If you're learning jazz piano, start learning melodies now. Not later; now. Open the Real Book and, pick a melody, and learning. Memorize it if you can and move on to the next one.
A lot of improvising musicians make the same mistake: they get "bogged down" with a few songs they're learning and never develop a broad repertoire. But you can avoid this mistake if you start learning melodies now and keep going.
Here's why you should do this:
If you're at the beginning or intermediate stages of learning jazz piano, it can take a while before you're comfortable improvising over a tune's chord changes. So you'll naturally need to spend a lot of time improvising over tunes like Autumn Leaves, Blue Bossa, and the other tunes that most of us learn at first. Once you learn these, however, it gets easier to improvise over new tunes, since many tunes have similar chord progressions and patterns.
But if you wait until you learn the basics of improvisation before you develop a jazz repertoire, you've wasted valuable time. There's a lot of songs to learn, and they're all wonderful and fun to play. So start learning at least the melodies of as many tunes as possible, now, and don;t wait until you feel "ready," improv-wise.
The great thing is that if you learn the melodies now, then when your improvisation abilities improve, you'll already know a bunch of tunes and you'll be able to play them well; both their melodies and chord changes. In other words, you'll already know the song structures and will be able to improvise on them relatively easily.
Here's a short video I made to demonstrate how to do this:
Jazz Piano Tip #2
Good luck, and remember: start developing a jazz repertoire now, not later!
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