I was looking through a piano book, trying to find a Bach piece that I could play reasonably well (I'm still at an early intermediate level) and in the informational section of the book (you know, the part with words, not musical notes) I read an interesting blurb about Bach and his membership in a group called "The Corresponding Society of the Musical Sciences." The purpose of this group was to find connections between math and music. Telemann and Handel were also members of this group, and Bach joined in 1747.
It is believed that this group inspired Bach to write The Art of Fugue, a monumental work, and a mainstay of the keyboard canon. The series of fugues in The Art are intricate and complex, are all in D minor, and are given the rather boring title of Contrapunctus. There is some speculation that the fugues were written as a sort of treatise, never really meant for performance. No instrumentation is given, so it's heard performed on piano or by ensembles of like or un-like instruments. It may be argued that the entire collection is a study of counterpoint. Counterpoint is the way notes move against and with each other and is the basis for musical harmony. An interesting thing to realize: in the very early years of tonal music history, chords weren't the basis for everything. Harmony was only the result of separate, moving lines. If two singers lined up on a pleasant sounding interval, that was noticed and developed. Certain intervals, therefore, were considered "bad". Which really means that they were dissonant. Hence, the eventual ban on the dreaded "Devil tone" or tritone (the most dissonant interval in tonal music.)
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