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I see that you are only experiencing this issue with music and not movies. Here are some steps that I would recommend starting with that I attached from the article below.
4. Check your network connection
Home Sharing requires a home network with an active Internet connection. All the devices you want to use with Home Sharing need to be connected to your home network.
In addition, verify that:
- All your devices are connected to the same router, if you have multiple routers. Using multiple routers may prevent discovery between these devices.
- Your devices are not using a Virtual Private Network (VPN), or that they are all on the same VPN. A VPN may isolate the device and cause connectivity disruptions.
- If you have a router set up with a guest network, make sure all devices are either connected to the guest network and devices on the guest network are allowed to communicate with each other, or switch all devices to the primary network on your router.
- If your computer is asleep or shutdown, or iTunes is closed, there's no access to the shared iTunes library. Wake up or start the computer and open iTunes to regain access to that library.
- Your router needs to be up-to-date. If you are using an AirPort or Time Capsule, learn about firmware updates. If you are using a router from another manufacturer, contact the manufacturer to inquire about available updates.
5. Check Firewall settings
If you have a firewall enabled in your router or computer, make sure that the firewall is not blocking communication between your computers. Home Sharing uses TCP port 3689 and UDP port 5353 to communicate with shared iTunes libraries.In addition, Apple TV and Mac computers will use port 123 to set the time automatically. Incorrect date and time on either the computer or Apple TV can cause errors for Home Sharing and connections in general.If you are unsure whether your router has a firewall or the required ports open, test additional devices or another network to help isolate the issue. If the devices tested work on another home network, it is your router or network configuration.For Mac OS X, you don't have to edit the port addresses, but make sure the firewall in Apple () menu > System Preferences > Security > Firewall are not set to:
- Block all incoming connections
- Allow only essential services
If you use another security/firewall software on your computer or router, follow this article or contact the manufacturer or check the documentation on how to open TCP ports 123 and 3689 as well as UDP ports 123 and 5353.
For more information on ports used by Apple products, see Well known TCP and UDP ports used by Apple software products.
Thank your or the mentioning the firewall settings, Jason! I use Norton on my Mac and had to go to the connection blocking configuration in firewall settings, allow iTunes, click the plus sign next to iTunes, change block to allow, and select "allow all computers on this network" or whatever to allow access. It worked like a charm for me.