They gather blocks from Harvard Square to greet the Sabbath with communal prayer, their eyes winced closed, hands clapping as they sing in fervent Hebrew. The group worships in the Jewish Orthodox tradition, but it's not traditional.

A woman leads the prayers, generally forbidden among mainstream Orthodox. The genders are separated by a white curtain, called a "mechitzah," but it's translucent so the sexes can see each other as they sway and sing. No rabbi leads or synagogue sanctions this service at the Minyan Tehillah, which is run by a software engineer and nurse practitioner.

The group is an "independent minyan," and dozens of these unaffiliated Jewish worship communities have sprung up in the past decade, mixing elements of the mainstream denominations while answering to none of them. Its prayers in Hebrew, with participation of everyone present, is a hallmark of the movement, and a reaction to mainstream alternatives where such prayer is not available, or limited to a designated soloist.

Anna Schachter of Cambridge said the minyan's dual commitment to traditional worship and egalitarianism was energizing.

"Everyone in this room, I feel I'm sort of bonded to them with this mission, this struggle, of 'How do you live a traditional life and a modern life at the same time?'" said Schachter, 29, a public health researcher. "If there was a synagogue that had this kind of style, I would go to it."

Ten years ago, the United States had two independent minyanim, plural of minyan. Today, there at least 70 involving about 20,000 people, said Rabbi Elie Kaunfer, who wrote a book on the independent minyanim, "Empowered Judaism."

"There is a mass of young people, taking hold of their Jewish identity, and willing to put in the volunteer time and effort to build a community that expresses their values," Kaunfer said. "That's extremely hopeful and significant."

The number involved is a small percentage of the estimated 5.2 million Jews in the U.S. But Jonathan Sarna, a professor of American Jewish history at Brandeis University, said the movement is driven by the most devout and educated Jews, and its ideas on worship, prayer and what defines a community will inevitably cross into mainstream practice.

"What happens in American Judaism over and over is that the margins influence the mainstream," Sarna said. "I don't expect many of the independent minyanim themselves will be long lasting. But I think we will look back and say that they had long-lasting influence."

In Jewish law, a minyan is a quorum of at least 10 people (10 men in the Orthodox tradition) that is required to read the Torah or say certain prayers. But a minyan is commonly defined as any community that comes together to pray.

The independent minyanim have formed primarily in urban areas, including New York, as far south as Atlanta, and west to San Francisco and Los Angeles. Sarna said with the middle of the country largely untapped, the movement will grow.

Meg Lederman, a member of a minyan in Brookline, said a major draw of the worship is as a link to her Jewish past.

"It's nice to be in a room where you're filling up the whole room with meaningful words," she said. "It's both the connection to the people in the room and really a connection to Jews across time and space."

The growth of independent minyanim is similar to the grassroots "havurah" movement in the 1960s and 1970s, which organized outside the synagogue with heavy emphasisis on lively prayer and including women. But Kaunfer said a key difference is that the havurah movement wanted to replace Jewish institutions, while independent minyanim aim merely at gaps that have appeared in Jewish life.

Many members are in their 20s and 30s, either single or with very young children, and part of a demographic that has developed as people postpone marriage and children, Kaunfer said. Jews in this group tend to be urban, mobile and unsatisfied by typical synagogue offerings, which are generally aimed at older adults or parents with school-aged kids, he said.

Group members are often highly educated in Jewish tradition — 40 percent are graduates of Jewish day schools. They seek the deep spiritual connection found in traditional prayer that the Orthodox practice, Kaunfer said, but they also want women to be more involved in worship, as in the Conservative and Reform denominations. So they've decided to lead their own services.

Some independent minyanim meet in synagogues, and members are active in them. But the decentralized movement has grown largely without the denominations, whose leaders say they welcome such committed groups of young people, an elusive demographic.

"These are exactly the kind of people we want and need in the community because they're going to be the leaders of the future," said Rabbi Eric Yoffie, president of the Union for Reform Judaism. "The fact that they don't always find a place in the synagogue is something that obviously is troubling to me."

Orthodox Rabbi Shmuel Goldin, first vice president of the Rabbinical Council of America, said he was "thrilled with the energy and the interest." But he added the groups' search for relevance in ancient tradition has led to violations of it, such as with women's role in prayer. Rabbis, he said, have always been crucial in maintaining tradition.

"We are troubled with the change in tradition," Goldin said. "We believe there are ways to find relevance and meaning without these radical changes."

Their self-governing nature means independent minyanim differ in style and emphasis. For instance, Lisa Colton, co-founder of a minyan in Charlottesville, Va., said her minyan's service, held in a friend's living room, stresses interaction between parents and young children that she wasn't finding at the local synagogue she attends.

Colton, 35, said the group isn't interested in changing tradition, just in sharing a kind of worship they realized they could create themselves.

"We don't feel like we're captive to the choices that are handed to us," she said. "That's very different than previous generations."

(This version CORRECTS Corrects spelling of 'Colton' in paragraphs 21-22.)