Jazz theory is the underlying technical ideas behind the playing of music in the jazz style (in reality, it's more along the lines of the bebop style). The fortunate (and unfortunate) part is that pure technical players can't properly perform in the jazz style, as it's not all theory. Jazz is also about self expression and understanding that the theory isn't always right. But those who know nothing else but that, and fail to understand the theory also can't properly perform in the jazz style. It's a discipline that escapes the grasp of many (myself included... it's a long road).

Jazz tunes move through chord progressions just like any other song, be it a classical tune, rock or even a polka. What makes jazz different is that the artists understand the chord structure of the tune in a very deep and unique way. They know that the structure can be altered at the whim of the individual and not have it compromise the integrity of the tune, or screw up the other players. In fact, the choices that the rhythm section makes can deeply complement the melodic line (either improvised or scripted). A simple example is the following II-V-I progression that is extremely common in all forms of music:

       Dm7     G7     CMaj7

That's very common, and pretty dull most of the time. True jazz players will read that and will alter it, usually without even thinking, into a form that is more interesting to the player and more enticing to the ear. The following change is a simple one:
       Dm7b9     Db7#9     CMaj7

Where the color of the first chord (the II chord) is altered to give it a higher level of dissonance. That dissonance is part of the raw material that one can use to construct a tune, in both the harmonic and melodic sense. With that said, the dissonance is extremely light in that chord and is really considered a consonant chord by today's standards. The next chord (the V chord) is extremely important and contains a lot of dissonance to the target key but is strangely related to it as it is the flatted fifth substitution of the V chord. Since the V chord is the closest moving interval to the I chord, its parallel chord (from the idea of a "parallel universe" of chords stated by Bob Mover) is also just as close to the I chord as the V chord is. However, since it's a semitone from the tonic, it is in the half step key which is highly related to the I chord and provides an exceptional amount of movement to the resolution key.

That's about the smallest taste I've ever seen about jazz theory. With any luck someone will add to this node and flesh it out. It's probably far too complex to happen any time soon.

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