My jazz journey has been a long one. I struggled for years trying to play strictly by ear. Jazz was like religion; everyone had a different take and approach. Slaves to major modes, melodic minor modes, the George Russell Lydian-Chromatic religion (modes off the Lydian scale), etc. One thing is clear. Fundamental knowledge of theory and harmony is the starting place. Numbers. Lots of numbers. Intervals. Harmonic distances. The other key starter is transcription.
Two things I have been doing that can help start the journey. Importantly, these different approaches can be used as long tones for saxophone when taken very slowly. First, work basic chords in all keys. Major 7, dominant 7, minor 7, half-diminished and whole diminished. Then try different inversions, first starting on the third, etc. It helps to do it with a piano, using the sustain pedal. Second, start with the modes of the major scale. The key is finding a device or mnemonic that lets you figure out each mode as you go. Do all the modes for a given key. For saxophone, Db and Gb are the toughest, so this is the best place to start. In any event, try one a day, or one a week; it is up to you. C Ionian, C Dorian, C Phrygian, etc. My trick is to think in steps. C major is clearly C. C Dorian is one full step down. In other words, you start on C but use Bb as the key signature. Phrygian is easy, moving down a second full step from C to Ab, So, you start on C but use Ab for the key signature: C-Db-Eb-F-G-Ab-Bb-C. Lydian is tricky because it is not another full step down. Instead, it is a half step. So, from C, it is 2 1/2 steps down from C. So, start on C with a key signature for G major: C-D-E-F#-G-A-B-C. Mixolydian is simple; it is the dominant scale, which is 3 1/2 steps from C. So, start on C and use the key signature for F: C-D-E-F-G-A-Bb-C. Aeolian is 4 and 1/2 steps down from C. So, start with C and use the Eb key signature. Locrian has another easy trick. Start on C and then use the key signature for Db, which is a half step UP from C.
Second, four-note patterns related to intervals are very helpful. I give two examples, which are both very easy to master on the saxophone. They build great muscle and ear memory for saxophone improvising. For example, Bb, B, D, F. Analyze the intervals between notes to identify a numerical pattern from which to transpose: half (Bb to B), 1 and 1/2 (B to D), and 1 and 1/2 (D to F). The four-note patterns provide an endless set of uses. Like with pentatonics, you can start anywhere within the four notes. D-F-Bb-B or D-Bb-F-B, etc. You can also practice large leaps, using mid-Bb, down to low B, up to mid-D, then to high F above the staff. Another approach is a pattern that moves up, then down. For example, E up to F; F down to D; and D down to Bb. This second pattern moves up 1/2 step (from E to F), then down 1 and 1/2 (from F to D), then down again 1 and 1/2 (from D to Bb). These patterns can be joined with related patterns one full step up or down—for example, E-F-D-Bb; F#-G-E-C; G#-A.
Finally, challenge yourself to identify the wide variety of chords each of these patterns, when viewed chromatically, can apply to. This will help you use them. Try using iRealPro to set a simple dominant chord, like C, and then playing several versions of the pattern to determine which sounds good to your ear. Then, consider why it works or does not.