There's no actual need to put the music into separate accounts. Doing so may have unintended consequences, paricularly if you purchase music from the iTunes Store (using one account).
Instead, you can Sync by Playlists and/or genres, rather than syncing the entire library.
Using this method, which is simple to set up for each device, you can select only what you want for each of those devices.
- connect the first device to your iTunes Library (iPad for example)
- when if shows up in iTunes, click on the device icon (see the screenshot below):

- ... which will show the device Settings/Summary pane
- select the Device/Settings/Music pane (1. in the screenshot below):

- Presumably, Sync Music (2.) will already be selected. That's what you want still, so leave that as it is
- choose selected playlists, artist, albums and genres (3.). Only now will section 4. appear
- now that section 4. is displayed, scroll down and beneath Playlists (4.), you will find Genres. (also 4.)
- if you have the iPad connected:
- select Classical in the genres section (4.) (put the tick in the box)
- click on the Sync button in the lower right corner of the iTunes window (not shown). Once the Sync is completed, safely disconnect the iPad
- only Classical music genre will now be on your iPad
- at future Syncs with iTunes, you do not need to go through this procedure again. ITunes will recognise the iPad and Sync only Classical music to it
- now connect the iPhone to your iTunes Library
- repeat the steps above - until you get to choosing the genre (4.). To get everything except Classical music onto the phone:
- in the genres section (4.), if you hold down the CTRL button and click on any box in the genres field; every genre will be selected. This is what you want (see next step)
- still in the genres section, click on the tick box for Classical, to turn off the Classical genre. This will leave every other genre still selected*
- click the Sync button
- once the Sync has finsished and you safely disconnect the iPhone, it will have all the music on it that is not Classical
- future Syncs will work in the same way as above; you have set the phone to have everything except Classical music on it and iTunes will recognise this.
- All the music remains in your one iTunes Library
If you have Playlists on your devices, you can select the ones you want on the particular device when you select the genre in 4.
If you wish to play only the Classical music on your PC (in iTunes), simply select the Classical genre.
* Edited by author after intiial posting, for clarity