Disabling system sounds and alerts without disabling application notification sounds

Is there a way to disable all alerts without disabling notifications for certain apps? For instance, every time I adjust the volume with the keyboard it plays an annoying bing sound, and the only way I know to disable it is to mute System Sounds in settings. This is fine except muting System Sounds mutes the notification sound that plays whenever my thunderbird inbox receives a new message. System Sounds