As for the connection between jazz and the Grateful Dead, Miles Davis shared bills with the band and wrote in his autobiography: "Jerry Garcia, their guitar player, and I hit it off great, talking about music – what they liked and what I liked – and I think we all learned something, grew some. Jerry Garcia loved jazz, and I found out that he loved my music and had been listening to it for a long time. He loved other jazz musicians, too, like Ornette Coleman and Bill Evans."
Here’s a more analytical approach to the matter I found on a Dead website.
The question of whether the Dead even played "jazz" has been debated – just the fact they're playing with electric guitars instead of horns makes a huge difference – not only that, but their style is so unique from other bands anyway.
To me, the connection is clear – even from early '68, the whole idea of medleys of jammed songs linked together, many of them directly quoting jazz … using feedback and space as musical concepts, composing several improvised jam-songs that go on long wordless musical journeys.
1973-’74 is thought of as the jazziest years because of these big jams where the Dead skitter around from one theme to another, dropping into noisy spaces or funk-jams or unknown spontaneous melodies at the drop of a hat – there's not much like that in rock music.
The “Blues for Allah” period was perhaps the peak of jazzy Dead – in those '75 studio sessions we hear them playing with many new themes like “Slipknot” or “Stronger than Dirt” just like a jazz combo.
There's a wider sense in which jazz influenced their music early on, in the idea that their songs could be changeable and stretched-out, and played differently each time. Various rock groups in the late '60s were taking up this improvisational challenge (Cream the most famous, but also many California bands), so it wasn't exclusively a jazz concept. But the Dead keep improvisation within a rock context – the jams are always kept within a limited space in a few select songs and always return back to familiar ground.
So the Dead's music is not quite jazz and not quite rock, but like some of Miles' fusion albums, somewhere on the border.
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