Whether the is required in your examples depends on the context:
It was made by machine
is a way of saying that it was made mechanically and not by hand.
It was made by a machine
means that it was made by a machine that has not been identified.
It was made by the machine
means that it was made by a machine that you have already identified.
You cannot say: It was designed/built by architect without an article.
Either: It was designed by an architect (who has not been identified)
Or: It was designed by the architect (whom you have already referred to)
Thus you could write either: It was designed by John Smith, (who is) an architect, or: It was designed by John Smith, the architect (which assumes that John Smith is well known as an architect.
The same rule applies to band. Music is not performed by band, but either by a band (unidentified) or the band (already identified).