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Jazz is rhythmical
Above all jazz is rhythmical music. It is wrong to study jazz only from a harmonic point of view. You should listen to recordings and live music, and then play. As it is impossible to get the right feel in folk music if you only study note sheet music, you cannot learn jazz from just learning notes.
The development of Jazz
Similar to the classical music that started up as pentatonic, got into 7 tone-scale, which got into triad harmony in the renaissance, and 4 part harmony in the 16th century, the jazz has experienced a similar development in the century it has existed. The early blues was pentatonic and moves into triad based chords, the New Orleans music of the 20-ies develops 4-tone harmonies, while the Bebop is based 5-part harmony chords.
The Blues progression
The mostly used chord progression in jazz is the blues progression. It usually runs over 12 bars (though other number of bars are possible) and the basic progression looks something like this (here the chords are in F-major).
The blues progression is also used a lot in rock music.
You can then extend and modulate the chord progression in many ways. Below is strongly modulated blues (Charlie Parker's blues for Alice.)
You may use various scales when playing a blues It is common to use a minor third even if the blues is in Major, this gives a "bluesy" sound. The threetone (the note between the fourth and the fifth. It is also good to use, as well as the minor seventh. The blues scale contains following notes.
The tonic, the whole tone, the minor third, the fourth, the threetone, the fifth and the minor seventh.
For a C-major blues the "blues scale is:
C, D, Eb, F, F#,G, Bb, C.
About practicing scales
I have an ambivalent relationship to scale, and particularly the above blues scale. It is quite boring to practice scales. However when I pull myself together and do the practicing, I do feel that I get better. I think the secret lies in
However the blues scale is just a help to get started playing blues, you don't have to stay within it. You may construct a pretty good solo just playing the blues scale, but it gets even better if you use the blues scale just in a part of your improvisation.