This question can be answered at a broad level by considering the full breadth of historical music. Although we are most aware today of professionals like Bach, who worked for the elite of the time(church and royalty), popular music appears throughout history, although it isn't afforded the same prestige. Think of church hymns, slave songs, drinking songs, or street busking. These musical forms are more immediately reminiscent of today's Billboard Top 40 music because they rely on catchy melody, memorable hooks, and simple "sing-a-long" qualities. So there isn't a definite "turn into" point for three minute songs - those songs were there and existed concurrently with the lengthy works, it's just a question of how much we remember them, how popular they were at the time, and their relationships to prior and future music. For example, here is an archive of 19th century popular songs. A quick sampling shows that typical song lengths are between 2 and 4 minutes - and the in-hindsight-obvious fact that Yankee Doodle is one of the oldest "pop songs" still remembered in the United States.

And, of course, music always appears in new contexts with changes in technology and culture - opera, ballet, soundtracks, recorded singles, elevator music - and each new context changes the expectations afforded. Die Zauberflöte is written as an opera, but we are equally likely today to listen to it outside of the context of the opera. As with other historical artifacts, contextualization is key to getting some understanding of why music was written a certain way at a certain time.