Giants in the march toward equality; King's gifts for eloquence and nonviolence; Let the Trumpet Sound: The Life of Martin Luther King, Jr., by Stephen B. Oates. New York: Harper & Row. 560 pp. $19.95.

Is it really almost a quarter of a century since Martin Luther King Jr.'s Crusade for Citizenship tried to double the number of black American voters? In this summer of '82 the slain civil rights leader's father has made news in another drive to get out the black vote. He doubtless remembered what his son said in 1958: that black citizens' political apathy was ''a form of moral and political suicide'' and that one of the most decisive steps they could take was ''that short walk to the voting booth.'' This is but one of the timely reminders in a compelling new biography (to be published later this month) of the crusader for a dream of freedom who won the Nobel Prize for peace.

Today there are fewer obstacles to that short walk for black Americans, thanks to the Voting Rights Act of 1965, which was spurred by King's voting rights march in Selma, Ala. In fact, Congress has overwhelmingly passed a bill to extend the act, though the White House at first seemed reluctant to go along with it.

''Let the Trumpet Sound'' recalls just how often King had to sound the trumpet in the '50s and '60s before the federal government would take a firm stand for civil rights. He spoke to a continuing need when he said: ''The key to everything is federal commitment, full, unequivocal, and unremitting.''

King faced reluctance, not only from President Eisenhower, but from two Presidents -- Kennedy and Johnson -- who are now regarded as champions of civil rights. They warned against demonstrating and then hailed its success. Johnson went so far as to compare the march in Selma to Lexington and Concord as a turning point in ''man's unending search for freedom.'' He saw the far-reaching goal of ''not just legal equity but human equity -- not just equality as a right and a theory but equality as a fact and a result.''

Johnson rejected King when he started criticizing the Vietnam war before it was fashionable to do so. From his platform of nonviolence King argued that it was consistent to oppose violence both at home and abroad. But King could never get his war views taken seriously -- like some members of the Johnson administration themselves, as David Halberstam notes in ''The Best and the Brightest.''

In this matter, King proved closer to the temper of the country than Johnson. The present biography challenges Americans as to how far his civil rights ideals still flourish. He showed what ''black and white together'' can accomplish when they are determined that ''we'' shall overcome.

King had to resist not only the brutality of some white authorities but the separatism of some black militants who wanted to fight violence with violence. ''Darkness cannot drive out darkness: only light can do that,'' he insisted. ''Hate cannot drive out hate: only love can do that.''

It is the achievement of Stephen Oates to trace King's religious, intellectual, and political development as a strong human narrative without the ''fictionalizing'' of dialogue and events. He does seek colorful atmospheric detail (and slips when he refers to a hot night spot in Boston's ''Negro district'' as the Totem Pole, which was the name of a cool, non-alcoholic ballroom in the suburbs). His depiction of a meeting between black leaders and President Kennedy draws on Kennedy aide Arthur Schlesinger Jr.'s firsthand account, but omits Schlesinger's criticism of King.

But this 500-page (plus references) volume gives an impression of balance and authenticity befitting a professor of history (University of Massachusetts) and seasoned biographer (Lincoln, John Brown, Nat Turner). Clearly sympathetic to King, it nevertheless does not overlook mistakes, misjudgments, or personal failings of the sort sought out to discredit him by J. Edgar Hoover, who was then FBI director.

The net effect is to confirm for a new generation the extraordinary legacy of Martin Luther King as a generator of concern and action for liberty and justice. He marched for the rights of the black and the poor which are so often neglected. But the dream conveyed in this book is for the rights of all.

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