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Now; my thoughts on improvisation......
You have to realize that performing in the jazz idiom is all about creating new music. Even when performing with a big band, there are plenty of opportunities for improvised solos. If you don't include the quarter-tone and micro-tonal things people have done from time to time, there are only 12 notes to work with and by now, all of them have been played a few billion times. Our "job" as improvising musicians is to give something original to the listener; something they have never heard before. This is much easier than it sounds and my intent is to provide you encouragement, advice, and the tools to make it easier for you to express yourself on your instrument. Ready?? Then, let's get started!!
I have two hard and fast "rules" about improvisation.
1. There are no wrong notes
2. The half-step is your friend.
I push these rules during one-on-one lessons and in clinics and a lot of folks think I'm crazy. They may be right but that's a different discussion! Obviously, I don't take a hard academic approach to this. Instead, I prefer to give the players tools and advice. Let me expand on the rules a bit.
Rule 1. "There are no wrong notes". Yup.... there are NO wrong notes.... there may be better choices but there are no wrong notes. Here's why. It's your solo. Not the person sitting/standing next to you or if a big band, someone in a different section of the band. You are in charge of creation. You have the support of the rhythm section to back you with time, tempo, and chord changes, and you'll have the support of the rest of the band playing background music as well. Still.... there are no wrong notes. You, as the soloist, are allowed to create as you choose. Having said that though, there are definitely better choices of notes for your solo. Choosing to continuously play "wrong" or "clunker" notes is likely to get you thrown off the band stand, fired, or worse, hired to play in a concert band. Ok, I'm kidding about the concert band part but, it could happen!! :-)