------------- ------It's awesome to see this thread back from the dead.
It took me months to figure out what the issue is.
Now I am used to seeing Gmail pop up on the screen when that sound is made.
It was driving me crazy.
Glad I could help.
I have had 1 new iphone and 3 new ipads set up and updated the OS in the past two weeks. The chime problem has occurred in all of the new iPads, using all default options, and with gmail. It appeared to be like a bell dinging every quarter hour. I don't recall exactly what I did, but it is something like this.
The name of the regularly occurring sound is Note (default). Notifications-Email-Sounds -- remove sound or change it to something like swoosh, which is faint. gMail was never listed in the notifications section.
Also, change settings-mail,contacts, calendars-fetch new data should NOT use Fetch, because (surprise!) one of the selections for Fetch is every 15 minutes or hourly or every 30 minutes. You want the Manually option.
Perhaps one of you can fine tune this a little better, but the ding is gone.