This is a subject that is often a struggle to master for beginning jazz players so I figured I’d write one approach that I use when learning tunes and also that I teach to students who wish to learn jazz. The method is fairly simple, but still requires a bit of preparation technically and theoretically. My blogs are written for guitarists with tabs as well as notation, but essentially it works for all instruments of course.
The goal is to become able to make melodies over chord changes so that it is clear when the harmony moves from one chord to the next. This is obviously not the only way to do this, but just a simple approach that is easy to do on a few chords and fairly easy to move to simple songs.
As an example I’ve taken a II V I in Bb, I assume you are familiar with what that is. Since we are trying to practice making coherent melodies in 8th notes over these chords I’ve chosen the following arpeggio fingerings:
It is important that in the arpeggios are in the same range and pretty much the same position on the neck, that helps getting more freedom while improvising. I found it to be more important than starting on the root. There are many ways to construct fingerings for arpeggios, and I leave that up to you for other examples. You need to know the fretboard and you need to know what notes are in the chords you play on to do this.
I was taught by Bjarne Roupé, who I studied with in Copenhagen, that constructing lines that point forward to a target note in the next chord is a good way to build logical sounding 8th note lines. I think Hal Galper has written articles and books on the subject.
In the beginning it is handy to aim for notes that are not in the previous chord so that if you play that note on the 1 of the bar you really hear a new harmony introduced. This is a restriction you can leave out quite quickly though.
In voice-leading you learn that the 3rd moves to the 7th, but in this case that would give you the same note on the Cm7 and the F7 and that is less clear than introducing the A on the Cm7. In general you can use other notes. Melodically the 3rd and the 5th are very strong and clear.
Of course the idea is that you sit down and practice making lines like these playing towards the different target notes. Some thoughts on how to practice that can be found here: http://jenslarsen.nl/convert-theory-technique-exercises-solo-lines/
The type of lines you end up with in the beginning will (like my examples) very much be moving through the II V I and then stop which is a very predictable movement, but for learning the harmony it is in part a necessary step. This procedure is not so difficult to move to a simple song like Tune Up, Take The A-train or Blue Bossa. And once you’re familiar with how it works on a cadence like the II V I it is easier to free up the rhythm and amount of notes per bar for more musical lines.
Here’s a final audio example of a solo only using arpeggio notes, but freed up a bit when it comes to target notes and rhythm: