At various times it was suggested that engines primarily for freight service should have single tone whistles, while passenger engines should have multiple chime whistles. (The more "chimes" on whistles does not necessarily mean louder) I have seen a air horn catalog that recommends 3-chime (3 seperate bells) horn for freight and 5 chime for passenger. Right now the FRA has a minimum and maximum sound level for air horns (not whistles); Transport Canada specifies the chord their horns must sound.
Horns started out as single bell "cow horns", mostly Leslie or Wabco of various sizes resulting in different pitches. These shifted to multi-chime horns - a few 2 or 4, most were 3. THe 5 chime seems to becoming the modern standard, previously just a few railroads had standardized on 5 chimes for either all or passenger power.
The biggest builders were Nathan/Airchime and Leslie/Supertyphon, Prime made a knock-off of the Leslie. The Leslie S3L (sound a triad) used to be the most used horn (Santa Fe, Union Pacific, others), but that seems to have now shifted to the Nathan/Airchime K5 series (sound a chord).
The reason for multiple tones is to overcome any background noise to provide warning. If you sound a horn or whistle near the same "note" or pitch range of background noise, its sound is lost in the noise. In addition, high pitched noises are more noticeable (aka obnoxious), but do not carry as far due to their short wavelengths. Lower pitches carry farther, the reason all the big ocean going ships and foghorns are very low pitched.
The sound of mainline horns is rapidly changing. TO meet the new FRA standard the railroads are trying to standardize the horns on classes of locomotives. Because of their goofy mounting, the standard arrangement I have seen on many GE's is one bell foward and four bells reversed - bouncing the sound of the top of the radiator hood. Which bells are reversed (aimed back) also changes the pitch. Complaints about the K5LA ("Amtrak" horn) and K5L (Candian tuning) caused some experimentation with the chord. Many of the new horns are now pitched a little lower with Nathan/Airchime making a new larger bell (lower pitched than the others) replacing the smallest bell (highest pitch).