This year sees a deluge of anniversaries of major American speeches. In August, the world marked the 50th anniversary of Martin Luther King's "I have a dream" speech to the 1963 March on Washington. This month is the 150th anniversary of Lincoln's Gettysburg address, and the 50th anniversary of JFK's assassination has provoked memories of his great speeches, including the 1961 inaugural. It's 80 years since President Roosevelt's first inaugural ("the only thing we have to fear is fear itself") and 25 since Jesse Jackson's "keep hope alive" speech to the 1988 Democratic convention. And on 4 November it is five years since Barack Obama acknowledged his victory in the 2008 election with the mantra "yes we can".

These speeches were delivered at different lengths, on different occasions and under different circumstances. The Gettysburg address (all 272 words of it) followed a two-hour eulogy by Edward Everett, the president of Harvard, celebrating a key civil war victory. The King speech was delivered at a rally in support of civil rights. Roosevelt's inaugural was given in the depths of the depression, Kennedy's at the height of the cold war. Jackson had lost the democratic nomination, Obama had won the election.

There is, I want to argue, a crucial difference between the content and therefore the rhetorical method of Obama's speeches and the rest. Nonetheless, they share much more than divides them: in style, reference, technique, subject and inspiration. In his definitive study of Lincoln at Gettysburg, the American scholar Garry Wills points out that the address not only followed Everett's sprawling oration, but supplanted it with a new, plain style of delivery that was to dominate American public speaking from then till now. "All modern political prose," Wills argues, "descends from the Gettysburg address."

No wonder, then, how many of these speeches start with reference to anniversaries and go on to refer to each other. The opening of Gettysburg harks back to American independence ("four score and seven years ago our fathers brought forth upon this continent a new nation"), the "I have a dream" speech to Lincoln's emancipation proclamation. Both Kennedy and Obama quoted Lincoln; accepting his party's nomination in 2008, Obama quoted and cited King. Unsurprisingly, there are myriad references to and quotations from the Bible. Although there is an important difference between how and why they use them, all of these speechmakers draw on the same repertoire of rhetorical devices.

As Wills argues, Lincoln uses repetition of words as "a kind of hook-and-eye method for joining the parts of his address": there's hardly a sentence that doesn't repeat a word in the preceding one, from "nation" and "conceived" to "consecrated" and "dead". Lincoln hands on one particular form of repetition, the anaphora (a word or phrase repeated in the same place in successive phrases or sentences), from Kennedy's "let both sides …" to Obama's "it's the answer … ". All of them use contrasts, from Lincoln's "the world will little note, nor long remember, what we say here, but it can never forget what they did here," to King's "we cannot be satisfied as long as a Negro in Mississippi cannot vote and a Negro in New York believes he has nothing for which to vote". In Kennedy's case, contrast takes the particular form of the chiasmus, in which one phrase is echoed in the opposite direction ("Let us never negotiate out of fear, but let us never fear to negotiate"); a figure taken up by Jackson ("I was born in the slum, but the slum was not born in me"). Most follow the rule of three, from Lincoln's "in a larger sense, we cannot dedicate – we cannot consecrate – we cannot hallow this ground" to Obama's "America, we can come so far. We have seen so much. But there is so much more to do."

Of course, these devices are by no means exclusively American. As Max Atkinson makes clear in his analysis of speechmaking, Lend Me Your Ears, contrast and tripling appear in speech after speech, time after time. In his wartime broadcasts, Churchill used anaphora ("we will fight them" on the beaches, landing-grounds, fields, streets and hills), contrast (so much "owed by so many to so few") and chiasmus (not "the beginning of the end" but perhaps "the end of the beginning"). But it's the sheer quantity of these devices that gives American rhetoric its peculiar rhythmic power, its musicality, and – often – its meaning.

So Lincoln's repetitions are not just a baton passed from sentence to sentence, but a drumbeat (the word "dedicate" appears in every sentence but one). Kennedy uses chiasmus like a hammer ("ask not what your country can do for you; ask what you can do for your country"). Obama's 2012 victory speech had four anaphora (as did Jesse Jackson's speech in 1988), and King's no less than seven (apart from "I have a dream" itself, "one hundred years later …", "we refuse to believe …", "now is the time …", "we can never be satisfied …", "with this faith …" and "let freedom ring").

