In addition to Not Quite (written for a previous gig), Pen and Paperweight are the two songs I wrote for the Mr. Tako set. Both of them are attempts to present one discrete idea in the written music, with the improvisational element stemming from that one idea.
For instance, in Paperweight (score, sound), the idea is about pacing: repetitive, improvised monads are balanced against periods of space in an attempt to establish a compositional balance between the two. For the guitar part, a big part of the piece involves keeping the repetitive ideas on the left side roughly equivalent to the space on the right side, treating both as equal parts of the improvised composition. The drum part is supposed to improvise throughout, responding to this. Finally, there is a written ending to bring a sense of balance to the alternating sections.
This piece combines two approaches to improvisation, each of which stem from the compositional idea of balance and form: in the song itself, the guitar is improvising both what monads to play on the left, and how long each section should be. The drums play a more open role that is both supportive and soloistic.
With Pen (score, sound), the one compositional idea is a relatively quick, flowing chord that is rhythmically interrupted by the dotted eighth notes. Finally, the interruption wins out, collapsing into a chord that sets the tone for a free improvisation. The opening material returns at the end, if it wants to. The improvisation, being open, is only informed by what has come before it.