Bill Werde, Billboard’s editorial director, said the shake-up was necessary to reflect changes in the way people consume music these days. There was a time when radio programmers — and the record labels who lobbied them — largely defined the charts, using surveys of their listeners and their gut instincts to select hits. Now the Internet gives fans a greater say, as people buy music from online stores, stream it through services like Spotify or listen to it on video sites like YouTube and Vevo.

“Three weeks ago, the main genre charts only reflected FM radio play,” Mr. Werde said. “Every fan out there in the world knows and everyone in the music business knows that is not the business we are in anymore, that a stream on Rhapsody or Spotify, or a download at iTunes or Amazon — all these different things — are a meaningful part of the fan experience. And to have genre charts that don’t reflect that? I can’t believe anyone would be arguing for that.”

Still, some people did. The changes caused a backlash on Twitter and other online forums from some purists among hip-hop, country and R&B fans. A headline on one commentator’s blog was “Billboard Chart Changes — R.I.P. R&B Music.” The Web site Saving Country Music lamented that “these new rules could cause the largest wholesale power shift to superstars that music has ever seen.”

Psy’s climb up the rap chart was also criticized. “Trust me when I tell you hip-hop does not consider Psy rap,” said Ebro Darden, the program director at Hot 97 (WQHT, 97.1 FM) the leading hip-hop station in New York. “Billboard has pull, but they cannot make people who live hip-hop believe Psy is rap.”

Most of the criticism, however, has come from fan groups with narrow interests. Carrie Underwood fans were furious that her song “Blown Away” was blocked from No. 1 by Ms. Swift’s pop tune, even though Ms. Underwood’s track is being played far more on country radio stations.