This got me close, but for did not work on My HTC 10. Maybe it is provider related, mine is Verizon based (software update 3.18.605.13 9.0_g CL1016573 release-keys). I never saw 'three dots at the top right' per
On my HTC10, this is what I did to fix the problem: Go to Settings -> Sound & notification -> Advanced -> Notifications (at the very bottom).
Then click on the three dots at the top right of your screen to the right of the search icon. Choose "Show system".
If that does not work for you, I went through the Apps path to make the change......Here is the step by step of what worked for me on my HTC10:
Go to settings -> Apps ->
Then click on the three dots at the top right of the screen next to the search icon and choose 'show system'
Scroll down to 'System IU' and select it
Tap on 'App Notifications'
Scoll down and tap directly on 'VZN' letters (that is key here).
Tap 'importance' , then select 'Medium/no Sound'
Thanks to grizzwaldt for getting me close. Hope this might help others turning off that pesky sound if the grizzwaldt approach does not work for you.