Mute Fuchsia City or Cerulean City is a glitch in Pokémon Red, Blue, Yellow.
If the player runs out of Safari Zone steps in the Safari Zone gate when the welcome NPC should be telling the player if they want to continue playing, they will be warped and after stepping out to Fuchsia City there will be no music. Getting on and off the Bicycle will enable the music again.
Muting locations other than Fuchsia City
The following method has the same effect on the music, and combines the Glitch City trick to mute the gatehouse, and then any location which you warp to (which hopefully loads the location correctly), so you don't necessarily have to mute Fuschia City.
The aim is to enter the Safari Zone, enter an entrance and then black out at the same time. If you do this you will black out and return to the location of the last Pokémon Center, and then after one step return to the Safari Zone gatehouse (with no music). Then, if you walk out you will be returned to the last location, also with no music.
1) In front of the Safari Zone, have a poisoned Pokémon and aim it to faint and make a black out when you enter a door and use what would be your last 500th Safari Zone step at the same time (125 HP works). Oddly, walking automatically (e.g. via the Safari Zone P.A) does not affect the poison count. (The poison count is usually 1 HP every 4 steps).
2) Land the last step on a Safari Zone door, then simultaneously black out.
3) You technically have 0 Safari Zone steps now, but the P.A. hasn't called you.
4) This is where the glitch happens; if you make an extra Safari Zone step, technically you've walked an extra step you weren't allowed.
5) This mutes the Safari Zone gatehouse, the location you walk out to and for some reason certain buildings within that location.
6) Other buildings, using the Bicycle, walking to a new route, teleporting and flying away restore the music.