Dann was born in Canton, Pennsylvania to a musical family and studied music in Boston before returning to his hometown to teach music lessons and lead a church choir and community chorus. In 1886, he became principal of the academy at Havana, New York (now Montour Falls).
In 1887, Dann was hired to teach penmanship in the public schools in Ithaca, New York with the promise that he could also begin instruction in music. Music education was rarely included in the school curriculum in this era. Dann founded and directed a high school chorus and men's chorus, while also directing the local Presbyterian Church Choir. After the founding of the Ithaca Conservatory of Music in 1892, Dann served on the school's executive committee. He remained the supervisor of music in Ithaca schools until 1905.
In 1889, Dann became director of the Cornell University Glee Club, a position he would hold for 32 years. He significantly raised the musicality of the ensemble, beginning a tradition of tours and bringing the choir to England in 1895, one of the first international tours by an American choral ensemble. On this tour, the men were hosted by the Savage Club of London, and a similar organization was founded in Ithaca upon their return.
After judging a local band competition in 1894, Dann helped persuade bandleader Patrick Conway to relocate to Ithaca to form the Ithaca Band, teach at the Ithaca Conservatory, and lead the Cornell Cadet Band (now the Cornell Big Red Marching Band).
Dann was hired by Cornell University in 1903 as instructor of music to begin a department of music at the university. He was promoted to assistant professor in 1904 and full professor in 1907. In addition to leading choral activities and overseeing music at Sage Chapel, Dann organized annual music festivals between 1904 and 1920, bringing nationally famous soloists and orchestras to Ithaca to perform major works. He also began the Cornell concert series to regularly bring noted musicians to campus.