Boston — ''R-e-s-p-e-c-t,'' Aretha Franklin, the popular ''queen of soul,'' sang in the 1960s. ''And respect is what the black voter is gaining with the triumph of Rep. Harold Washington in the Democratic Party mayoral campaign in Chicago,'' remarks Eddie N. Williams, president of the Joint Center for Political Studies, a black political think tank in the nation's capital.
The primary victory of a black mayoral candidate in Chicago could signal a surge of black political influence in US polling places during the next two years, he says.
Black mayoral candidates in two other major cities, Philadelphia and Boston, have renewed enthusiasm about their own chances. Operation Big Vote, a national campaign to register blacks, has gained new momentum, says its leader, Gracia Hillman of Washington, D.C.
Some analysts point to a possible dampening factor in Washington's victory, however. He depended on getting at least 85 percent of the vote in the black community. A question remains whether he'll be able to attract enough votes from other parts of the city to win in a head-to-head contest with a white opponent. Experts warn of a possible white backlash vote in the final election.
Still, ''Score one point for grass-roots organizing,'' says Ms. Hillman of Mr. Washington's win in Chicago. ''This shows what a nonpartisan, concentrated effort to reach black people on a person-to-person level can do.''
During the past year more than 100,000 new black voters were registered in Chicago, she says. Operation Big Vote is set up in Philadelphia and Boston, too. Overall, it has offices in 35 communities, with plans to expand to 22 more in 1983, she says.
''Our goal is to gain political clout in the 1984 presidential election,'' says Ms. Hillman, director of the National Coalition on Black Voter Participation, which conducts Operation Big Vote.
Observers see increased political activity in black communities during the next two years for these reasons:
* Black candidates are becoming more acceptable to the white electorate. Los Angeles Mayor Tom Bradley's narrow loss in his race for governor of California, the support given black congressional candidate Robert Clark by major newspapers in Jackson, Miss., and Washington's victory in Chicago have all shown that blacks can make a good showing in areas that have been traditionally controlled by white politicians. Such campaigns have also brought ''more respect'' to the black voter, Dr. Williams says.
* The concentration of black people in urban communities, North and South, has given black voters collective power in most of the nation's major cities as well as in key states. In 24 out of 25 of the nation's largest urban school districts, a majority of students are black or other racial minorities.
* Black mayors are gaining in political influence. As a group, they could rival the power of the Congressional Black Caucus, recognized for the past 15 years as the nation's most visible black political force.
The numbers story is told by the 1980 US Census. Blacks have a voting population of more than 1 million in four of the five states with the largest number of electoral votes: California, New York, Texas, and Illinois. They constitute 11 percent or more of the voting-age population of 17 states and the District of Columbia.
More than 100,000 blacks live in 28 of the nation's largest cities, ranging from 17 percent of the population in Los Angeles to 70.8 percent in Gary, Ind. Both cities have black mayors. And black mayors head 30 of the nation's cities with a population of 30,000 or more. These include Detroit; Washington; and Hartford, Conn., outside the South, and New Orleans; Atlanta; Birmingham, Ala.; and Richmond, Va., in the South. All these are cities with crucial votes in state and federal elections.
Mayor Richard G. Hatcher of Gary hosted a Feb. 13 meeting of black political, civil-rights, and community leaders, who discussed the possibility of offering a black presidential candidate in the nation's Democratic Party primaries in 1984.
The black mayoral candidates in Philadelphia and Boston are encouraged by the victory of Representative Washington in the Chicago Democratic primary.
'' My new bumper stickers will read, 'Boston can win, Mel King for Mayor,' '' says Melvin H. King, a former state legislator running among a host of candidates in this city. He is modeling his bumper stickers after those used in Chicago, which said ''Chicago can win, Washington for Mayor.''
In a more serious tone, he adds, ''Black people understand the importance of voting for what they want, not for what they're told they can get. Boston is similar to Chicago, a crowded field, making the black vote more potent. I'll need 85 percent of the (black) vote here to win, too.''
In Philadelphia W. Wilson Goode is facing former Mayor Frank Rizzo in the Democratic primary scheduled for April.
The Chicago vote proves the point ''I'm emphasizing in Philadelphia - voters will choose a candidate with programs for the future over those looking back to the past,'' says Mr. Goode.
Both Philadelphia and Chicago are 40 percent black, but Goode will need more white votes because he is running head to head with Rizzo, says his campaign communications director, William Epstein.