… It isn’t only the gift and the nerve I notice, it is also the strict discipline of ear nobody has imposed on them but they themselves.
This is from ‘The Nutcracker‘  found in Edwin Denby: Dance Writings, edited by Robert Cornfield and William MacKay (1986):
… there is a powerful dramatic expressiveness in the large opposition between the so-to-speak forest-thick pantomime that fills the first act and leads only too a small clearing where snowflakes dance, and the spaciousness of the second act,with its clear dances that appear and disappear as free as shapes in the sky. The choreographic originality of the second act is not (where I had expected to find it) in decorative fancy. It is in the suddenness with which a dance shape, the shape of a dance, appears and vanishes.
[line break added] Each dance is instantly specific, it keeps its solidity as it rushes through the air, and is instantly gone. It has the grandeur of being complete, of asking nothing, of creating around its brief form a sense of airy stillness, of spacious calm. It seems impossible that so complete an image can be produced so suddenly, prolonged at will, and be so suddenly withdrawn. The effect is magical and powerful.
This next is from ‘In the Abstract’ [1959-60]:
Take the aspect of rhythm which is familiar to everybody when they first learn ballroom dances, the matter of stepping to the measure or beat of music. When you watch couples dancing on the dance floor, most of them step to the measure, but they seem to first hear and then step with a sort of tiny lag. That is the respectable or “square” way of dancing.
[line break added] Other couples, particularly to soft music, don’t hold to the beat, they also step across it — now a bit too soon, now a bit too late — with a swooping flow that corresponds over several measures to a phrase of the music. … These are two kinds of dance rhythm, the first with an even beat, the second with an uneven one, and neither of them builds pressure in the long run.
The high school couples [i.e. teenagers] cultivate a third kind, a kind that builds up pressure. They dance with a rhythmic thrust that is quick and exact, but percussive, not staccato. Watching the beat both as a pulse and as a time unit, they can take the exact lift of the upbeat to dance on. So they dance on top of the beat.
[line break added] They seem to keep on the edge of the upbeat awhile, getting their double balance on it, and they explode in a counterrhythmic break, like wire walkers turning a somersault in the air and landing on the wire again. It isn’t only the gift and the nerve I notice, it is also the strict discipline of ear nobody has imposed on them but they themselves. They are absorbed and dance all-out.
Quite a lot of Americans have danced “on top of the beat” in high school, or have recognized the thrill of it then, watching classmates; and some recognize it in the second generation watching their children and their children’s friends.
… While dance ballets like these are going on, you can recognize the pattern game that music and dance are playing. … Like in a familiar game, you catch the surprise of a fast play. You catch the sudden image the play leaves. And as you follow the nervy, personal impetus by which each of the dancers is individually creating the composite dance, you begin to sense between dance and music — as if it were a slower and larger image that took time to communicate — the image of a real quality of motion the vitality of which is a secret art.
What does “a quality of motion” mean? A girl walking down the street looks wonderfully pretty one moment and average pretty at another. It is your luck if you see her at the right moment. … In art that luck is an image, but in art to really have that luck, a flash isn’t enough, it takes some time.