Don’t start by thinking about the notes. Start by listening to the song and the rhythm section. The bass, drums, and piano. Think about what you can play as a saxophonist that fits in the music.
You really should also know the melody very well before you try improvising.
Experiment when you play and see what works. You’ll find that certain counts in the measure should be accented (pay attention to the drums to figure that out). Listen to see when the piano/guitar plays something and try to work with them rather than compete. You’ll also find that certain notes tend to work better.
Notes are not the only thing that matter!
Think about rhythm, space, articulation, phrasing, dynamics, tone, everything else too.
The notes/harmony can get pretty complicated in some songs, and at the start of improvising you want to simplify things as much as possible. So that’s a reason to start with blues tune. You can stick with a minor pentatonic scale or the blues scale and then you don’t have to worry about the notes very much.
(mp3, right click and save)
Bb (concert) will be C for tenor and G for alto. Try thinking of it as the numbers for the chords: I, IV, and V.
I7 | I7 | I7 | I7
IV7 | IV7 | I7 | I7
V7 | IV7 | I7 | I7
The chords will be the one chord, the four chord, and the five chord. They are dominant chords.
I, IV, and V are the Roman numerals. They stand for 1, 4, and 5. For scales, say we’re in a certain key. C for example, then the first note is C, the fourth note is F, the fifth note is G. You can make scales starting on those notes.
The number seven next to the chord symbols indicates a dominant chord, which has a lowered seventh. It corresponds with the mixolydian scale.