So much of the symphonic thinking of the late 19th century is bound up with doing so many things at the same time, through densities of structure and motive, of harmony and counterpoint, that some of the most obvious yet hardest things to achieve in music can get forgotten in a complex symphonic maelstrom of ideas and technicalities. I'm talking about the art of writing tunes: not just any old tunes, either, but composing a whole symphony that teems with tunes that appeal straight to the musical pleasure zones of any listener, but which can also carry and create a whole symphonic edifice.

Which is all an upbeat to this week's symphony, Antonin Dvořák's Eighth. I'm not going to cast Dvořák as some earthy Bohemian in touch with his roots in a way that those bunged-up Germans and Austro-Germanophiles could never be: the Eighth, composed in 1889, would be impossible for Dvořák to have imagined without Beethoven and Brahms as models and catalysts. Yet Dvořák does have a gift that neither of his symphonic predecessors had in the same way, which is that he could compose a seemingly unending torrent of indelible melodies, and he could cast them in crystal-clear orchestration. What's more, in the Eighth Symphony he found a way simultaneously to serve his melodic over-endowment while also creating a kind of symphonic discourse that was definitively his own.

But as well as all of its felicities, this symphony is also, frankly, a popular and even populist pageant of a piece that disguises the brilliance of its construction because its expressive effects are so completely, thrillingly direct, from the miraculous, melancholic waltz of the third movement to the self-assured tune that propels the finale. But you can't have one without the other, immediacy without architecture: Dvořák's is an art that conceals art, and which appeals on many different levels precisely and paradoxically because this symphony's initial impact is so powerful, because Dvořák has distilled his melodic gifts to their symphonic essence.

I'm making this more tortuous than the experience of listening to this perhaps most joyful of all late 19th century symphonies (but you can't have true joy without a sense of darkness, which this piece also contains). So let's begin, with a symphony in G major, as it says on the tin, that actually starts in an achingly expressive G minor with a tune in the cellos, and music that's supposed to be an Allegro con brio ("with movement"), but which sounds in all the world like an andante. A bird-like, arpeggiated tune in the flute signals the movement's true tempo and tonality, but there's still the feeling of an introduction about this section of the symphony, as if Dvořák's just warming us all up for what's to come. You could describe this as an unprecedented elision of time, tonality, and structure in Dvořák's music – which it is! - but the effect it has on you is of unforced naturalness. All of that music comes before a palpitating, perfectly judged crescendo gives way to the main theme of the movement in the strings. Well, I say "main theme": there are a lot of them in this first movement! Instead of Dvořák pulling his melodic material together in some pseudo-'organic' coherence, it's rather that he gives all his tunes space to breathe while also ensuring that they have some resemblances to each other so as to keep them in your ears and brain. That's true on a much bigger scale as well: for example, the main tune of the variations in the finale is based on the same rising arpeggio as the flute's bird-song, which also relates to the first tune you hear in the third movement, and it's expressively comparable to some of the chirruping woodwind music in the slow movement.

The first movement has its most thrilling and adventurous moment at the stormy climax of its central section, which also functions as a kind of bridge to what was the second subject area of the exposition. Ah, those labels – second subject, exposition – how useless they are (as ever) in describing the experience of listening to this piece! The first movement is really in two parts, because you hear what you think is a return to the opening music just over a third of the way through the movement, and then the rest of the Allegro is really an improvisation on those themes, and it ends in a marvellously brusque coda.

I hear the slow movement – in C minor, but it also contains a lot of triumphant, fanfare-festooned music in a major key – as a kind of ironic homage to the C minor funeral march from Beethoven's Eroica Symphony. Some of the melodies and gestures of Dvořák's symphony are similar to Beethoven's, but Dvořák transforms the oppressive tragedy of his Beethovenian model into something much more optimistic. The fanfares in the brass might also derive from those strange militaristic irruptions in the slow movement of Beethoven's Ninth Symphony, but Dvořák's' heartfelt, and hard-won joyfulness by the end of the Adagio is his own achievement. Hard-won? For sure: listen to the chromatic darkness Dvořák creates at the centre of the movement, just when you think the music has found its positivity and major-key solidity; the way the cellos and basses subside into a new and dangerous tonal region, called out by the horns and woodwind – the most chilling image of doubt in the whole symphony.

The Allegretto third movement is pure melancholic deliciousness, and the finale, starting with that bracing trumpet fanfare (as Dvořák's Czech countryman, conductor Rafael Kubelik, has pointed out, trumpets in Bohemia are calls to the dance, not to war) pricks the potential pomposity of the cello theme you hear next with raucous brass writing. Here, it's as if an East-European brass band have suddenly taken over the orchestra – and contains, for me, the symphony's most thrilling moment: the major-key breakthrough of the trumpet call, now accompanied by the whole orchestra, after a violently visceral minor-key episode. After a magnificently lyrical come-down after all this excitement, the very end of the symphony is pure, unalloyed joy, as the music threatens to run away with itself – so much so, it trips up, and ends on the wrong beat of the bar.

Dvořák's musical energy didn't just transfuse new life into his own music, it showed a way for the late 19th century symphony to be profound in its musical implications as well as brilliant and immediate in its communicative power, without all that Teutonic introversion and angst. It's 35 minutes (or so) of life-enhancing joy.

Five key recordings

Rafael Kubelik/Berlin Philharmonic Orchestra: Kubelik's is a benchmark Eighth: expressive, exciting, and irresistible.

Charles Mackerras/Philharmonia Orchestra: Not the quickest Eighth on record, but it's somehow among the most vitally energised.

Herbert von Karajan/Vienna Philharmonic Orchestra: Karajan's is an opulently muscular performance, with an especially sumptuous slow movement, and an outrageous, orgiastic finale.

Charles Munch/Boston Symphony Orchestra: Munch revels in the crispness, clarity, and communicative power of Dvorak's symphony.

Bruno Walter/New York Philharmonic Orchestra: my favourite performance of the Eighth: lithe, flexible – and fast!