The teachers have been picketing the organization's offices in Manhattan since January 19.
According to the New York Times, the starting salary is $40 per hour. But teachers told the paper that they generally work only an hour or two a day, and are not paid for the time spent traveling to schools.
Alan Fischer, the chairman of Midori & Friends, told the Times that the group had offered a 7.5 percent pay increase, but the union asked for a 25 percent raise. He added that it was standard practice to withhold pension payments during an initial probationary period.
Founded by the violinist Midori in 1992, Midori & Friends sends teachers into New York schools for live performances and instrumental instruction. Twenty-three schools, and a total of about 7,500 students, participated in the program last year.