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Thanks in advance, Matt
In more advanced pieces, Jazz music modulates constantly unlike the blues scale where the key signature follows mostly a "three chord wonder" format, i.e. G, C, D, G. In many instances, when you change chord in jazz, you play the key signature relating to that chord which is why the music often takes on that floaty, undefinable quality. If the music was written out, you would see constant accidentals but it does help as I say to think of the key signature relating to that chord. It doesn't happen all the time, but where soloing is involved, I would say that it is unavoidable in order to stop it sounding as safe or stationary as blues or country. Having said that, there are patterns in the behaviour of the music such as the 2-5-1 progression for example. It appears also in urban/gospel music styles.
No quick fix on this except start to brushing up on your major seventh chords and your 9th and 13th chords.
Improvising Blues Piano - Tim Richards. - This starts from the basics of blues and shows you how to develop you improvisation. As the title suggests, it's mostly blues pieces, but I think it would be best to start with this book before his other book, 'Improvising Jazz Piano'
Jazz Piano from Scratch: A How-to Guide for Students and Teachers (ABRSM) - This is a very well thought out and useful learning guide for how to improvise in jazz. It really breaks down how you go about creating improvisations and techniques you can use.
ABRSM - Jazz scales Grades 1-5 and Jazz pieces Grades 1-5) - These pieces are obviously the graded pieces from the abrsm jazz syllabus and the pieces contain improv sections. These go well with the other abrsm book above.
Hope these are of some use. It's a great jounrey.
If you are based in the north west- band on the wall used to run jazz improvisation classes - Also- get yourself a drum machine and have a go at playing along to different jazz rhythms- latin rhythms are a good beginning, big band and dixie land swing are also a good start - I found it challenging to learn in isolation and had to get out there and play- also if you can get a few cds of your favourite jazz artists and jam along with them - there are as many different types of jazz as there are stars in the sky!
Learn the classic american song book selection first as written and then improvise round the chords- use major 7ths, 9ths, Learn the jamie abersole scales to give you some ideas about what notes to play.
ABRSM jazz exam books are good Grades 1-5
Hope this helps