This thread has caused me to wonder something.

Though the historical record is far from clear, it seems that the major scale was all figured out by the 1200's. The sixth and the seventh notes were the last to be 'defined.'

Now, the 'seventh' chord we usually use (e.g., D A F# C) doesn't actually use the seventh note of the scale. It uses the 6th-and-a-half.

But maybe in those earlier centuries, people couldn't say 'six and a half.' When were fractions invented? who first thought of expressions such as 'one-half' or '15/16'? It occurs to me that I have never seen an early representation of a fraction.