That milkmaid Maharaj portrayed at one point: what was she doing, so interestingly, with her hands? Petting a dog? Making dinner? Because kathak is such a perfect, specific flower of Indian history and religion, it looks foreign, like Kabuki, and therefore it might seem that, despite the large Indian populations living in Western capitals, this form could have no effect on Western dancing.

Maybe a jazz musician could have counted out Sen’s nine-and-a-half-beat phrase, but I couldn’t. Occasionally, for this reason, it is confounding. Kathak is probably at least eight hundred years old, and in that time it has developed extraordinary subtlety. In a tale from the Ramayana, Sen was now a virtuous wife, now the god who seduced her, now the enraged husband, and also the river flowing by. In these routines, the kathak performer often plays several characters. And that’s not to speak of the mime dances, usually based on Hindu mythology, that are done in alternation with the rhythm studies.

You can’t believe it-that so many different things are coming out of one source. The dancer may be spinning like a rotary blade, but, from second to second, the head and arms are making exactly this shape, then exactly that. She accomplished it by taking some of the beats at double speed, and that is something else about kathak: how fast it gets, with no sacrifice of clarity. Saswati Sen did a dance to a count of nine and a half, a feat few people would have dreamed of. He showed us how to lay a three-count foot-stamping phrase over a four-count musical phrase, and how to fit fives into sixteens. Nevertheless, he was soon demonstrating the advanced-math rhythms that kathak is famous for. In this show, he was spelled by two disciples, Saswati Sen and Mahua Shankar. Maharaj is sixty-eight, and he has slowed down.

Early this month, Pandit Birju Maharaj, the reigning guru of kathak-a dance form that grew up in the Hindu temples and the Mughal courts of northern India-gave a concert at the Peter Norton Symphony Space that may have been the most remarkable display of musical chops to hit the New York dance stage this year. Globalization may have its downside, but it could do something for modern dance that a lot of people would appreciate namely, restore musicality.

Kathak music beats