I'm really new to playing jazz piano but not so much to theory. One thing I've really been wondering is how you play straight piano chords, like E- or Db in a lead sheet.
For example, in Autumn Leaves, bar 7 calls to play E-.
In bar 8 after the repeat of Body and Soul, it calls to play Db.
Do you really only play E G B and Db F Ab, respectively?
Why are some chords not sevenths? For minors, I suspect that since -7th chords can give a dorian rather than tonic feel, plain minor chords should feel like a tonic minor or minor 6th. Is that right? Is every plain minor chord supposed to be the tonic minor?
As for majors, why are some just not major 7ths?
More importantly, how would you recommend I play them? I understand I should do whatever I think sounds best, but I don't know how to sound 'best' yet. How would you approach these chords?
Simple answer- you can generally turn basic minor chords into minor 7ths, 9ths, and other permutations. With the major chord, you can often turn that into a major 7th or 9th.
You'll still need to see if the extended chords sound right, and the easiest way to do that is record your practice session on your phone or something and listen to it. It's hard to be objective while playing, especially at first when you have other things to think about, but when you're just listening you can hear all sorts of things you didn't pick up while you were playing.
To get a little deeper into this, chord symbols are there to give you the sound, the harmony of that point in the music. The way I look at it, there is no difference between a C minor triad and a Cm11th. They are both built on the sound of C minor, what flavor I want to play will depend on things in the music.
I'm not saying a person shouldn't know how to accurately spell chords because it's important to know that stuff, but it's just as important to play what goes best with the music at the time, as well as evoking the kind of mood you're looking for in your own performance.
As you observed, doing what you think sounds best is the right way to go, and you also mentioned not know how to sound "best" yet. If you try that tip and record your practice sessions and listen to them, no matter how painful it might be at times, you will improve twice as fast, if not faster. Why? We all know what good music sounds like, or at least what we like to hear. It follows that you'll want to play the music you like, so if you record/listen to your practice sessions, you'll immediately hear what you like or don't like and be able to make changes.
That's one of the reasons why people who record a lot are also often better knowing how to sound their best; they are always listening to their own playing.
Volume 1 of this educational jazz piano book contains 15 jazz piano exercises, tricks, and other interesting jazz piano techniques, voicings, grooves, and ideas Scot Ranney enjoys playing.
Volume 2 has 14 jazz piano exercises and tricks of the trade, and quite a bit of it is Calypso jazz piano related material, including some Monty Alexander and Michel Camilo style grooves. Jazz piano education is through the ears, but books like this can help.
Volume 3 contains 12 jazz piano exercises and explorations by the acclaimed jazz piano educator, pianist, author, and recording artist Tim Richards.
Volume 4 is by Jeff Brent, a jazz pianist, composer, teacher, and author of "Modalogy" and other acclaimed jazz theory and education books. In this book Jeff shares detailed analysis of transcriptions of live performances. He covers everything from the shape of the songs to the tricks and licks he uses in improvised lines to the ideas behind his lush chord voicings.
Jeff Brent's Jazz Piano Notebook
Fundamentos Físicos del Sonido
Aprendiendo a tocar PIANO gratis con partitura
5 Pro Tips for Practicing Jazz Piano
"Danny Boy" Jazz Leadsheet
Tim Richards' Jazz Piano Notebook