In 2015, when Alex Poots, then artistic director of the Manchester International Festival, persuaded the painter Gerhard Richter and composer Arvo Pärt to collaborate for the first time, the result was a quiet sensation; Richter’s enamelled diptychs and sombre abstracts both contrasted and chimed with Pärt’s sweetly innocent and heartfelt chorale, Drei Hirtenkinder aus Fátima, sung by an Estonian choir scattered around the Whitworth Gallery, individual singers emerging from among the visitors, who were at first startled and then enchanted. It was a magical, moving occasion, and one that deserved to be repeated.

Now Poots has moved to New York and is artistic director of The Shed, a $500m cultural centre that opened this weekend, part of the $20bn redevelopment of the Hudson Yards district, currently the largest building project in the United States. His appointment at The Shed was his chance to repeat his success, only this time, with the help of his co-curator, the Serpentine Gallery’s Hans Ulrich Obrist, it is handsomely embellished with new works by Richter and, most importantly, by the additional collaboration of Steve Reich, who has composed a 30-minute piece to complement and enhance a new Richter “moving picture”.

On Friday, visitors to The Shed admiring Richter’s new abstract “wallpapers” and jacquard tapestries found members of the Choir of Trinity Wall Street appearing around them to sing Pärt’s beguiling chorale, its pure-voiced sopranos taking particular advantage of the gallery’s warm acoustic. This served as a prelude to Richter’s moving picture and Reich’s accompanying piece for strings, woodwind, vibraphones and piano.

This second project had its genesis in a book entitled Patterns, in which Richter took an abstract painting from 1990 and, using computer technology, divided it vertically into two halves, then into quarters, making a mirror image of the two quarters. He then divided the painting into fourths, eighths, 16ths and so on up to 4096ths. The result was an image that became more and more dense until it evolved into simple bands of colour, the essence of the original painting.

For his new moving picture he and film-maker Corinna Belz took another painting and reversed the process, multiplying, rather than dividing, so that it starts with plain bands of colour, the image becoming more and more complex until it gradually returns to the original bands.

This is perfect Reich territory. He adopts the same arc process, starting with a simple two-note oscillation which mirrors the two-pixel width of the colour bands. As the pixel count increases so Reich multiplies from two to four to eight, introducing his own colours in his instrumentation – a vibraphone appears when white bleeds into the picture; woodwind chatter excitedly when the patterns become more complex.

The music shifts a gear and becomes denser as the image increases its kaleidoscopic gyrations but the metre changes, with sustained chords sitting underneath playful melodies that jump between strings, woodwind and piano. In one delightful section the vibraphone doubles with a solo violin to produce moments of dazzling, musical light which sail over the velvety harmony like small twinkling stars.

The overwhelming sensation left by Reich’s writing is one of optimism. This is joyful, tonal, clever music. It may be the result of mathematical rigour but it never feels forced or cramped. I long to hear it again, which looks a distinct possibility, as the work was co-commissioned by several European institutions, including London’s Barbican Centre. Lucky New Yorkers can enjoy Reich Richter Pärt until 2 June.

Future performances should not repeat the simple mistakes made at The Shed. Placing the players at one end of the room and the film at the other was one. Providing insufficient chairs, forcing some of the audience to stand, was another. It meant most people had an obscured view of the moving picture. Putting the band in the middle of the room and arranging the audience around it would have solved this. With four shows a day, these problems could have been spotted and solved straight away.

But for all these gripes, Ensemble Signal played with great style, conducted with admirable clarity by Brad Lubman. They had the unnerving presence of the composer in the audience, listening intently to every note – but ready with charming, warm congratulations at the triumphant close.

London should pay close attention to The Shed. It is the work of architects Diller Scofidio + Renfro, the firm commissioned to design the new Centre for Music, and Rockwell Group. While The Shed has extraordinarily adaptable spaces – the roof and walls of the giant main auditorium are on huge wheels and can be rolled back in five minutes to reveal a piazza for open-air performances – its public areas are in an unrelentingly dull black and grey, with polished concrete floors already looking dirty after only a few hours on launch day. The staff, while friendly and eager, often cheerfully admitted to not having a clue about where anything was or why some escalators weren’t working or why some floors had no lavatories.

All these things can be addressed, and London has the advantage of being able to learn from The Shed’s mistakes, before the first spade hits the ground.