Early on in my musical development I struggled with jazz improvisation. Heck, what am I saying? I STILL struggle with jazz improvisation (less than before, though). At first, I didn't understand chord changes. Once I figured out what they meant, I didn't have a great jazz vocabulary. Once I started developing that, I couldn't figure out why what I was playing sounded "wrong" against the chord changes. Surely, if Brecker was playing C#'s and Ab's over a G7 chord, it should sound "right"... right?
To get over this part of the struggle I had several people suggest that I practice with a drone... but what does that really mean? Do I just turn on a single pitch and blow? How does this help me recognize a chord or what certain notes sound like against a chord so they don't sound "wrong?" Let me lay out some of the steps I take when I personally practice with a drone and what I have my students work on:
Step 1: Practicing Scales/Patterns With a Single Drone Pitch - This part of the process really is THAT simple. When you're first starting out and trying to wrap your ear around things, turn on a drone and play. Ideally you have that drone playing over a speaker and not headphones but sometimes the practice conditions aren't ideal. Take the scale/pattern you're working on (we'll talk about which ones to work on later) and play it in half notes. The point of playing in half notes isn't just to get comfortable with the technical aspect of the scale but to also focus on what each note of the scale sounds like against the fundamental pitch, or tonic. What is the quality of the interaction between those two notes? Is it consonant or dissonant? Happy? Sad? Angry? Flustered? Melancholy? This kind of practice is especially helpful when working on adding dissonance to your playing (ie: a tritone substitution). You can, of course, speed up your scale/pattern practice after this initial period of analysis.
Below is a screenshot of what my Tonal Energy Tuner app looks like when I set up the drone pitch. I like to sustain the 3rd and 4th octave together to give the drone some depth.
Step 2: Improvising Over a Single Drone Pitch - Now we take the material we just worked on in Step 1 and explore the different ways we can use it over a single pitch. Again, this can take many forms depending on what level of improviser you are. For beginners I generally take a "start from nothing" approach where the only definites are the drone pitch and scale/pattern we are using. As students advance you can lay down a steady beat, incorporate walking a bass line for each other, and other techniques. Still, the main focus here is using the scale/pattern while improvising and exploring how everything relates back to the fundamental pitch.
Step 3: Practicing Scales/Patterns With a Chord Drone - Here is where we add more context. Depending on what scale/mode you are using, or what chord you are trying to improvise over if you're working a pattern, you can add pitches to the fundamental to build a sustained chord. So, if I'm practicing my Bb major scale, I would sustain the root (Bb), 3rd (D), and 5th (F) of the chord. If I wanted to work on major 7th chords I would add an A to that. If I was working on the Mixolydian mode to get better at playing over a dominant chord, I would sustain the root, 3rd, 5th, and lowered 7th. Much like with Step 1 I would play the scale in half notes and focus on how each note interacts with the CHORD as opposed to just the fundamental.
Below is a screenshot of how I set up a sustained chord. Again, I'm mainly using the 3rd and 4th octaves just because those tend to resonate well without making my ears bleed (Bb being in 3rd and everything else in 4th).
Step 4: Improvising Over a Chord Drone - The final step is to actually improvise over a held chord. Again, much like in Step 2, this is going to look different for each person but the primary goal is to really listen to how what you are playing sounds against the chord.
Now this is all great but you're probably wondering what scales or patterns should you practice. You can do this with any scalar, modal, or pattern-based materials. When students are just beginning I generally stick to major scales, Blues scales, and the two modes that all beginning improvisers should be comfortable with, Mixolydian and Dorian. I like to take ONE of these scales/modes through this entire process and then start the process over with the next scale/mode. We normally cover 3-4 scales/modes in a half hour lesson. If you're working out of a pattern book like Coker's "Patterns for Jazz" or Fishman's "Hip Licks" then you might take 2-3 patterns you're working on and take them through this process. The possibilities are truly endless.
I don't claim to be an outstanding improviser by any means but I have spent a lot of time trying to figure out how to help myself get better. This process started with suggestions from my former teachers and colleagues and has, without a doubt, improved my ability to hear what I'm playing and how it fits into the underlying chords. Hopefully it can help you as well.