I've been using ViPER4Android (V4A) for all my recent devices including the Droid DNA, S3, and the S4. So, naturally, I needed to get it on my Note 3 ASAP. There's two apps as part of this sound mod, but one is optional. The main app is called ViPER4Android FX. The current version is 22.214.171.124 and is compatible with stock rooted VZN Note 3. I use the optional app, ViPER4Android XHiFi, for superior bass and treble adjustment.
The newer versions of V4A allow for both system and user installations, but I've always installed it as a system app to ensure that it works 100% of the time (including watching movies with MX Player, YouTube, streaming with Google Play Music, etc.) So, my N3 installation instructions are as follows (note: your device MUST be rooted):
1) Download the app(s) from the original xda thread. Extract the 4.x versions of the apks from the .zip files.
2) Push both apks to system\app. Reboot so permissions get automatically fixed or manually change to rw-r-r-. (First screenie using Root Explorer).
3) Launch each app separately. Grant root access to each of them to install their drivers. They'll both prompt you to install drivers on first launch. Choose "Super Audio Quality" driver for FX. We have a quad core processor, so it can easily handle it. XHiFi is being phased out but still adds a richness I can't find in using FX alone. You must manually choose the bottom option. Reboot so it automatically fixes the permissions of the newly installed drivers.
4) After reboot, immediately go to settings\sound\music effects and choose ViPER4Android FX as the default sound processor (second screenie). NOTE: If you have a custom ROM, Music Effects may have been removed by your developer. Continue to the next step.
5) Open up /system/build.prop in text editor using any file explorer with root access. Change these lines (the bottom two apply to the VZN N3):
Ipa.decode=true to lpa.decode=false tunnel.decode=true to tunnel.decode=false lpa.use-stagefright=true to lpa.use-stagefright=false
6) Plug your headphones and start your favorite music app. Start up FX and enable it at the top and then check the driver status. If everything says you're processing, you're good to go. Enjoy the BEST sound on Android.
This is my tried and true installation. You can see from screenies 3 and 4 that it's definitely work on my N3. I'm not sure if installing it as a user app (just clicking the FX apk) will work or not as I didn't even try it. YMMV.
UPDATE: Tip for newer versions since this post was created:
Using the convolver is one of the most important things you can add to customize sound to your liking. You can access the convolver by going the UI Setting in the menu and selecting Moderate or Expert. The app will close and when you open it again, it will be under the equalizer. Once enabled, Download and extract IRS files to <storage>/ViPER4Android/Kernel/<paste files here>. If the directory doesn't exist, simply create it using a file manager. IRS's can be found here: http://forum.xda-developers.com/show....php?t=2216193