How do I unsync without losing music

If you deselect Sync Music under the Music tab for your iPhone sync preferences, all iTunes music on your iPhone will be erased. The same applies to Movies and TV Shows under the Video tab for your iPhone sync preferences, and for photos under the Photos tab for your iPhone sync preferences. This is by design.

If you are syncing an iTunes playlist or multiple playlists, unless you add additional music to an iTunes playlist that is selected to be transferred to your iPhone, or remove music from the selected iTunes playlist with iTunes, music is not included with the sync process.

If you have sync all music and playlists selected under the Music tab for your iPhone sync preferences, I suggest choosing selected playlists instead under the Music tab for your iPhone sync preferences. This way if you purchase new music from the iTunes store with iTunes on your computer, or import music into your iTunes library from another source, the new music added to your iTunes library will not be transferred to your iPhone when syncing unless you add the new music to an existing playlist selected to be transferred to your iPhone.

You're welcome.

This must be your first iPod, since it has always been this way since the first iPod which I don't expect to change with the next iPhone model.

You can't select individual songs or albums in iTunes under the Music tab for your iPhone sync preferences and the same for any iPod.

I have always made use of iTunes playlists to listen to selected music only - by order in the playlist or by shuffle with the playlist. To burn selected music to a CD, you do so by creating a playlist first.

You also have the option to manually manage music and videos with your iPhone. This provides for being able to select and drag selected music in your iTunes library to your iPhone in the iTunes source list. To remove a song from your iPhone, you select the song in the Music section for your iPhone in the iTunes source list and select the Delete key.

When switching from syncing to manually manage music and videos, all music and videos transferred to your iPhone via syncing will be erased first. The downside of this is if you ever need or want to restore your iPhone with iTunes. If you manually manage music and videos, you must manually re-transfer selected music to your iPhone. If you are syncing when doing a restore, you select the same iTunes playlist or playlists to be re-transferred to your iPhone. One click and done.

Exactly what is "unsync?"