No. It just happens about every 10 minutes. It rings twice and sounds like a bicycle bell. I think it has something to do with when the phone sinks the emails, but I have the setting on it to silent.
Other things to try:
In your e-mail notification settings, do you have Priority Senders turned on and if so, is the notification sound Postman? If so, change it to silent or turn it off.
Are you using Verizon Messages? If so, tap the three lines in the upper left-hand corner, then Settings, then Repeat Reminder and ensure it's set to Never.