I cannot, for the life of me, figure out how to turn off the notification sounds. I found the option in settings for the notification sounds, but none of the options are to turn it off or silence it, without silencing the whole phone!
OK. I think I figured it out. It's this whole stupid interruption mode feature. Setting the phone to Priority Only, and then enabling all incoming calls and messages achieves the same result as disabling the notification sounds. This is a horrible design IMHO.
Go to settings, sound and notifications, apps. Then select which apps give you notifications and how they do it (sounds, notification bar etc)
Use a silent tone, meaning a notification tone that doesn't include any noise. You might find some here.
Go into the email app, click the three dots in a row, select settings, select the email account you will see notification settings; select silent
The one person above had the correct answer. You have to go into your email account, click the three dots on top left, choose settings, and then click the account you want to change. In there is a notification setting where you can silence the notification.