My MGX-21 makes a noise after you shut it off on a hot day that has been described as a whale in heat. The whining noise comes from under the tank. The bike is releasing air pressure slooooowly through some sort emission friendly canister. The noise is embarrassing when people approach you to ask questions about the bike, which happens a lot. So here's how I took care of it.
1. Remove the two allen screws holding the metal cover that extends from the gas cap to the key hole. (see pic)

2. Remove gas cap then carefully pull the metal cover back towards the seat and it comes right off. (see pic)

3. Cut about 1/2 inch off of the black vent line and add a "Y" to it. You can get an assortment "Y" vacuum adapters from the your local auto parts for about $5.
4. I added a "Gas Tank Vent Line" purchased on Ebay for about $4 on the 3rd output of the "Y" (see pic). It's designed to let the tank breath, but not let any gas out should the bike fall. Many dirt bikes use these vent lines.

5. Put your metal cover back on and tighten the two allen screws.
6. Done!! No more whining noise.
I've seen similar complaints for the California 1400. I assume a similar modification would work for that bike too.