How a lone theorist’s pursuit of symmetry shaped music history
On the second Sunday after Trinity in 1724, the congregation at the Thomaskirche in Leipzig heard Johann Sebastian Bach’s new cantata that began with the words Ach Gott. Bach set the word Gott to the most dissonant triad known at the time: the augmented triad. Bach’s own son, Carl Philipp Emanuel Bach, wrote in the second volume of his treatise of 1762 that the offending augmented fifth of this harmony requires careful preparation. His father did not prepare it at all. Acclimatized as we are today to all kinds of dissonances, this harmony might pass the modern listener by. But it would have disconcerted the ears of the eighteenth-century congregation, giving them a God-fearing shudder, while setting the scene for the biblical message of the day. Bach, after all, was setting the tune and words, Ach Gott, vom Himmel sieh darein, that Martin Luther had penned exactly two hundred years earlier, in 1524. Based on Psalm 12, Luther tells of a perilous world filled with those who shun God.
The augmented triad has long been a headache for music theorists, only partially on the basis of its harsh sound. Mostly they are perturbed by its construction and their inability to pinpoint a convincing origin for it. It would be no exaggeration to say that, just two years before Bach composed his cantata, the harmonic theory of Jean-Philippe Rameau, a towering figure in the history of music theory, brought about a paradigm shift in how chords were categorized and understood to have been constructed. Although much of Rameau’s theory still holds sway today, a now defunct aspect of his Traité de l’harmonie led him to deem the augmented triad “worthless.” It belonged to the rubbish heap of potential chords because it did not contain the right kind of fifth, and therefore it must be an incomplete chord. According to Rameau’s newly minted theory, all valid, complete chords must contain a perfect fifth; the augmented triad gets its name from the fact that its fifth is “augmented” (it is a semitone larger than the perfect fifth).READ MORE>