Here's a page of elements for putting together a basic Elvin Jones-style jazz waltz— I hate to treat his playing so reductively, but what are we supposed to do? It's a thing, it's sometimes asked for, and people need an easy entry into it. When I first learned this groove, or a take on it, I had no specifics at all to go on; I just listened to the records, and tried to match the vibe. Now we've got pages and pages of exercises for putting a similar thing together, but there's a lot to be said for just listening, learning a few basic things, and going for it.
Swing the 8th notes— Elvin generally played a very triplety swing feel. We're emphasizing the 1 and the & of 2 with our swing feel here; I've written them as accents, but just lean on them a bit. First learn the base pattern with the bass drum and cymbal, then learn the left hand parts— once you are familiar with them, you can improvise moving them around the drums. Then play them again with each of the cymbal variations, and again with the different hihat parts. You could go one step further and learn the left hand parts with every combination of cymbal parts and hihat parts, but I think once you've done what I suggested, you'll be able to begin improvising your own things. Then, if you feel the need, you can dive into the many Pages o' Coordination I've written on this subject.
Get the pdf
Don't neglect the listening— there are some tracks after the break.
These tunes are from these albums, all of which you should own:
John Coltrane — Coltrane, My Favorite Things, Live At Birdland
McCoy Tyner — The Real McCoy
Inchworm, from the John Coltrane album Coltrane:
Your Lady, from the Coltrane album Live At Birdland
My Favorite Things, from the Coltrane album of the same name:
Out Of This World, from the Coltrane album Coltrane:
A slow one: Contemplation, from the McCoy Tyner album The Real McCoy: