Istvan, Sometimes, mentally rearranging the sentence can help: Plucking the strings of their instruments, STREET MUSICIANS were going from tavern to tavern. a. As you can see, "plucking the strings of their instruments" refers to the street musicians. (Of course, taverns cannot pluck the strings of instruments.) Thus, your sentence needs a comma after "tavern" to indicate a pause when you say the sentence. Compare: The teacher walked from desk to desk, complimenting each student on his or her good work. Women love to go from store to store, just looking at and sometimes buying the merchandise.

Istvan, It is obvious that the participle phrase "plucking the string..." refers to musicians and not tavern. That gives you two correct choices. If you consider the participle phrase as defining information, then treat is as a restrictive clause without a comma. = Street musicians were going from tavern to tavern plucking the strings of their instruments. On the other hand if you consider the participle phrase extra information, treat it as a non-restrictive clause and use a comma. = Street musicians were going from tavern to tavern, plucking the strings of their instruments.