Here comes another hedge fund with plans to shake up media companies it thinks are underachieving ... Harbinger Capital Partners has served notice that it wants a major say in running the New York Times Company (NYSE: NYT) and Media General (NYSE: MEG), notifying both that it will nominate its own directors for their boards.

NYTCo announced late this afternoon that Harbinger sent notice today of its intention to nominate four 4 Class A directors for election Apr. 22 when the company holds its annual meeting. Chairman Arthur Sulzberger, Jr.: “We have a strong and independent Board, but our Board’s Nominating and Governance Committee will review the nominations and make a recommendation to our shareholders in due course.”

Harbinger told Media General Thursday that it is nominating three candidates for election at its 2008 annual meeting, Apr. 24: Eugene I. Davis, chairman and CEO of turn-around specialist Pirinate Consulting Group and essentially comes close to being a professional board member (Atari, Delta and more); Jack Liebau Jr., a former journalist, who is now an investment manager with his own firm, and J. Daniel Sullivan, a veteran broadcasting executive. The fund claims to own or control more than 21 percent of Media General’s shares.

Media General statement: Marshall N. Morton, president and chief executive officer:  “We are frankly puzzled as to what Harbinger hopes to achieve by its hostile actions. ... we have sought repeatedly to talk with Harbinger and learn what is on their mind.  Harbinger, however, has persistently refused to return our calls.” Morton details strategic changes he says would have been shared with Harbinger, including “dramatically” reduced costs and sales of non-core assets

NYT:  “The hedge fund, Harbinger Capital Partners, a part of Harbert Management Corporation, controls less than 5 percent of Times Company stock, a level that would require a declaration to federal regulators. ... Even if it were successful in electing a slate of directors, Harbinger would not be able to take control of the board without an about-face by the controlling family at each company.”

Update: WSJ reports via an unidentified source that the Harbinger nominees for the NYT board are Scott Galloway, a professor at NYU’s Stern School of Business; Allen Morgan of VC firm Mayfield; Gregory Shove, a former AOL (NYSE: TWX) exec and a director at RedEnvelope Inc.; and James A. Kohlberg, co-founder of PE firm Kohlberg & Co.