CCGemini asked Verizon Wireless:
Q: Can you set different ringtones for text messages on the Samsung Galaxy Note 3?
A: Yes, you can set different ringtones for text message alerts in the Samsung Note 3:
1) Open Messages application
2) Press "Menu" button
3) Select "Settings"
4) Select "More" tab
5) You can change the ringtone via the "Select ringtone" option
