Do four programmes constitute a season?  Let's not quibble too much; though brief, the ballet season airing on BBC2 and BBC4 this week has some appealing offerings. Judging from the strong focus on famous names (Fonteyn, Bussell) and the best known Tchaikovsky ballets, the Beeb is aiming at a broad general audience, but balletomanes will be happy to see several eminent dancers crop up as talking heads, as well as lots of lovely footage of both contemporary and historic performances.

Clement Crisp, veteran ballet critic, once expressed his appreciation for Ashton’s Scènes de Ballet by saying that “if one had to throw ballets off the back of a sleigh, this would be the last to go.” Charming though the train of thought was that this metaphorical situation provoked (an insomniac ballet critic could muse on it for several nights), it can’t accommodate The Sleeping Beauty, which is to other ballets like the QE2 to Crisp’s sleigh. This behemoth is not going to be thrown anywhere.

Is it odd that, in a bill containing an achingly contemporary première and a classic meditation on the First World War, a pastel-painted present for the Queen Mother’s birthday should race away with the honours?

"Be careful what you wish for," fairy tales teach us. After I wished in December for more bite in Scottish Ballet’s saccharine Hansel and Gretel, along comes this revival of Liam Scarlett’s 2013 version of the same story for the Royal Ballet. Depicting as it does child neglect, domestic violence, paedophilia, murder, psychosis and suicide, Scarlett’s Hansel and Gretel has bite all right.

Ah, Giselle. Despite being cobbled together from a huge stack of 19th-century literary and dramatic tropes – fans of La Sylphide, Robert le Diable, Lucia di Lammermoor, Walter Scott and German Romanticism will feel right at home – and having a score from Adolphe Adam that is definitely not in the first league of ballet music, Giselle is endlessly compelling: the ballet sticks in your mind.

It has been said that Mozart, so prodigiously talented so young, seemed to be merely a vessel through which God, or the music of the spheres, or whichever higher being one chooses, channelled the sounds of heaven. So, too, sometimes, does Balanchine appear to be a vessel through which music is channelled, to take solid form in front of our eyes. And never more so when the music in question is Tchaikovsky.

When dealing with the big beasts of the classical repertoire, the Royal Ballet has a history of both playing it straight and playing it very, very well. Peter Wright’s venerable production of The Nutcracker is a case in point: although sticking close to the original scenario and choreography, Wright (along with designer Julia Trevelyan Oman) created in 1986 a show that feels ever-fresh in 2013.

This triple bill is of works commissioned for the Royal Ballet: Kenneth MacMillan’s The Rite of Spring was first performed in 1962, Wayne McGregor’s Chroma had its debut in 2006 while this is the world premiere of David Dawson’s first ballet for Covent Garden, The Human Seasons.

The opening night of the autumn season brings a gala first night, Carlos Acosta’s staging of Petipa’s Hispano-Russo-Austro-Hungarische castanet-fest, Don Quixote, with starry leads (Marianela Nuñez and Acosta himself), a very obviously expensive new production courtesy of West End musical designer Tim Hatley (Shrek and Spamalot), and an amped-up re-orchestrated score from conductor Martin Yates.

The mighty adorable Carlos Acosta is at the London Coliseum this week in all his might and all his adorableness - four times, you may like to know, he appears without his shirt on. This is relevant, because it’s not the preening bare-chestedness of a showbiz egomaniac like some I could name, it demonstrates the desire of a man to shed trappings, to be himself at his most unadorned, adorning the art he loves: classical ballet.