hi guys, like other guys here, i've been playing piano for quite some time, but am kinda new to jazz piano.  i've been able to improvise pretty well for stuff like pop power ballads, but my jazz stuff sounds really square, and i'm guessing that it's a problem with my chord voicing and intervals.

i noticed that in jazz chords there are a lot of 13ths and 11ths.  my question is, what's the difference between writing 13ths, 11ths, and 9ths instead of writing 6ths, 4ths, or 2nds in  the chord names? is it supposed to tell you what kind of inversion to use, or something?  if there is a big difference, this will probably cure a great deal of my squareness.
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Jazz Piano Notebook Series
Scot Ranney's Jazz Piano Notebook, Volume 1 - jazz piano tricks of the trade

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.

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Scot Ranney's Jazz Piano Notebook, Volume 2 - jazz piano tricks of the trade you can use today
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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.

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Tim Richards' Jazz Piano Notebook - jazz piano tricks of the trade

Volume 3 contains 12 jazz piano exercises and explorations by the acclaimed jazz piano educator, pianist, author, and recording artist Tim Richards.

Tim wrote the well known "Exploring Jazz Piano" and "Improvising Blues Piano" books and has several others to his name.

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Jeff Brent's Jazz Piano Notebook - jazz piano tricks of the trade

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.

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