The problem with jazz is that it means everything from Kenny G to Madeleine Peyroux to New Orleans' Preservation Hall Jazz Band. No definition of the American music seems adequate. One I saw recently described it as "cerebral music with rhythm". This one is about as OK as I can find. Even the word itself, the American Dialect Society's Word of the Twentieth Century, has been hard to nail down.
Jazz is about discovery. This article expresses the wonder of discover that jazz can bring.
Ultimately, though, jazz can't be adequately described. It must be experienced. These are all songs I own.
Tutu (live)- Miles Davis
Tutu was one of the last albums I got as an LP; i.e., on vinyl.
Cassandra Wilson - Harvest Moon
A Neil Young cover.
Benny Goodman & His Orchestra - Sing Sing Sing
As the title suggests, this song DOES have lyrics, but I think it's better as an instrumental.
Ella Fitzgerald & Louis Armstrong - STOMPING AT THE SAVOY
Also recommended: any of the Ella Song Books. Or all of them.
Oh, there's so much, I can't do the topic justice.
Here's a peculiar thing about Jazz that perhaps folks not in the United States or Americans who don't follow basketball might not know. There is a basketball team called the Utah Jazz. Utah is not generally known for jazz, and in disposition seems to be the antithesis of that music. The Jazz was formed in New Orleans in 1974, a most likely place for a team with such a nickname, but the team moved to the Rocky Mountains in 1979. (New Orleans got the Hornets, a team formerly in Charlotte, NC in 2002.)
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