In my opinion, all bandstands are different and do stand apart from each other be it in their size, shape or overall style along with their general location and setting.
The important and very necessary components of a bandstand includes, of course, its stage and roof with every other element lending to its style. Normally the roof of the structure shows the marked difference between each of them. But in the turn-of-the-century bandstands, many were just raised platforms with railings and no roofs which did afford the audience a full view of the band being showcased but in time, it was found that these performers, their instruments and sheet music, were not protected from those fast-moving summer storms which sometimes raised havoc on the band concerts. Also, the sound reverberated upwards with no soundboards (roofs) controlling the essence of the music.
Thus the bandstand's roof is a very essential part of the structure since it not only affords the bands performing protection from the wind and inclement weather, but also sets the "tone" of the music being played as well as adding to the decorative style of the structure. Many of the bandstands' roofs being built during those earlier days were peaked or rounded with added decorative vanes that helped showcase these roofs which really mimicked a trend in homes built then that had large porches with elaborately decorated octagonal corners. Those large porches were platforms for people to socialize on, during the warmer months of the summer, and were places where people could just sit back and relax and enjoy each others' company while discussing the general topics of the day.