I think whistles were designed around a particular musical chord. Took a recording of 487's 5-chime and found the notes on my mom's piano and came up with an A minor chord above middle C. One thing that made it hard is the notes travel on all directions on a 5 chime whistle. Because of the Doppler shift, the notes you hear that are coming from the "backside" of the whistle will be flatter than the notes on "front side" The position of the chime on the base (is the note facing you a lower note or a higher one?) makes a big difference in the appearent tone. This accounts for many otherwise identical appearing whistles to sound so different.
I friend of mine who posesses perfect pitch told me the individual notes on every whistle are a bit off pitch. We theorized that was to take into account doppler pitch shifting.
It is science? Pure luck? Probably a bit of both.