I know I've typed this a few times in the past, but there've been a couple of requests, so here we go again.
First let me say that this isn't anything that I came up with on my own, this is the approach my teacher uses that he got from his teacher, Lennie Tristano. And for what it's worth, I think ANYBODY at ANY LEVEL will benefit from studying one on one with a player who has a deeper understanding than they do. The following set of exercises work BEST when you have some objective, knowledgable person who can listen to what you are doing and provide guidance to keep you moving in a focused and progressive direction.
1. PICK A TUNE - something from the "standard" repertoire; my 4 tunes are STELLA BY STARLIGHT, THESE FOOLISH THINGS, BODY AND SOUL and ALL THE THINGS YOU ARE. When you pick a tune , you want to find the most vanilla version of the melody that you can. Look in older "fake" books, pull it off some Judy Garland record whatever. The idea is to get as close to the composer's concept of melody and changes than you can. The REAL BOOK (old ones, not the Sher or Leonard versions) tend to contain somewhat dubious transcriptions of specific recordings; again the idea is to get the composer's idea, not Sonny Stitt's version of the composer's idea. Kind of like the game Telephone or doing a book report from reading somebody else's book report; you stand a better chance of coming up with "your" interpretation if you know what the actual original was.
2. LEARN THE MELODY - set the metronome at quarter note=60bpm and PLAY the melody through. Over and over and over and over and over and over so that you can SING the melody if somebody drags you out of your bed at 4am. Get off the paper as soon as you can, I've found that learning the lyric that goes with the melody is a great way to internalize the melody.
3. PLAY A CHORD LINE - what do I mean by "chord line"? Simply this, a line that arpeggiates the changes but with a couple of important parameters:
A. PROXIMITY - you want to use not only root postion arpeggios but also all inversions to maintain "close" fingering and common voices through the tune. For example, a progression of D-7 G7/ Cmaj7 - instead of D F A C G B D F C E G B (root position, root position, root position) one choice could be D F A C D F G B C E G B (root, 2nd inversion, root).
B. IN TIME - the chord line shoudl reflect the harmonic rhythm of the tune. If the chord lasts one bar, the chord line is quarter notes. If half a bar (two beats) the chord line is eighth notes. One beat would be 16ths, two bars would be half notes. Let me know if this is not clear.
3. THE EXERCISE
PART 1 -with the nome at qnote=60bpm( and without the sheet), play one chorus of the melody and one chorus of the chord line, then one chorus of the melody. This is getting the sound of the melody and the sound of the changes in your ear.
PART 2 - For the purposes of this exercise, use the major scale for all major7th chords, the mixolydian for all dominant 7th chords and the dorian for all minor chords. Play one chorus of melody, one chorus of chord line and then improvise one chorus of half notes, ending with one chorus of melody. The half note chorus should try to emphasize MELODY over BASS LINE, you are not "walking two feel" but buidling a melody. It may be a little mechanical at first, but once you relax and let your ear start telling your fingers what notes to use, you can really get to some nice melodic material. Again, this is MUCH harder to do without somebody listening to your progress form teh outside, if you insist on doing this without a teacher, RECORD all of your exercises and listen to them without your instrument in your hands. When you get to the point that you are consistently creating some nice music with half notes, move to the next part of the exercise.
PART 3 - Play a chorus of melody, a chorus of chord line and then play 1 chorus in the following manner: the first 3 bars of each 8 bar section play the melody and then starting on beat ONE of bar 4 begin your improvised line of half notes. So you will have (in a 32 bar tune) 3 bars melody, 5 bars improvised, 3 bars melody, 5 bars improvised, 3 bars melody, 5 bars improvised, 3 bars melody, 5 bars improvised. Again, don't move on the first time you get this to sound like music, wait until you hit that every time.
PART 4 - as above, but the improvised chorus will have the 3 bars of melody dropped into a different place for each 8 bar segment( moving melody). That is, if you start the first 8 bars with meldoy, NO OTHER 8 bar section can start with melody.
PART 5 - as above, the improvised chorus now becomes only improvised half notes and rests. You should play (approximately) as many beats rest as you play measures of half note per 8 bar section.
When you've made it through this whole exercise, you start over and use quarter notes for the improvising rhythmic "denomination". And so one through accent 1 eighth notes, accent 2, accent3 , accent 4, accent 1 triplets, accent2 accent 3, 16ths etc.
This AIN'T quick; I've been studying with Joe for about 10 years now and I'm only up to accent 3 triplets with moving melody. But after about 7 or 8 months of starting this exercise (and a few others) , the amount of sense I made whiel improvising increase exponentially. And all the work I've put into really tearing apart these 4 tunes has translated into me being able to learn and play SO many more tunes. And has increased (along with the other ear training I'm doing) my ability to play tunes by hearing my way through them. If the piano player really knows the tune or if I can hear the melody in my head clearly enough , I can pretty much hear my way through the tune.
