Lyric discussion by DNungester 

This song is about the sinking of the R.M.S. Titanic (April 15, 1912) and the band that played on the deck of doomed ship. Note: Ships were often referred to by feminine names such as "Her", "Lady" and/or "She".

Here is my interpretation:

We skipped a light fandango, (Unsure about this line)

Turned cartwheels 'cross the floor. (It was reported that children were doing cartwheels across the "deck" during the day light hours and adults were afraid that they would fall overboard)

I was feeling kind of seasick, (Just as it says)

But the crowd called out for more. (The Titanic hit the iceberg on April 14, 1912 at approximately 11:00 pm ship's time and sank at approximately 2:20 am on the 15th of April. The passengers knew their fate and that they were going to die. To take their minds off of their pending deaths, they played cards, got drunk, or just listened to music).

The room was humming harder, (The Titanic's crew keep the lights on and the light bulbs back then made noises when the lit)

As the ceiling flew away. (There was a glass and steel dome over the "Grand Ballroom" on the Titanic. The Titanic was sinking bow first and when the water got over the dome, it could not support the extra weight.)

When we called out for another drink, The waiter brought a tray. (The waiters knew they were going to die too, so they gave out all of liquor.)

And so it was that later, (The Titanic hit the iceberg at 11:40 pm and sank at 2:20 am)

As the miller told his tale, (I believe that the correct line is "As the Mayor told his tale". He was just trying to divert attention from his pending death).

That her face at first just ghostly, Turned a whiter shade of pale. (What color does your face turn if you KNOW you are going to die? A whiter shade of pale!!!)

She said there is no reason, (The correct line is "HE said there is no reason. The ship owner Joseph Ismay kept telling passengers that the ship was unsinkable)

And the truth is plain to see (Despite that fact that Ismay kept telling passengers that the Titanic was unsinkable, the truth was plain to see)

That I wandered through my playing cards, And would not let her be (Maybe by some miracle, the boat would STOP sinking)

One of sixteen vestal virgins (Correct line - "One of sixteen vessel virgins" There were 16 new ships making their first voyages in 1912)

Who were leaving for the coast. (Coast of United States from Europe)

And although my eyes were open, They might just as well have been closed. (The narrator could see that the ship is sinking but did not want to believe it)

And so it was later, As the miller told his tale, That her face at first just ghostly, Turned a whiter shade of pale.

"We skipped the light fandango" is in reference to Milton's poem "L'Allegro", "Com, and trip it as ye go, On the light fantastic toe." Wikipedia defines "tripping the light fantastic" as "to dance nimbly or lightly, or move in a pattern to musical accompaniment. It is often used in a humorous vein." It goes on to actually cite Procol Harum's 1967 hit song, "Whiter Shade of Pale", that this phrase is typically attributed to Milton's poem in a modernist perspective. I had no idea that this beautiful song was about the Titanic, and of all the lyrics, the only one...

I'm sorry, but no. Procol Harum sang this live in 2006, and the video is available on YouTube. He clearly says "she said there is no reason" and "Vestal." And a fandango is a dance, which goes along with "cartwheels cross the floor."

Although I was at first tempted to believe your theory about the Titanic, listening to the song I clearly hear him say "miller", "she", "vestal". The "she" is the same person as "her", I think. I have no absolute theory about the meaning of the song but it might actually be about someone sinking, but in some kind of drug trip or alcohol party... ?

An error occured.