To James' point: Bernie's 3 chime would rattle my eardrums, but only on the fireman's side. At some point the loudness exceeds the dynamic range of our ears. In my experience this worsens with age. Higher frequencies are worse.
On the other hand, the point is for it to be heard at a distance. So we have conflicting requirements.
Whistles work by putting a loud noise (the steam hitting the lip) into a resonant chamber, the bell, which emphasizes the frequency whose wavelength is roughly 4 times the length. Other frequencies produced are harmonics whose wavelengths are at odd multiples of the fundamental. See Wikipedia for 'Steam whistle'.
http://en.wikipedia.org/wiki/Steam_whistleThere will be a quiz.

For the tone, or shrillness, a larger diameter to length ratio should emphasize the lower harmonics and make it less shrill, but, there are other factors too,
such as the material of the bell and the width of the gap that the steam comes out of, the height of the lip of the bell, and the position of the lip with respect to the steam gap (larger diameter or smaller). Of course, once built, the proportion and material of the bell, the gap width, and position are fixed, with the height adjustable.
As Bernie noted, raising the bell height should reduce the amount and pressure of the steam hitting it and therefore the 'shrillness', but may reduce the loudness as well. As suggested, a small deflector might help the loudness in the cab.