These are all "live" concert recordings, and all recorded "live" to mono or stereo tape master. Although plenty of post processing happens over the decades.
One of the first live concert jazz recordings was in 1954, Art Blakey Quintet "A Night at Birdland." 23 yo trumpeter Clifford Brown appeared on this album, recorded live on location by Rudy Van Gelder. Then he went off to Europe for a few months with Lionel Hampton, and when he returned he was a star! A friend of mine attended this concert as a teenager and said the atmosphere was electric, everyone knew something very special was happening. The birth of Clifford Brown's star, the birth of the Jazz Messengers, the first big album for Blue Note Records, one of the first live jazz recordings by a record label.
Probably the most famous live jazz recording of all time is Ellington at Newport. Notice it doesn't say live at Newport? The legend of the live concert was well known, but the actual live recording was not released until 1999! A studio session recorded the next day in NYC famous Columbia studio was overdubbed with applause and other effects to make it sound like a live recording. The liner notes imply the recording is live from the previous night's concert. The new 2 CD release from 1999 contains both recordings, the studio session and the real live concert, including the spine-tingling, riotous audience reaction to the famous Paul Gonsalves astonishingly long tenor sax solo. Cat Anderson, Johnny Hodges, Sam Woodyard, all unbelievable. This recording brought Duke Ellington's career back from the brink when the country was tired of big band jazz, starting to go for cool jazz and rhythm&blues/rock. Recording quality is mostly excellent. Not to be missed!
https://en.wikipedia.org/wiki/Ellington_at_Newport
These two records had a huge impact on the renaissance of jazz in America in the 80s. Many of the well known jazz musicians of the last two decades played this music in high school and college. IMO there is no more exciting big band music ever recorded, but they say Kenton fans are of a "very special breed" and it's not for everyone. If you're gonna love Kenton, you'll love this. I was honored to have the trumpet soloist on these records, Tim Hagans, come to one of my gigs in Boston when I was a kid. I wanted his job sooo bad!
A more recent favorite live jazz recording is Kenny Barron's Live at Bradley's. 2 volumes, excellent recording quality, mix, superb SQ. The performance is classic modern New York piano trio, performed at the peak of the period, at ground zero home of the genre. The piano is Paul Desmond's Baldwin Concert Grand piano, which he bequeathed to the club owner. It's not Bud Powell or Monk, but it's all the refinement of the trio genre that developed after them.
One final recco is Dizzy Gillespie Live at Newport, 1957. Some of Dizzy's best playing and entertaining. On the Horace Silver tune Doodlin, Dizzy dramatically introduces the "Star of the Band" as Pee Wee Moore, a local Raleigh musician, RIP. I brought this album to one of his gigs and got his autograph around 1997? He seemed glad someone still cared about this music.
Oops one more, the very definition of swing. The essence of Count Basie, imo. I saw him in concert 4 times. The players of this era all say this was the best jazz band ever.
And another.. last one, I promise. This one is from the first concert of Miles' second great quintet. A young Tony Williams makes himself a legend on this.
