The three-minutes thing was established before Vaudeville. It dates back so far, before the formal definition of “minutes”, it has not yet been tracked.
The principal is that this is the amount of time that it takes to complete the telling of a story. While not being so long that those not interested stop paying attention or, in the 20th Century, tune to another radio station. No science supports this. It is a tradition. One of things that “seems to work”.
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