In the swinging big-band era, the team of Bill Basie and Lester Young — known as the Count and the Prez, respectively — began playing a brand of jazz that looked forward, in many ways, to the bebop era of a decade later. In the 1950s, Basie’s music could be described as equal parts swing and bop. Basie and Young were the fathers of what the critic and producer Stanley Dance deemed “mainstream jazz”; they also were the spiritual forebears of one of jazz’s most remarkable families, that of the tenor saxophonist and composer-arranger Al Cohn (1925–88), and his son, the guitarist Joe Cohn. The talents of both remarkable musicians are on display in a pair of new releases: “Mosaic Select: Al Cohn, Joe Newman & Freddie Green” (www.mosaicrecords.com) and Joe Cohn’s “Restless” (Arbors Jazz).

“Mainstream” is the variety of jazz played by many veterans of the swing era, and lies somewhere between the poles of Benny Goodman and Charlie Parker. It combines the melodicism of swing with the harmonic intricacies of modern jazz, as well as the tightly arranged ensembles of the former with the latter’s emphasis on improvisation, and a rhythmic language that splits the difference between the two. In many ways, it was the best of all possible jazz. Mainstream jazz flourished in the ’50s — when, thankfully, there was a recording boom in place to document it.

In 1948, Cohn replaced Herbie Steward in Woody Herman’s Second Herd, joining fellow saxophonists Stan Getz and Zoot Sims, and began to make an impression as a player and, more important, an arranger. After leaving the group two years later, he teamed up with two of the greatest of Basie’s sidemen: the guitarist Freddie Green, who since 1936 had been the most essential figure in the band after the Count himself and Lester Young, and the trumpeter Joe Newman, a major star of Basie’s postwar band.

The three instrumentalists — Al Cohn, Green, and Newman — played on five albums in 1955 alone, all produced for RCA Records by Jack Tracy, all of which have now been collected on the three-disc Mosaic Select box. Two were done under Cohn’s leadership, two under Newman’s, and the last is the only album ever released under the direction of Green, the greatest of all rhythm guitarists, who was reluctant enough to solo, let alone lead a band.

The instrumentation varies from project to project: Cohn’s “The Natural Seven” album takes its inspiration from Basie’s Kansas City Seven sessions of almost 20 years earlier and adds the trombonist Frank Rehak to the lineup. Contrastingly, Cohn’s “Four Brass, One Tenor” offsets his solo horn against what was more or less Basie’s trumpet section of the time. Both of Newman’s albums utilize an octet of trumpet, trombone, alto and tenor saxophones, plus four rhythm pieces led by Green, whose own album, the suitably named “Mr. Rhythm,” also sounds like a Basie small group project. “Sometimes I’m Happy,” from Newman’s “I’m Still Swinging,” sounds like a direct response to Young’s classic 1943 treatment of that song. On three albums, the Count’s royal role at the piano is filled by Nat Piece, the most accomplished of all count-erfeits, while the astute Dick Katz (who is still playing brilliantly today) deputizes on the other two; both pianists ably replicate the famous all-American rhythm section, which would have been impossible without Green’s steady-four beats.

The repertoire consists of only a few Countish classics (“Doggin’ Around,” “9:20 Special,” the forlorn, mysterious “Topsy,” and one sequel, “The Daughter of Miss Thing”). For the most part, Cohn, Newman, and Green played standards, blues, and variations on standards.

The late Al Cohn was a major, if relatively quiet, voice in jazz, taking charge with special command on the “Four Brass, One Tenor” project, where he solos dynamically on every track and splits the arranging chores with the equally gifted Manny Albam. He preaches his own interpretation of the Prezbyterian faith, and you can always tell it’s him, not Zoot Sims or Stan Getz or Paul Quinichette.

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Al Cohn’s son, Joe Cohn, likewise takes charge on “Restless,” his second full-length album. The younger Cohn, who can capably play at least half the instruments in the orchestra, here steps into his father’s shoes and at the same time comes into his own as a small group arranger. On this project, Mr. Cohn leads a quintet featuring the veteran bop pianist Hod O’Brien and the young the Russian-born alto saxist Dmitry Baevsky; his frequent partner, the brilliant tenorist Harry Allen, also guest stars, particularly winningly on the title song, a longtime favorite of swing players. For half the album, Mr. Cohn sonically wedges his guitar between two saxophones, producing a musical combination that is fully as ingenious as anything his father might have come up with.

“Comes Love,” on which Mr. Cohn engages in a rapier-like three-man duel with the two saxophones, could have fit neatly into one of his father’s 1955 sessions. In another savvy stroke of orchestration, the Busby Berkeley-associated “Shadow Waltz” becomes “The Shadow Bossa Nova.” Most of the high-points are similarly ebullient bouncers, but for the blues and ballad department, Mr. Cohn has chosen one song that fulfills both requirements: Buddy Johnson’s “I Wonder Where Our Love Has Gone,” linked to Billie Holiday and Arthur Prysock, done here as a touching duet between Messrs. Cohn and Baevsky.

Sadly, the music that was once known as mainstream jazz essentially died along with the veterans of the swing era. There is a current generation of excellent players in the style — Ken Peplowski, Wycliffe Gordon, Warren Vache, and Scott Hamilton come to mind — but no club in New York presents them regularly. The best you can do is keep your eyes peeled for any opportunity to hear Harry Allen and Joe Cohn.

wfriedwald@nysun.com