Unlike classical compositions, most jazz compositions are written in a kind of shorthand - the melody is written out, but the harmony is represented by chord symbols, and the rhythmic feel is called out in a word or two at the top of the page. If it's a swing feel, the melody may be written in 4/4 or 3/4, but there is an implied triplet feel which if written out, would look more like a 12/8 than a 4/4 time.
The players are left to interpret the harmony as they choose - voice leading, chord extensions and sometimes alterations are part of the improvisation. In order to make this work, the pieces are generally short structures (32 bars used to be typical for show tunes, for example; blues is usually 12 bars). These structures repeat so the piece becomes variations on a set harmony as well as variations on the melodic theme.
For a student learning to improvise, the task of playing melodies on a set chord structure is the main skill to learn, one can play their scales and chords and can play the thematic melodies of the tunes. In order to become fluent at this, you have to learn chord connection and voice leading. Here are two exercises that will help:
1. Take the chord progression and start on the third or seventh step of the first chord. Create a stepwise (whole and half-steps) descending line just using the thirds and sevenths. Notice that when the roots change in fifths (Am7 to D7 to GM7, for example), the thirds turn into sevenths and the sevenths into thirds. For example, in the above progression, you can play the notes:
C (third of Am) to C (seventh of D7) to B (third of GM7).
Or, you can play:
G (seventh of Am7) to F# (third of D7) to E (seventh of GM7).
2. Start at your lowest note that fits in the first chord and ascend, with the next note fitting the second chord, etc. When you get to your highest note, turn around and descend the same way. Vary this by using two notes per chord, or three, or four notes per chord. this teaches stepwise chord connection.
You can also do this exercise with arpeggios - i.e. limiting yourself to chord tones (1,3,5,7).
Try these first with very simple progressions - just two chords, and build up to more complex changes. Then try it with larger intervals.
David Widelock is a jazz guitarist who would love it if you visit his web site at
http://beegumrecords.com/
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