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2/9: Journey Away from Eden

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The Journey Away from Eden Continues


Equal temperament carries with itself its comfort and its discomfort, like the Holy estate of matrimony. –Johann Niedhardt, 18th century

The best meantone temperaments still sounded at least reminiscent of just intonation in their preferred keys, and, over time, the ears of the listeners were able to adjust to the out-of-tune perfect fifths. In addition, the spaces between the notes in a just intonation scale are uneven because the harmonic series is asymmetrical. Meantone temperaments are also asymmetric, so the ear recognizes the pitch variety and is reminded of the patterns of just intonation. But the journey away from harmonic paradise had only begun.  With a mere twelve notes to work with, composers and theorists asked, how far out of tune can we go for the sake of compositional complexity before audience ears simply reject our music? The most out-of-tune solution was 12-equal tuning. The fourth century Chinese theorist Ho Cheng-Tien was the first to explore 12-equal tuning, but it was so far out of alignment with the natural harmonics that it was not taken seriously by performers. 1300 years later, the Dutchman Simon Stevin revived the 12-eq theoretical system, and the French mathematician and monk Marin Mersenne described the 12-equal tuning system with guidance on how to tune organs and other instruments in this way. The system was still being hotly debated 75 years later. Descartes rejected equal temperament in favor of rational, perfect intervals. He led some theorists right back to the overtone series, which unleashed yet another approach to the already-disheveled tunings of Renaissance theorists. Zarlino and Kepler joined Descartes in hailing the overtone series as “nature’s divine plan.” Nicola Vicentino invented a 36-key-per-octave archicembalo on which one could play both 3-limit and 5-limit scales, and which influenced Gesualdo (who employed a 21-note scale) and Frescobaldi, among others. He also designed a 44-fret lute, a 19-tone per octave keyboard, a 17-tone per octave keyboard and 31-note, 13-limit keyboard.

Most Renaissance theorists rejected 12-eq as both out-of-tune and “monochromatic,” in that all the distances from note to note are equal in every key. By 1700, Andreas Werckmeister (1645 – 1706) and others developed a variety of “well-tempered” tunings. Instead of a perfect circle of fifths, “well” temperament creates a kind of oval shape with varying degrees of harmonic inaccuracy. A chosen home key is closer to just intonation and the more distant keys gradually go more and more out of tune. But even the most distant keys are still playable, and each key has a distinctly different flavor, depending on how out-of-tune the thirds and fifths are in that key. “Werkmeister III” is considered by many to be the best example of this “oval of fifths,” and may have been the tuning system preferred by Bach when he composed his Well-Tempered Clavier. In fact, well-tempered tuning systems were preferred by Bach, Mozart, Beethoven, and Brahms, to name just a few. Jean-Jacques Rousseau resisted the new tunings as part of his “back to nature” philosophy.

By 1779, 12-eq was on its way to becoming the new standard tuning. Well-tempered systems reconditioned our ears to accept ever-increasing “out-of-tuneness,” especially when composers like Bach explored the more distant key signatures. Rameau embraced 12-eq in his theoretical works. But Francesco Antonio Vallotti (1697-1780) published yet another well-tempered tuning a full generation after Bach’s death, even as 12-eq was coming into vogue.  As late as 1800, the great polymath Thomas Young (1773-1829) offered another temperament he considered superior to 12-equal. Why did all these theorists fight so hard to preserve some semblance of natural tuning? Because 12-eq sounds so bad! Harry Partch went so far as to call the 12-eq tuning a “complete divorcement of the science of music from music theory… a siege by the industrialized harmony-armies of mediocrity.” The well-tempered systems offered one last glimpse of the glorious beauty of the simple harmonies of the ancients. But the train was out of the station, and the simplicity of 12-eq and its standardization of all keys made it the inevitable choice of the Industrial Age. 12-eq was the final “rounding of the bend” which rendered the ancient tunings inaudible to us. It was a big loss. Our ears were served up a plate of drab, monochromatic, stultifyingly symmetrical, out-of-tune pitches. We had to put up with a “background noise” of unrelenting dissonance—not the kind that grows and retreats for musical-dramatic purposes, but more like the irritating buzz of an ungrounded amplifier on your home stereo. Still worse, singers and performers on unfretted strings kept naturally gravitating towards those musical “sweet spots” that pianos, winds and most brass instruments can’t achieve with their 12-eq keys, so when they play together they have to deal with even more intonational challenges.

Some people went to extremes to try to find their way back to our musical paradise. It was a valiant but losing battle. Not long after meantone temperament came into vogue in the 1500s, a few theorists were further exploring King Fang’s ancient discovery of 53-equal temperament. Even the great Isaac Newton left behind some unpublished manuscripts from around 1664–65 indicating his awareness of the theoretical possibilities of 53-eq (Barbieri, Patrizio. Enharmonic instruments and music, 1470–1900. (2008) Latina, Il Levante Libreria Editrice, p. 350). Perhaps he never took them to publication because he was aware of the practical failures of even 24-note keyboard attempts of the century before.  At that time, no one was taking seriously the possibility of a 53-note-to-the-octave keyboard! Unaware of Isaac Newton’s papers, Nicholas Mercator (c. 1620–1687) precisely calculated the incredible accuracy of 53-eq regarding the perfect fifth. In 1694, William Holder noted that 53-eq also very closely approximates the just major third (within 1.4 cents), so  53-eq accommodates the intervals of 5-limit just extremely well.

If you would like to learn more about the 53-equal tuning that embraces all of ancient music, you can buy the entire book, The Grand Unified Theory of Music, in pdf form for $25 with hundreds of embedded musical examples of scales and chords from all over the world.

A free introduction to what The Grand Unified Theory of Music offers is on this website and includes both text and a few musical examples from each webpage. If you would like to learn more about this chapter and the full contents of this entire e-book, you can buy The Grand Unified Theory of Music for $25, with hundreds of embedded musical examples of scales and chords from all over the world — and ideas for how to set up your computer system —


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