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Mathematics Marches On

In the 1100s in Paris, an innovative experiment was brewing.1 After five hundred years of Gregorian chants which featured a group of people singing a single melody, attempts were made to make music more interesting by dividing the singers into two groups and assigning to each a different melody!

1No, not beer - the monks preferred champagne.

The idea was simple and brilliant - the hard part was deciding what notes to give the second group. The first group, of course, sang the original melody. To give you an insight into the way this was, and is, done, we must speak briefly about music theory.

Now the entire subject of music is very mathematical, as you shall see. The basic notes of Western music consists of the C scale, whose notes c, d, e, f, g, a, b, c ascend in pitch. No doubt, you have sung this at some point and you might even have used the names do, re, mi, fa, sol, la, ti, do, as immortalized in the movie The Sound of Music, in the amusing song which describes "do" as a female deer.2 These notes are, by the way, the white keys on a piano keyboard.

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