Hello All, I made a video which briefly summarises the basics of Jazz theory - from modes to the chord-scale system to available tensions and a few other things. Check it out if you're interested. Thanks
As woodwind players we are (generally) just playing one note at a time. Yes, you can play by theory and have lots of choices of notes to play, but what communicates best to an audience is when you have constructed a melodic line that gives stories, emotions, or at least a variation on the theme that's in the head. IMHO thinking through theory is like translating. Instead of the sound coming from you directly, it's going through a mental process which disconnects you from the potential of a melodic context.
Make no mistake, you need to be able to hear the structure, and understand how to build a melodic line from that including tension and release and building climaxes. But if you are continually trying to visualize a written chord or intellectualize a flow of notes based on theory, the result will be at best "mechanical".
Understanding music theory is a very good intellectual exercise, and the video quickly goes though these explanations quite clearly. However when playing an improvisation theory may explain what you did, but it shouldn't be dictating what you do. The best improvisations always seem to be from a musician singing through their instrument in a very personal manner that communicates to an audience. The alternative seems to be playing by theory by using finger memory riffs and arpeggios where the player may not hear what they are playing until it's come out of their instrument. Theory playing can assist in organizing those riffs and arpeggios so that the result is a technical "cut and paste" exercise which can be played very quickly and may impress due to the speed of play. However it's ultimately like watching the world's fastest typist. You can be amazed at the speed, but what have they written? Is it the next great novel or just a bunch of meaningless words?
An improvisation that solely consists of playing theoretically may be a missed opportunity to personally communicate as an artist and musician.