*** WORKED FOR ME
SOLUTION: I hooked up my iPhone 5 to sync it with iTunes, unchecked "Sync Music" and thus wiped all iTunes music from the iPhone; completely shut off both my iPhone & Mac; restarted both; opened iTunes again with iPhone plugged in for a sync; re-checked "Sync Music" (I have "Entire music library" selected), and did a new sync. It took nearly 3 hours; I was doing other stuff in the background & was plugged in some but not all of the time.
I did NOT try any of the following or anything else, for various reasons: removing passcode, authorizing computer (I had verified that it was authorized already), restoring iPhone, deleting iTunes library, uninstalling anything, backing up to iCloud (I never have used it; don't pay for it; my library is bigger than what I believe to be the free amount of storage), etc.
Problem I had encountered, which led me to search for a solution & find this thread: at least one album did not show up at all when I repeatedly did a sync with iPhone. However, that album showed up on iPad & iPod, every time. So it was a quirk with iPhone only, even though I had the correct / same settings for all devices. It could be that other albums were impacted, I just happened to notice one album always missing.
Parameters: I have an iPhone 5 (not S or C), 64GB, iOS version 7.0.4; MacBook Air (about 2 years old, OS X 10.7.5, 1.7 GHz Intel Core i5 Processor, 4 GB 1333 MHz DDR3 Memory, 256 GB Flash Storage); iTunes version 11.1.3 (8) 64-bit. The iPad that worked before is 64GB, running iOS 7.0.4, and is over 2 years old. The iPod that worked before is the very old wheel type - say 5 years old or more, assume updated software, 160GB. My iTunes library says it has 5,667 songs (but the sync showed 5,555 during, and 5,590 after; 5,653 are on iPad). The songs are a dog's breakfast of iTunes purchases, Amazon purchases automatically imported to iTunes, burned CDs, MP3s, from BTs, etc.
Hope this helps.
dmt