When A Piece Is Not In a Key

Somewhere along the line music teachers decided that the only way to teach music to children was to teach them about keys, scales, all that formulaic stuff.

But that is just what it is: formulaic.  As such it is of limited usefulness.  One must always be on the lookout for pieces that do not conform to the formula.

Today it was a piece by Bartok that relies on the dichotomy between black and white keys.  After musing (!) about all kinds of motion within a total black-key sound he suddenly introduces the two "missing" white keys: C and F (below).  This sudden stark perfect fifth arrests all forward motion.  Along with it comes a new note value:  so far the longest value has been the equivalent of four eighths, all of a sudden it is five.

I asked the student what the difference is.  His answer: "immeasurable."  Spot on.  The musical distance between four and five is not simply one unit; rather it is leaving the universe of balance and symmetry for the opposite, which feels foreign, even intolerable.