To the fans and critics, it’s “country-punk.” To the band itself, it’s Western-folk-thrash.” Whatever you call the hybrid, Blood on the Saddle’s 78-r.p.m. blend of traditional and newfangled strains as much to Jimmie Rodgers as to Johnny Rotten. It may sound like a joke, but this is a band that makes the incongruous congruous.

Founder Greg Davis is certainly a study in contradictions. After quitting his job as guitarist for an L.A. punk band called Dead Hippie, he picked dobro with a friend who played banjo for handouts on the streets of New Orleans. He noticed that punk and bluegrass shared the same frantic tempos and returned to Los Angeles to form a band in which the twain would meet.

“Blood on the Saddle,” the band’s ’84 debut album, was one of the most absorbing vinyl wonders the city has produced in the last few years. Behind the harsh, driving Sturm and Drang of the live group were lovely melodies and a sense of traditionalism. More than any other so-called “cowpunks,” Davis captures the lonely spirit of the original folk-cum-country singers who sang to ward off the isolation of the open range.

In recent months Blood on the Saddle has been “flirting” with a major label but whether Davis is willing to make what might seem like compromises to bring out the accessibility of the material is a question mark. The group plays Saturday at Safari Sam’s. June 14 at Fender’s (with the Knitters) and June 15 at Al’s Bar (with the Long Ryders).