Music Index
Indexes hundreds of music journals and magazines from many different countries, and provides full text of many articles. It originated as a print publication in 1949; the database covers the years from 1970 to the present. Unlike RILM, it has always included all kinds of music, so it is a good resource for research in fields such as jazz, popular music, ethnomusicology, and music education. 

RILM Abstracts of Music Literature
RILM (Répertoire International de Littérature Musicale) is a vast international bibliography of scholarly writings on music and related disciplines. It covers music journals and other scholarly sources such as Festschriften and conference reports. It began as a print publication in 1967, providing citations and abstracts of articles. The electronic product now has full text of over 300,000 articles. Although its former focus was historical musicology, it now includes many other fields of music.

MULTI-DISCIPLINARY SOURCES:

JStor
A full-text database of journal articles from a large number of disciplines; provides backfiles of whole runs of many important journals in numerous fields, including music. 
CAUTION: JStor is very popular. However, since its specialty is backfiles, this means that it may not provide current issues of the journals you need. Thus, do NOT limit yourself solely to it when searching for articles.

Academic Search Complete
A database providing full-text journal coverage for thousands of journals in diverse academic disciplines, including social sciences, humanities, education, computer sciences, engineering, language and linguistics, arts & literature, medical sciences, and ethnic studies. Helpful for interdisciplinary research.