Though initially disguised under a variety of names, such as German Dance or Landler, as it emerged in central Europe in the mid-18th century, the waltz has always exploited triple time - three beats in a bar - whether as a slowish glide or a fastish dash, and has always involved clasped partners whirling one another around.
The latter development soon moved moralists to denounce the lascivious waltz as the downfall of civilisation, but to no avail - not least, because composers of the calibre of Mozart, Beethoven and Schubert realised that they could turn a penny on the side by scribbling sets of waltzes for court occasions or for the bourgeoise music trade. In the 1790s, the waltz was already a popular craze - by 1819, it was aspiring to the highest flights of art.
That year, the Viennese publisher Anton Diabelli sent a modest little waltz of his own making to some 50 composers, including Schubert and the very young Liszt, requesting a variation from each to put out in a collected volume. Yet what he got back from Beethoven some three years later was a set of no less than 33 variations comprising one of the profoundest masterpieces in the history of piano music. Meanwhile, Weber published a rondo for piano comprising a chain of waltzes enclosed between a more poetic introduction and epilogue. Subsequently orchestrated by Berlioz under the title of L'Invitation a la Valse, this was to become the model for the waltz sequences developed by such dance band leaders as Joseph Lanmar and Johann Strauss the elder in the 1830s and '40s, and brought to perfection in such masterpieces of Strauss's most famous son as On the Beautiful Blue Danube (1867). By now, the introductions were symphonic elaborations, magical summonses to the couples at an Imperial ball to drift dreamily on to the floor before moving as one into the great circle of the opening waltz itself.
In fact, Berlioz had long since introduced the waltz into the symphony proper in his Sonfonia Fantastique (1830), while Chopin and Liszt had developed the piano waltz into a vehicle for the subtlest nuances or the most diabolical display.
By the mid-19th century, the waltz seemed ubiquitous, infusing the symphonies of Tchaikovsky as audibly as his ballets, and insinuating its way into the most private piano pieces of Brahms. Even when the young Richard Strauss (no relation) sought to evoke the "dance song" of the Nietzschian Superman in his tone-poem Also Sprach Zarathustra (1826), he moved without the slightest inhibition into a Viennese waltz.
And this pervasiveness was not confined to ballroom or concert hall. The chorus of Hebrew slaves in Verdi's early opera Nabucco was already a kind of slow waltz; Gounod contrived to slip the flightiest French valse into Faust, and even Wagner ultimately succumbed, evoking the Flower Maidens in Parsifal in what he called an "American waltz" - by which he can only have meant the slow genre known as the Boston.
Then in the 1900s, as if the pre-eminence of the waltz had raised it to a kind of early-warning system of the zeitgeist, something happened. Suddenly the waltz passages in Mahler's Fifth Symphony (1902) turned self- conscious and satirical; suddenly, in the run-up to the First World War, there appeared a whole clutch of scores - Ravel's Valses Nobles et Sentimentales, Debussy's Jeux, Berg's Reigem from his Three Orchestral Pieces - in which waltz structures seem to dissolve, leaving mere drifts of feeling. Meanwhile, Stravinsky was syphoning off the feeling, leaving the mere mechanics in such dry little numbers as the waltz in A Soldier's Tale (1918), though it fell, once more, to Ravel to deliver what some have heard as the symphonic deathblow with his vision of Imperial Vienna whirling itself to oblivion in La Valse (1920). True, the cult of the waltz lingered longer among composers of genteel light music and in the domains of the musical and the film score, but it was increasingly fodder for modes of nostalgic pastiche. As for waltzing itself, this now seems mainly confined to the ever more stylised world of ballroom dancing.
Well, doubtless the most popular forms have had their day, and, if we no longer write or dance waltzes, neither do we minnets or jigs. But there is something else here. Any survey of dance music since it began to be written down in quantity during the Renaissance period will quickly reveal how the dominant dances at particular periods have tended to divide rather evenly between those in duple time - two or four beats in a bar - and those in triple. This complementary relationship even held in the 19th century when the waltz, at its zenith, was almost rivalled in popularity by the duple-time polka.
It is at this point that one comes across a historical anomaly in 20th century dance music - indeed, in popular music as a whole - so pervasive it is rarely even remarked upon. If one surveys the commercialisation of the popular, from the emergence of ragtime, jazz and such dances as the tango, before the mid-20th century and the evolution of rock, pop, disco and so on since, one finds it has been overwhelmingly cast in duple time. Of course, exceptions spring to mind, from the odd ragtime waltz by Scott Joplin to the occasional emergence in the charts over more recent decades of slow triple-time ballads. But the bias remains striking. Nor is it any longer confined to popular genres.
Admittedly, the history of rhythm in 20th century classical music has been complicated by a sustained effort of several generations of "advanced" composers to get away from any sense of regular pulse whatever - to achieve a perpetual irregularity of rhythm in keeping with the perpetual turnover of pitches freed from traditional tonality. Yet in the widespread retreat from such avant-garde aims over the last couple of decades, attempts to restore tonality, particularly in more trundling modes of minimalism, have brought corresponding obsessions with duple time. It is almost as rare to find Philip Glass coming out with a triple-time number as it is Oasis.
In this supposedly pluralistic era, we are therefore confronted by the singular and possibly sinister paradox that the casting of the vast bulk of the most marketable music in one of the two basic metres in Western tradition threatens the marginalisation of the other. No doubt it would take the aesthetic, economic, psychological and philosophical insights of a latter-day Adorno to tease out the implications. For instance, if we accept the old association of duple time - the rhythm of marching, hammering and so on - with masculinity and of triple time with femininity, what does the dominance of the duple really tell us about the status of women? And, as the disco beats boom through the shopping malls, do we begin to sense the oppression of social control behind the glittering consumer choices?
In duple time, after all, the metre is all downbeats, whereas triple time offers the vastly expanded possibilities of complementary upbeats. Which is just one of the reasons why composers seeking to achieve something genuinely fresh could do worse than to sample once more the resources of rhythm and phrasing latent in the evolution of that old, old Straussian waltz.
Composer of the Week, BBC Radio 3 from noon, Monday 4 May.