For the first writing assignment I want you to do a simple description of the style of a particular improviser on any instrument. The idea is to translate your listening into words. don't write at length if you don't have a lot to say. Try to say as much as possible in the fewest possible words. Be creative in writing style, but note that creativity doesn't mean carelessness. Find a recording or two to listen to: enough to get a good impression. Sax players and trumpets work well for this exercise, but you can do singers, pianists, bass players, etc... You can be as technical or non-technical as you wish, and expand or contract any part of the discussion.
There is not any particular format to follow, but here is what someone might write about alto-sax player Benny Carter (these would be notes for a finished paper, not the paper itself, which would have fewer sentences fragments and lists.):
Timbre: Warm, but not too sweet. A rough edge. Breathy in the lower register, bright at the higher range. Timbre, intonation, articulation, are not constant but expressive, variable.
Vibrato is noticeable on longer notes, and is highly controlled. One of his trademarks is to crescendo through a long notes while increasing the vibrato. His normal style at fast tempo has virtually no vibrato at all.
Phrasing and rhythm: Phrases tend to be long, with logical connections between phrases. At slower tempi there is a rubato feel, even when he is playing over strict time. There is no nervous edginess; the rhythmic conception is pre-bop. At medium tempo plays on the beat, rather than lagging behind or pushing it. At slower tempi he plays more behind, but not as much as the later Lester Young. Articulation is fluid, legato, with sensitive dynamics, especially at slower tempo. Attack is sharper at fast tempo. (Always sharper than Johnny Hodges.)
Improvisational style: There is a lot of direct statement of the melody, with variation in rhythmic phrasing but not a lot of excess ornament. There is more melodic paraphrase than simple "blowing over the chord changes." (You can always tell what song he is playing!) Ideas are inventive, memorable, melodic, exploitating the full range of the alto sax. A strong sense of logic in the development of solos. Limited use of too obvious formulas. However, if he comes upon a phrase he likes he will repeat it a few times before moving on. Very "tasty" aesthetic, similar to Teddy Wilson (who plays on some of these tracks.) In the same general feel as Lester Young.
Emotional range: he excels both at melancholy and exuberance. (He has different approaches to slow and fast tempi.) He is not afraid to be lushly romantic, but doesn't lapse into bad taste, because there is a wry tone of resignation in his melancholy.
Overall qualities: Intelligence, warmth, flexibility, amiability, confident ease, equanimity. Emotional responsiveness. Good taste ("tastiness"). A pleasant up and down "lilt" to his playing, resulting from overall rhythmic and melodic approach. Along with Hodges, Young, Hawkins, the best representatives of the classic "swing" style on the saxophone.