There are countless jazz piano books that contain fancy chord voicings, a million ways to solo over a Dm7 chord, and transcriptions of every solo Charlie Parker ever played. But what about the melody? How well do you know the melodies of the tunes you love to play? Or, to put it another way, is the melody just something you have to play in order to get to "the good stuff?"
Do yourself a favor and take some time to really learn the melody to the tunes you play. Spend some “quality time” with it. Many jazz pianists know a tune’s chords and can improvise, but they don’t know melodies very well. For a while, pretend that you’re a horn player and just practice the melody. There’s a lot in there which you’ll gradually discover as you spend time exploring its intervals and melodic structure.
You'll also become a better player. Great jazz musicians know how to play melodies. The melodies are just as much a chance for creativity and self-expression as our solos are. Sometimes more, in fact.
To get started, take a tune you like to improvise on and spend some time playing just the melody. Play it as written. Play it fast. Play it slow. Caress it. Sing it through the piano. Embellish it. Enjoy it.
In general, horn players are better at this than pianists (with notable exceptions, of course.) And even the best melodic pianists are often influenced by singers and horn players more than other pianists. To hear what I mean, listen to this recording of the great John Coltrane playing the Rodgers and Hart song "It's Easy To Remember."
Now no one could get "farther out" than Coltrane, but when he played a melody, he really played that melody! Try it... you'll like it!!!
I've made a list of 10 jazz standards you can practice the melody on. Enjoy!