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There are four popular ways to learn to improvise over a song.

  1. Learn "vocabulary" from the masters. This approach is particularly popular with jazz musicians. Find solos by the greats on your instrument and learn them note-by-note, ideally by ear. The idea is that by doing this, you gradually internalise the "vocabulary" of licks and patterns which sound good in a solo. Realistically, you also need to couple this with quite a lot of music theory study to know which bits of vocab will work in a given situation, be able to adapt your built-up repository of improv ideas in new musical situations, and create solos which are your own and not just you performing other people's solos.
  2. Learn the theory. Although many musicians shy away from it, music theory is a powerful way to find your musical creativity. Like it or not, music is built on theory, and understanding that theory allows you to know with confidence which notes are going to sound good in a certain musical context. When it comes time to play a solo, knowing the theory behind the song's chords and which scales go well with those chords can allow you to feel quite free in choosing notes for your improvisation that will sound good.
  3. Pure instinct and experimentation. This is perhaps the most romanticised approach: the musician who just instinctively knows what notes to play and can effortlessly produce amazing-sounding solos. The idea is that you just sit in your room and practice (a.k.a. woodshedding) for hours and days and weeks and months until eventually you emerge, with an incredible ability to play audience-wowing solos every time. That end result sounds great - but the process is a total black box. You're essentially just experimenting at random and hoping that somewhere inside, your brain is making sense of it all. It is possible to improve with this approach, but it's slow, frustrating, and ultimately risky: if you have no idea how you are improvising, there's never any certainty that your next note will sound good. In fact it's a risky approach in two ways: you might never "make it" to that ability after months or years of practice, and even if you think you have, every solo is still going to be a gamble.
  4. Train your ears. This last approach is, in my opinion, the best. It's the approach that actually underlies #1 (vocab) and #3 (instinct), and it goes great with #2 (theory). Musicians learning to improvise are actually training their ears passively without being conscious that this is what they are doing. By instead actively and consciously training your ears you can dramatically accelerate the process of learning to improvise, and reach the goal of "playing whatever you imagine" much sooner. It also avoids the risk of the "instinct" approach because although you are utterly free in your improvisation, you actually understand what you're doing rather than choosing notes seemingly at random. You can still make use of theory rules and be inspired by the vocabulary of the masters, but you are truly improvising something new and entirely your own each time you play a solo.
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