Improvisation by ear 101
There are two intertwined aspects to becoming a proficient improviser with the ability to play whatever you can hear in your head. The first thing is to exercise your innate ability to hear variations or create melodies. This requires practice and lots of listening to develop a mental library of references/influences. The second aspect is making the sax your voice and that’s a lot tougher. It’s a project that takes years...but is well worth the effort.
This is a good time to mention the alternative. Many learn to improvise mechanically. This is (as a generalization) interpretation of chord changes by memorizing patterns of riffs and arpeggios that can be cut and pasted to fit. It generally features fast technique but lacks creativity, melodic ideas and is mostly suited to 1950s style jazz. Some players after years of playing by formulae can develop the ability to play what they hear through this technique as well, but not many/all. Be aware of this alternative if you find these exercises don’t fit your abilities.
Choose four notes on your sax and play these in any random order until you are positive that you can anticipate the sound of each note before playing it (this can take a while). With these notes in your head try to create a melody with them (in your head and not on the horn). When you have a melody set in your head see if you can play it on the horn. The object is to link the sound in your head with the notes you were playing. Try to be conscious of NOT thinking of your fingering or trying to visualize dots on a page. You are on a path towards rewiring your brain and developing a direct link between sound and your hands. This exercise sounds simple...it’s not and can occupy you for years by using a different set of notes and hearing different melodies. Make it a regular part of your practice.
Turn on the radio and put it to a random station. It can be any kind of music but especially tunes you DON’T know. Student/University radio stations can be good for this exercise. Using your voice or whistling or just using your inner voice try to hear what the music is doing, where it’s going, and sing along. This means that you are in the right pitch, hear the chord structure, and anticipate changes of chords. Depending on how different and unusual the music is (compared to what you are used to) this can be easy or difficult. By forcing yourself to join in you are accomplishing several things. You’re not just listening, but HEARING and understanding the music to a point of being able to anticipate where it’s going. You’re matching in your head the pitch and chord changes. Don’t be afraid to sing wrong notes, but also see if you can correct them to right notes. This is another exercise that can be done for years with various styles/types of music and will increase your mental library by actively engaging with the music.
There are lots of exercises that can be posted. These are basic, yet can keep you busy for years. More exercises can be posted on request.
I’d be happy to hear questions or have feedback on this post or by PM.