I have had 4 "real" teachers.
At the beginning of my "playing" life, I was around 12 and the school woodwind teacher was an older gentleman. (I must add, I was starting on the flute) who was an amazing player but was a little intimidating. I could play well by ear but had never learned to sight read. He used to bark at me for making reading mistakes. For him it must have been a little frustrating, but for me it was terrifying. Every now and then he would try my flute to see if there was something wrong with it and leave a little lip-slobber on it. :x
Needless to say, I started bunking lessons and playing tunes by ear. My theory didn't get anywhere, but I certainly enjoyed NOT being in lessons
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He left and a wonderful lady teacher called Jenny replaced him. She was a rock chick teacher (red lipstick, big hair, leather jacket 8) and she really inspired me to play. We'd go through the head of a tune and then jam for the rest of the lesson. I learned loads of standards and spent loads of time memorising them so I could spend more time jamming

Again, my theory didn't develop much but my "playing by ear skills" really took a leap. What made her such a great teacher was that she homed in on what I really loved about jazz and worked with me on it
Fast forward around 10 years of bedroom playing and jam band at university. I went to a jazz jam session with a certain cocksureness that real ignorance brings. "I know the standards, I can improvise" >.< Got spanked, realised that there was more to it than noodling and that I needed some direction.
Looked up another teacher who took a more traditional approach. I played a tune, he gauged my level then got me to sight read. The instantly horrible results gave us a starting point. He told me "You're not a beginner, but we need to work on some basics", which I agreed with. He was a wonderful guy who started me on some basics of sightreading and intonation, standards and melodic improvisation. I always enjoyed turning up to his flat, sharing a joke or two before getting down to the fun stuff. What made him such a good teacher was that a certain benevolent wisdom that made him kind. He knew how to make a point without belabouring it and let you run with a mistake before stopping you and pointing out how you could improve. Almost like a favourite uncle who you wanted to show off to and so would practice really hard for
🙂
My last teacher was a young dude I went to in order to learn about improvisation. We started with scales and the basic structure. He listened to me, then summed up my improvisational ability: "You're waffling. We need to work on teaching you how to say something with your improvisation"
I really liked his directness. He was able to explain a lot of the mystical terms that I had seen on several other well-known saxophone websites such as "tritone substitution" and broke loads of things down as an explanation and then showed me what he meant by playing it. And then getting me to play it.
Another thing I liked most about him was the fact that you could see he was interested in making sure I understood the concepts and why they mattered. He never spoon-fed me, but would give me enough information for me and then make me work it out. Additionally, if we were on a roll, we often went over time and he never minded. It was more important that we reached understanding.
Unfortunately, my job kept me from keeping a regular timetable with him and then I left the UK and have been teacherless since. However, from each of these teachers, I have learned the following:
Teacher 1:
The best players do NOT always make the best teachers and lip slobber is nasty if left it on the flute being handed back :x
Teacher 2:
If your teacher makes it enjoyable, it stops being a lesson and becomes fun. You want to practice.
Teacher 3:
Basics are important. The difference a good grounding in fundamentals can make, even at a late stage, is not to be underestimated.
Teacher 4:
Jazz is a like language. You need the tools (scales, arpeggios, articulation, tone) in order to be able to say something. It's obvious when you waffle :whistle: Instead of playing everything that'll fit the chord, stop and think about what you want to play. That element of deliberation will give shape and character to your solo
Sorry about the long post, but you did ask
😉