A starter's guide to improvising
Improvising or soloing is, in short, playing stuff that's not written down.
There are two hurdles to overcome when learning to improvise. The first is the fear of playing a wrong note. As we get older, we become far more conscious of what people around us think and there's an internal pressure to not look foolish or inadequate, or do something wrong. The second (somewhat linked to the first) is not being fluent enough with your music theory, ie not knowing what to play. As your knowledge of theory improves and you start mastering the notes and key signatures, so the confidence grows. And as you get more confident with the notes, the fear of playing a wrong one lessens. The more you play along with backing tracks and the more scales you learn fluently, the easier it becomes to 'play what's not written down'.
In my experience people who come from a classical training (myself included) have a larger barrier to overcome on the route to improvising. After spending many years being conditioned to play from dots, it's a much larger step to become comfortable playing 'what's not written down'. That said though, classical training, I believe, is one of the best starts anyone could have. The major scales, key signatures and music reading have all been learnt to a high level which is a huge bonus on the road to learning jazz chords and improvising.
Listening to anyone accomplished at improvising, you might think you have a lot to learn. However, the best solos are the simplest, choosing notes and licks carefully to match the style, feel and rhythm of the song. In fact, the best solos, first and foremost, are rhythmically interesting. The choice of notes are the next most important thing. A sax player in a previous function band bet our trumpeter that he couldn't do a solo on one note. The sax player lost the bet. A solo on a single note can have feeling, character, drive and sound just as good as a solo with many notes because the one thing that stands out is the rhythm.
There is no panacea for learning to improvise, but here's a few hints and suggestions that might help you on your way.
Concentrate on the rhythm to start with, hearing the beat, feeling the song's groove using the tonic (note one of the scale). Once you've experimented with rhythm and you're feeling more comfortable, start introducing extra notes into your practise. But remember, whatever you do, keep feeling and hearing the ryhthm..
All scales have strong notes. These are notes that 'go with the chord' and sound the best. They are notes 1,3 & 5 in a major scale (also known as the chord, triad or arpeggio), and 1,3,5 & 7 in a dominant 7th where the 7th note of the major scale is flattened (mixolydian cord). (There are more strong or quality notes in other chords, but these two examples should get you going for the moment). When playing to a backing track, play these strong notes. When you're confident doing this, join the strong notes together by playing the first 5 notes of the scale (1, 2, 3, 4, 5). Make sure you play in time against the beat of the backing, and also try and hit a strong note (chord tone) on beats 1 and 3 of each bar.
Now introduce the remaining notes of the scale, using these to join the strong notes/beats together. Start slowly and feel your way with the notes against the beat. As you get more confident you'll start to hear which notes/progressions sound the best. As a rule though, don't sit on the second, fourth or major seventh notes - these are considered 'avoid notes' or poor choices. Any 'avoid' notes should resolve to a strong one where possible straight away. Experiment with playing the notes so you can hear for yourself what works and sounds good.
The blues scale is perhaps the most versatile scale to use for improvising. When used in conjunction with the notes of the major scale, a great deal of colour and interest can be achieved. You'll start to pick out and hear little 'licks' (short phrases) and progressions that sound good. Transpose these into different keys and you'll start building up an 'arsenal' of phrases to roll out when required. As with practicing anything, start slowly. You're trying to develop patterns for your fingers to follow and remember to a point where they become automatic. A steady and reliable slow phrase, lick or progression will soon become faster with time, repetition and familiarity - don't try to play something fast straight away.
The aim of playing any instrument, including the sax, is to develop your finger memory so you can hand over what you're thinking and working out in your head directly to your fingers