Watch the Extended Performance online guitar lesson by John Stowell from Modern Chord Melody
For the extended performance, after the statement of the melody, I'm playing a free improvisation. To me, the best free players (John Coltrane and Dave Liebman, among others), are also well versed in improvising over changes. An interesting free improvisation involves superimposing harmony and creating an ad hoc structure, in some cases using a progression from an existing tune or a motif derived from a written melody as a basis for some of the improvisation. In my case here, I'm doing a bit of both, using abbreviated chord sequences to develop ideas for my solo, and using chord shapes from the melody to create lines and modified arpeggios.
Most of the best free players that I have heard are horn players or pianists, but I have listened to guitarists Jim Hall, John Scofield, Bill Frisell and Pat Metheny (the latter three all influenced by the former) all play convincingly in a free setting. Free improvisation can be atonal and chaotic, and a little of that kind of playing can be cathartic. But for me the best free playing is melodic, thematic in nature, and often filled with space and beauty.