substitution, the process of replacing one chord by another. Tonality hits the spotlight in modal jazz which develops modal harmony into a system in which a chord can span multiple modes. The chord scale system extends the idea beyond modes and enables a chord to span multiple scales. Finally, an altered chord is a chromatic chord that can simultaneously fit more than one key, at which point, jazz harmony morphs into chromatic harmony.