I do exactly this, using Resilio (formerly Bittorrent Sync). It's super fast, and you can set it to use only your local network.
https://www.resilio.com/
Okay, I tried it and I'm not too pleased with the results. Can you tell me how about your setup on your PC and phone. I'm going to paraphrase what I wrote in Resilio's forum:
I'm currently running Android Marshmallow 6.0.1, stock from my provider.
Folder A = Source folder on my PC
Folder B = On my phone's microSD card. I wish Folder B to mirror all changes, if any, from Folder A.
I only set up Folder A in my PC's Resilio Sync application. From there, I used my phone to scan the QR code [either Folder A's RO (read-only) or RW code (read+write)] to initiate synchronization between the two devices. In my phone's Sync app, I directed Folder A to transfer/update its contents to Folder B.
With the RO QR code, I believe new files/subdirectories in Folder A not present in Folder B were added to Folder B. However, conflicting files (Folder A files on Folder B with newer timestamps in the former) were not updated. With the RW QR code, conflicting files were resolved by files with newer timestamps overwritting older counterparts. However, subdirectories/files there were deleted from Folder A prior to sychronization were not deleted from Folder B and such conflicts were shown in Folder A after synchronization.
For example, in Folder A:
├───Alternative and Rock
│ ├───Built to Spill
│ │ ├───Album 1
│ │ └───Album 2
will look like this after synchronization (from Folder A, artist directory renamed and Album 3 subdirectory deleted):
├───Alternative and Rock
│ ├───Built to Spill
│ │ ├───Album 1
│ │ └───Album 2
│ ├───Conflicted.Built TO Spill
│ │ ├───Album 1
│ │ ├───Album 2
│ │ └───Album 3
The support suggested: 'Your Folder A should be RW, your folder B should be RO, with sync all enabled, enabling overwriting of changed files.' That suggestion made me confused, as I thought it should be the other way around: Folder A is immutable and Folder B is updated to mirror Folder A, so Folder A would be RO and Folder B would be RW.
FYI: Directory tree is 5525 lines long.