Thirty-five years is a long time to hold a grudge. In 1971, the Jazz Crusaders became the Crusaders, and most of us jazz “purists” never quite forgave them. In their “jazz” period, the Crusaders were a hard bop band with a pop sensibility that played memorable originals as well as intelligent arrangements of familiar songs. After nearly 20 albums as “the Jazz Crusaders,” the four key members of the band — the pianist Joe Sample, the tenor saxist Wilton Felder, the trombonist Wayne Henderson, and the drummer Styx Hooper — switched to an electric rhythm section with keyboards, Fender bass, and electric guitar. They began playing a lot less jazz — hence the dropping of the word from their name — and a lot more funk and pop.

The gambit worked: as the Crusaders, they attracted a huge following and helped open a whole world of soul jazz. In fact, about the only people who didn’t listen to the Crusaders were acoustic jazz snobs like myself.

So when the Crusaders opened Tuesday night for a week-long run at the Blue Note — for the first time in 20 years — I decided to let bygones be bygones. Of course, I still prefer what they played on their classic ’60s albums, such as the three separate concert albums recorded “Live at the Lighthouse” (1962, ’66, and ’68), but after hearing the non-jazz Crusaders live for the first time, I realized there was still a lot to like.

The current edition, which includes two of the original four core members in Messrs. Sample and Felder, is a sextet, featuring the Swedish-born Nils Landgren on trombone, Mr. Sample’s son, Nicklas Sample, on electric bass, and two contemporary players who are well-known for long careers as studio musicians, the electric guitarist Ray Parker Jr. and the drummer Steve Gadd.

The first hang-up to get over is that there’s no shame in making jazz for a pop audience: Many Frank Sinatra fans loved Count Basie and vice versa, Ray Charles’s gospel-tinged blues were in the same basic pocket as the churchy instrumentals of Horace Silver, and the Crusaders instantly appealed to the audience who loved ’70s soul stars like Barry White, Lou Rawls, Marvin Gaye, and especially the instrumentally oriented, melodically-rich compositions of Stevie Wonder.

For the opening show, the group featured two compositions from its well-received 2003 reunion album, “Rural Renewal,” including “Creepin’,” a slow blues that gave the elder Mr. Sample the chance to play an old-fashioned electric piano (the kind that automatically makes you think of Ray Charles’s “What’d I Say”), and “The Territory.” The latter was easily the high point, an excitingly funky piece that referred to the classic bluesderived jazz of the Midwest and Southwest of the 1930s and ’40s, but which was hardly a repertory exercise. Joe Sample, who evoked such fundamental players as Sammy Price and Jay McShann, described the tempo as a shuffle, but it could also have been described as a heavy funk backbeat.

Admittedly, several pieces were on the fluffy side, such as a litestyle treatment of Carole King’s “So Far Away,” a one-time hit for the band that sounded like a ’70s TV show theme à la Bob James. But there were more substantial vibes as well, like “Put It Where You Want It,” a hard-hitting, blues-based riff on which the Crusaders sounded like the natural successors to Cannonball Adderley’s later, funk-oriented bands, as well as the inspiration for the “Saturday Night Live” band. Both “So Far Away” and “Put It Where You Want It,” come from the first Crusaders album, “1” (1971); I would like to see Messrs. Sample, Felder, and company go back even further to their jazz days, to record some of their outstanding bebop-oriented tunes. Even more so, the band needs to break up its funk-jazz grooves with a few slow, sensual ballads, like “Round Midnight.”

The Crusaders still feature solid jazz elements; there’s a solid, twohorn frontline, the same unique combination of trombone and tenor sax that they perfected in the ’60s. Importantly, the band continues to make improvisation an important part of their music. There are many worse things a cat could listen to.