When I’m writing music, one of the primary challenges is figuring out how to notate rhythm in a way that is clear to the interpreters. When I hear a phrase in my head it is free of the confines of bar lines, but, in practical application, eventually it needs to get squeezed into recognisable shapes and containers. Every composer has their own strategy (some eschew bar lines entirely, or use alternative notational strategies outside the traditional western systems), but it’s always a negotiation: does the way the composer notates the rhythm correspond to how it should best appear on the flute player’s music stand?

I have distinct memories of being 13, hearing a piece (specifically, Stravinsky’s Symphony in Three Movements), basically memorising it from the recording, and then being absolutely shocked when I finally saw the score. “That’s where the downbeat is?!” Stravinsky’s sense of time and my understanding of the same were at variance in a way I still find exciting: the idea that there are infinite superimpositions of a practical system (notation) over a medium (sound) most often experienced by an audience without the score. Understanding that notating rhythm is artificial yet crucial requires both personal precision and empathy with future interpreters.

Watching a dance rehearsal as a score-addicted musician is surreal. You can have 30 people in the room, and only two of them will have the score. What is fascinating is that the choreographer has imposed an entirely different, invisible form of notation on the form of their counting, which, in consort with the music, becomes what the dancers memorise and take into their bodies. What I find the most interesting is how the choreographers’ counting system interacts with the score: if my system of notation can feel like dividing a loaf of bread into slices this big or that big, often the dancers are feeling larger, more structural counts. I could have 16 fussy little bars of varying lengths, equalling about 30 seconds, which they will mysteriously but magically hear, and feel, as two cycles of 11 equal beats. Eavesdropping, you’ll hear dancers say “OK, so there’s that pas de chat after the three eights, then five … six … seven …” which is a fantastic alternative cartography.

I don’t find this reality to be at variance with my own sense of time. Indeed, I have found myself, with over 20 years’ experience working with choreographers, learning so much more about the lengths of phrase and the subtle narratives they imply. I can have spent months on tiny details and can easily lose track of a bigger sense of shape, which choreographers and dancers have as a matter of physical instinct. We have a shared vocabulary (“line” or “phrase” come to mind) but I often feel humbled by their fluency in hearing, somehow, a larger heartbeat.

I think about this relationship as a very zoomed-in way in which we are all mostly tethered to the Gregorian calendar, but there are superstructures and microstructures unique to different communities. Just last week, I had a meeting with a director of music at an Oxford chapel, and we spoke about a multi-year project and not a single date was mentioned – it was only “Epiphany” or “the Thursday before Trinity Sunday.” The year can have little gravitational pulls towards bank holidays, birthdays, yahrzeits; the exigencies of the garden and its various plantings and harvests can become the dominant way of dividing up time.

Most of my work with dance comprises commissions where the dance and the music are developed together, sometimes in a round-robin way where I’ll provide some sketches, videos of movement will appear in an inbox, more sketches, and so on. I’ve found the best way to operate in that environment is to have the world’s fastest conversation about structure – Benjamin Millepied, my oldest collaborator, and I try to figure the whole thing out over a meal – followed by a list of things we both want to try out. A giant passacaglia for me, a sextet of just men for him. A section with only metallic instruments for me, an incredibly kinetic sequence of motion against spare, severe music for him.

This month, I have the enormous pleasure of having three works of mine choreographed by three very different choreographers: Michael Keegan-Dolan, Maud Le Pladec and Jules Cunningham. It goes without saying that their work is incredibly different, but what I’m finding most fascinating about the process is watching them juxtapose their own sense of time on the music.

Michael Keegan-Dolan, for instance, has taken a piece that sets a traditional murder ballad, The Two Sisters. The narrative of the ballad is still there, sung live by the singer Sam Amidon, but what Michael has done is to impose a sort of ritual, informed by his own deep theatrical engagement with any source material. It both amplifies and offsets the patterns of the folk music in a way I could never do with music alone.

Jules Cunningham has been working with a set of drone-based pieces. The solo lines are notated such that the rhythms are tight within the phrases, but there is room between them to play. Jules’ note to me after the first read-through with the ensemble was that they wanted a bit more breath before the phrases: a comment indicated with a small exhalation. It’s a musical request (happily obeyed!) stemming directly from their own embodied experience of moving to the music. We use the same term in rehearsals (“could you just put a little bit of a breath between bar 13 and 14”) but it usually comes from a more distant or abstract musical instinct, often given top-down from the conductor or composer.

And Maud Le Pladec has made a piece where her trio of dancers adhere to the music in an incredibly precise way. All three movements of the music are quite fast, but sometimes, fast music can be quite slow, and slow music can be hiding a rapidly beating pulse. Her movement picks up on this, and in response, the Britten Sinfonia are invited to imbue their performance with this fast-within-slow energy, “visualising” semiquavers even though the notes they’re playing are much, much longer. It’s an interpretative strategy informed by bodies – for me it’s also a welcome change from the sometimes theoretical and arbitrary practices which can govern modern performance.

The next time you find yourself at a dance show, opera or musical, take a moment and pay attention to how tightly the movement is adhering to the music. If the music feels as if it’s in comfortable cycles of four bars, is the dance reinforcing that, resisting it, or complicating it? If the music feels as if it’s floating in outer space, is the dance offering it a scaffolding?

When I first moved to New York in 1999, I found myself going to dance more often than I would go to the symphony. Often, my first experience hearing a piece of music live was choreographed: I cannot think about Stravinsky’s violin concerto without seeing Balanchine’s choreography in my head; there is a giant catalogue of chamber music which I can scarcely imagine without seeing whatever brilliant thing Mark Morris made out of it. I’ve also found that music to which choreographers are drawn can be found in a different aisle than whatever is at any given moment in concert halls and opera houses. Their sense of which music compels them is rooted in the body, and the immediacy of that engagement makes me hear music differently, and know it in a more complex and rich way.

• Marking Time: Nico Muhly / Michael Keegan-Dolan / Maud Le Pladec / Jules Cunningham and the Britten Sinfonia is at Sadler’s Wells, London, from 20-22 November.