But if all of these orators cram their rhetorical devices together to an unprecedented degree, they are differently distributed. Atkinson calculates that, in his inaugural, Kennedy employs contrast every 39 seconds, but uses hardly any triples. King's written text contains 18 contrasts, from "a joyous daybreak to end the long night of their captivity" to "transform the jangling discords of our nation into a beautiful symphony of brotherhood". Obama, on the other hand, favours triples (there were 13 in the speech that launched him to national prominence at the 2004 Democratic convention, and 20 in the "yes we can" speech).

The difference between King and Obama's favoured figure is much more than a matter of taste, technique or style. Contrasts and triples express different views of the world. Contrasts reveal binaries and present choices, multiples accrete evidence for a single case. Which you choose betrays not just your subject but your attitude.

So Kennedy's contrast-laden speech was (predominantly) about what he saw as the conflict between freedom and tyranny. The first section of Roosevelt's inaugural is about how the rich let down the American masses, and most of the paragraphs consist of two contrasting sentences. At the end, Roosevelt offers a prospect of national unity, and the paragraphs expand to a lilting three. And while Lincoln, King, Jackson and Obama all address the division between free states and slave states, north and south, blue and red America, King sees that contest in terms of unresolved binaries, Obama as a barrier that can be overcome.

Obama is a master of the personal anecdote and the telling example (neither of which feature in Lincoln, Kennedy or King's speeches at all). In this he follows Jackson, whose 1988 speech includes an evocative list of the sort of Americans who lost out in the 80s: redundant workers, farmers losing land to bad loans, students who can't afford college. Obama picks this device up again and again. In his 2004 critique of Bush's America, he cites children who can't read, seniors who can't pay for prescriptions, Arab-Americans rounded up without due process. In 2012 he accentuates the positive: an immigrant's daughter pledging allegiance to the flag, a Chicago youth seeing a life "beyond the nearest street corner", the furniture worker's child in North Carolina who wants to become a doctor or an engineer. When Obama challenges the division between red states and blue states, he lists examples of attitudes and phenomena – religious belief, hostility to censorship, gay communities – that are supposedly restricted to one or other but are actually present in both.

The fact that Martin Luther King is held to have taken a similarly conciliatory view is due to the most famous section of his 1963 speech, which King decided to substitute for the written ending as he spoke. As Gary Younge relates in his book The Speech, King's aides advised him against repeating the "I have a dream" mantra (which he'd delivered at least twice before) on the grounds that it was cliched and trite. Certainly, as black militancy deepened in the years that followed, the last section of the speech was seen as weak and sentimental. If it's true that contrasts are about conflict and multiples tend to the conciliatory, King's ending would be a wonderful example: following his seven dreams, King calls for freedom to ring from five northern and western states and three in the south.

Taken on their own, as a couple of soundbites, these tropes support the argument that King's speech was merely a call for peace, love and harmony. But in the context of the speech as a whole, with its insistent repetition of contrasts between the world as it should be and the world as it was, the end seems less a flight of fancy about the future than a critique of now. In the context of the failure of America to deliver on the emancipation proclamation, the extent of discrimination, violence and poverty, and the urgent need for what King called a "whirlwind of revolt", King's dream for his children to be judged "not by the colour of their skin but by the content of their character" is all about students and voters in the south being judged entirely by the colour of their skin. And when King demands that freedom ring from "the prodigious hilltops of New Hampshire" and "the curvaceous slopes of California", he does so not to celebrate these admirable places but to contrast them with Stone Mountain of Georgia, Lookout Mountain of Tennessee and "every hill and molehill of Mississippi". The soaring multiples are organised by the binary contrast between one kind of country and another, the same binary which Lincoln posited 100 years earlier at Gettysburg.

As Younge argues, both King's speech and Obama's victory have been celebrated for asserting that, now, African-Americans are indeed judged by the content of their character, and can succeed on their own. On election night last year, Obama asserted that "whether you're black or white or Hispanic or Asian or Native American or young or old or rich or poor, abled, disabled, gay or straight", you can "make it here in America if you're willing to try". But after citing a comparable list – "black men and white men, Jews and Gentiles, Protestants and Catholics" – King looked forward to something different: a day when "all of God's children" would be able to sing "Free at last! Free at last! Thank God almighty, we're free at last", not as individuals but as a people.

In finishing with a triple repeat and an extended last phrase, King anticipated Jackson ("Keep hope alive. Keep hope alive. On tomorrow night and beyond, keep hope alive") and echoed Lincoln ("that government of the people, by the people and for the people, shall not perish from the earth"). Fifty years on, would he feel that any of those ambitions has been fully achieved?

• Gary Younge's The Speech is published by Guardian Books