Thinking about Structure

What I really liked in this chapter was the discussion of improvisation versus composition. Just because and improvisation is not written down does not mean it was not thought up, or is less of a piece of music. Going back on it, it could easily be written down later on and used by other people. Improvisation truly is composition. So this led me to think of a truly great improvisation, Jimi Hendrix's start spangled banner. Taking a classic song and adding his own spin to it, and now it is extraordinarily well-known. How could this not be considered a composition?