Shortages in the two subject areas have led the Assembly government to make them a priority - along with maths, science, modern languages, design and technology, ICT, English, drama and second-language Welsh - for more grant aid.
Recruitment figures from the General Teaching Council for Wales (GTCW), published last year, showed music teacher posts, particularly in Welsh-medium schools, were particularly difficult to fill, with two or fewer applicants for each job.
Overall, applications for secondary posts were down 1.8 per cent. Jane Davidson, minister for education, lifelong learning and skills, said the new package of teacher-training incentives for those taking postgraduate certificate in education courses in these subjects would bring Wales in line with England.
But critics fear not enough trainees will know about them in time. Eligible maths and science PGCE students will receive a pound;7,200 training grant and a pound;5,000 teaching grant from September.
Other priority subjects, including music and RE, will receive the same training grant with a pound;2,500 teaching grant. Trainees on other secondary courses, including art geography, history, PE and all primary courses, will receive pound;4,200 for training alone.
Peter Black, Lib Dem chair of the Assembly's education, lifelong learning and skills committee, said last week: "The legislation appears to be coming out very late and it seems many students would not have known about changes."
Proposed changes were not put to the Assembly until June 22 this year. But officials said students would have been made aware of intended changes last September.
Monies should be made available to training providers this September, with students receiving their first monthly payment by the end of October.