I find its best not to think of anything when lisening. Just listen.
KNOWING about music may help you to appreciate how and why, it was made. The story of the musicians life and inspiration to make music is really interesting, BUT the appreciateion of listening is best done with a blank mind (for me at least).
Check it out
http://www.youtube.com/watch?v=aPCFGiWLfUM
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If you want some album suggestions, here are a few from the 1960's and current stuff. Its all on the more adventerous side, less traditional.
I remember being where your at now. I was new to jazz and didn't know a thing beyond Miles and Trane. I didn't have a website like this so I called up the local college radio station and begged for some suggestions. I was lucky, because that night the dj had a few of his friends hanging out in the studio with him. They were all yelling out albums, and getting excited about each others suggestions. I was writing them down as fast as I could.
They did me right. Now all these years later, I can pass on the short list version, with my own own approval.
Miles Davis Kind of Blue album. It's a great album for a beginner, and it's great even if you've heard a whole lot of jazz. Get it. http://allmusic.com/cg/amg.dll?p=amg&sql...
Thelonious is another great and important master of jazz. I suggest that you start out with the Monk's Dream album. Don't operate heavy machinery while listening. Monk swings the hardest of any jazz musician, in my little opinion. http://allmusic.com/cg/amg.dll?p=amg&tok...
This is the album that really turned me onto jazz. I still enjoy it and respect it. Roland Kirk's Inflated Tear album.
http://allmusic.com/cg/amg.dll?p=amg&sql...
Booker Ervin's album called The Freedom Book is completely amazing, from start to finish. The chemistry of the musicians is amazing.
Grant Green's Matador album is a great album, centered around the guitar playing, although McCoy Tyner is at his best (piano player from Coltrane's band). It's another great album that's easy to like. http://allmusic.com/cg/amg.dll?p=amg&tok...
Wayne Shorter's album called Speak Like A Child is a great album that you really have to hear. I can't even talk about it. The whole band is amazing. http://allmusic.com/cg/amg.dll?p=amg&sql...
Herbie Hancock's album, Maiden Voyage is another great and easy to like album. Freddie Hubbard is at his best through the whole album (on trumpet, fluglehorn). It's a concept album, and it really does flow like the sea, as Herbie intended it to. http://allmusic.com/cg/amg.dll?p=amg&tok...
Horace Silver plays piano with soul. The songs are great and so is the band. Everything works on this album called Song For My Father. It's another easy to like album too. http://allmusic.com/cg/amg.dll?p=amg&tok...
Oliver Nelson's album called Blues and the Abstract Truth is another classic. It features the great Eric Dolphy. Get it!
Honestly, I think that the jazz of the current scene is some of the best I have ever heard. I live near New York City, and I am lucky enough to be able to hear today's musicians in little intimate places. Today's jazz musicians are VERY creative. Its not popular because its not advertised, and like Frank Zappa said "Most people wouldn't know good music if it hit them over the head". Anyway, here is a short list of musicians/albums that are great, in my opinion, and easy for a beginner to "get".
Drew Gress- Seven Black Butterflies. This band is amazing. The songs are constantly changing and morphing. I saw this band a few weeks ago, and they were great. I really think you should hear this album if you are interested in whats modern in jazz.
I'm going to stop commenting on each one for the rest of the list. I am only listing the albums which totally blow me away. I don't know if they are good for your tastes, but I do know that if you like this kind of thing, you hear albums that are a complete success at what the artist was trying to create, and in all cases, the albums were motivated to make music that is completely unique and adventerous.
Drew Gress- Seven Black Butterflies
Scott Colley- Archetiect of the Silent Moment.
John Ellis- Roots Branches and Leaves
Kurt Rosenwinkel-Deep Song (any album)
Seamus Blake- Stranger Things Have Happened
Angelica Sanchez- Life Between
Tim Berne and Science Friction- The Sublime and the...(live)
Ried Anderson- Dirty Showtunes
Ari Hoenig- Inversations
Dafnis Prieto- Absolute Quintet
Mat Maneri Quartet- Blue Decco
Roy Campbell- It's Krunch Time
Human Feel- Galore
Aaron Parks- Invisible Cinema
Bernie Maupin Quartet- Early Reflections
Mario Pavone- Toulon Days
Chris Potter- Song For Anyone
William Parker- Painter's Spring
I don't listen to too many singers beyond the legends, but I can suggest some classic albums that I know are great.
Sarah Vaughan- Self titled album, also known as Sarah Vaughan with Clifford Brown. Great singing and great band. Also get Sarah's Like at Mr. Kelly's album.
Sheila Jordan- Portrait of Sheila Jordan. Very mellow.
I promise that my answers are from personal experience and that I listen to lots of jazz.
PS-The best radio station for jazz (BY FAR) is WKCR(.org). Check their schedule, because sometimes they play other styles of music too.