I, too, have this issue with notification sounds. It's the little "ring" when anything occurs and shows up in the top bar. Doesn't matter if it's email, text, app update etc. I just want to turn the damn thing off without using blocking. If I can set the "sound" I can use a blank audio file...just can't find where the sound file resides.
I'm surprised it hasn't been stickied already (I'll probably add this to the FAQ's, just in case) and this is likely been discussed before (apologies in advance for the redundant re-hash), but here are the different settings to check, just to be sure that no sound notifications go off:
General Notification Sound Settings
System Settings>Sound>Notification Sounds>Select "Silent" (should be one of the ringtone selections at the top of the sound list)
For Gmail Application
While in the Gmail Application
Menu>Settings>Click on Gmail Account that's logged in (or if multiple accounts, click on specific account)>Inbox sound & vibrate>Sound>Select "Silent" (should be one of the ringtone selections at the top of the sound list, below "Default ringtone").
*If default notification ringtone is set to "silent", then selecting "Default Ringtone" should work as well.
For Email Application
While in the Email Application
Menu>Settings>GeneralSettings>Select Ringtone>Select "Silent" (should be one of the ringtone selections at the top of the sound list).
For Facebook Application
While in Facebook Application
Menu>Settings>Notification ringtone>Select "Silent" (should be one of the ringtone selections at the top of the sound list, below "Default ringtone").
*If default notification ringtone is set to "silent", then selecting "Default Ringtone" should work as well.
For Twitter Application
While in Twitter Application
Menu>Settings>Click on acccount that's logged in>Notifcations Toggled>Ringtone>Select "Silent" (should be one of the ringtone selections at the top of the sound list, below "Default ringtone").
*If default notification ringtone is set to "silent", then selecting "Default Ringtone" should work as well.
For Google +
While in Google Plus Application
Menu>Settings>Click on account that's logged in (or if multiple accounts, click on specific account)>Notifications>Ringtone>Select "Silent" (should be one of the ringtone selections at the top of the sound list, below "Default ringtone").
*If default notification ringtone is set to "silent", then selecting "Default Ringtone" should work as well.
For Calendar
While in Calendar app
Menu>Settings>EventNotification>Select Ringtone>Select "Silent" (should be one of the ringtone selections at the top of the sound list).