Medievalists.net blog offers a link to an article by David M. Guion dealing with wind bands from the 14th through 19th centuries. The article, published in the Journal of Band Research, Vol.42 (2007) is entitled: Wind bands in towns, courts, and churches from the Middle Ages to the Baroque.
From the article:
In the middle of the fourteenth century, a new musical institution consisting of trumpets and shawms began to take shape. Scholars of Medieval and Renaissance music refer to these as alta bands. This term is never used to describe bands past about the middle of the sixteenth century, and yet descendants of the alta bands thrived until the middle of the seventeenth century and survived in some places well into the nineteenth century. Trombones rather quickly replaced the trumpets. Somewhat later, and much less completely, cornetts replaced the shawms. Bandsmen were expected to play other instruments besides cornetts and trombones. In many places, the other instruments eventually replaced them some time during the seventeenth century. Towns such as Bologna and Leipzig, on the other hand, continued to support what at least nominally remained cornett and trombone ensembles well into the eighteenth century. Alta bands first appeared in towns. By the end of the fourteenth century, they became conspicuous features in the courts of kings and other nobility. By the middle of the sixteenth century, many churches and monasteries also formed bands.