Temperament: The Idea that Solved Music’s Greatest Riddle

An excerpt from the book by Stuart M. Isacoff. Reproduced here courtesy of the author and Alfred A Knopf, publisher.

Read an interview with Author Stuart Isacoff

Chapter 14: Coda

Hefts of the moving world at innocent gambols silently
rising, freshly exuding,
Scooting obliquely high and low.
—Walt Whitman, “Song of Myself”

The change was gradual. Mean-tone tuning continued to be used on many organs throughout the nineteenth century; for acoustical reasons, equal temperament’s impure thirds sound much coarser on organ pipes than they do on piano strings. And piano technicians continued to face practical difficulties in achieving an equal division of the octave; there were some who still found it undesirable.

In truth, equal temperament is actually impossible to attain even on today’s pianos. A modern piano’s strings are in a condition of permanent out-of-tuneness known as inharmonicity. Such factors as stiffness, width, temperature, humidity and rust all exert an influence in this direction; a further complication arises from the fact that the various materials used in the construction of musical instruments each contribute different resonating properties. All these stand in the way of a perfect tuning. Indeed, inside a contemporary grand piano there are places where a single hammer strikes two or three strings simultaneously in order to amplify the sound of a single tone, and those paired strings never produce a true unison—the sound is fuller, and more characteristic of a piano, when they don’t.

Nevertheless, with Rameau’s help, the temperament wars, after centuries of struggle, had essentially reached an end. Despite the technical challenges that remained, equal temperament settled in as the philosophical ideal. And it made all the difference in the world.

Over the next centuries, Beethoven and Schubert, Liszt and Chopin continued to dissolve the limits of musical form, producing art that would not have been possible with any other tuning. At the turn of the twentieth century, impressionists and expressionists took advantage of equal temperament’s harmonic pliancy, painting musical portraits free of references to a particular tonal center. By 1923 Arnold Schoenberg began using his twelve-tone system of composition with the aim of eliminating the distinction between consonance and dissonance altogether. Schoenberg put an end to the very idea of natural law in music. Each tone in his system became an equal entity governed only by the hierarchy imposed by an individual composer.

The Steinway overstrung piano
Photo Credit: Steinway & Sons

The piano evolved and proliferated. By the mid–nineteenth century, there were more than three hundred piano makers in England alone. In 1868, Paris boasted more than twenty thousand piano teachers. Soon, the piano craze spread to other regions of the world—brought by covered wagons to log cabins on America’s western frontier, and by camels to Arabia. As the twentieth century began, Americans were buying more than 350,000 pianos a year. And they were all tuned, more or less, in equal temperament.

Iron frames replaced wooden ones, creating a more brilliant instrument, and this was followed by other innovations. In the United States, Steinway & Sons introduced the overstrung square piano in 1855 (a new, more practical design in which the bass strings cross over the treble), and in 1859, the overstrung grand. Within years, this single piano maker would garner more than 120 patents for changes and improvements to the old designs, creating an instrument with a power and nuance unimagined in the eighteenth century.

Today’s piano is a miraculous machine: a colossus of cast iron and wood—filled with screws, hammers, and felt—weighing nearly a thousand pounds. Its frame sustains twenty-two tons of tension exerted on its strings—the equivalent of twenty medium-sized cars. Yet it can respond to the slightest whisper of a pianist’s touch, producing a sound as warm and caressing as the human voice. Concertgoers the world over still flock to hear its magical sounds, unaware of the long controversy that once brewed over the way its tones are arranged, in twelve equal steps within each octave. For most, the idea that they might be formulated another way has simply never arisen.

Yet the temperament debate never completely disappeared. Even in the twenty-first century, a sense of intrigue and excitement over the ancient tunings keeps the topic burning with partisan heat. It is particularly fertile ground for early-music specialists, of course. But there is also plenty of action in other quarters.

Musicologist Ernest G. McClain, in books such as The Myth of Invariance, probes what he sees as hidden musical meanings in the texts of the world’s religions, from the Rig-Veda and the Egyptian Book of the Dead to the Book of Revelation. McClain, in his retirement years, invests a tremendous amount of time and effort pursuing what he calls “Davidic musicology” (named for the biblical David). “It’s a little astonishing to attribute temperament theory to someone who lived in 1000 b.c.e.,” he admits. But he cites evidence in the Bible, in the Sumerian Kings list, and in Babylonian legend of a very early awareness of the mathematical calculations used for a range of musical proportions. “The oldest stories we have of gods and heroes are really about music,” he says.

Contemporary composers who place temperament at the core of their work include Lou Harrison—who has employed the mean-tone tunings of Johann Philipp Kirnberger, a student of Bach who was decidedly against equal temperament—and distinguished composer and scholar Easley Blackwood, a longtime professor at the University of Chicago. Blackwood has written music using a variety of equal temperaments, dividing the octave up into from thirteen to twenty-four slices. These “microtonal” works are stunningly strange—sometimes edgy and dark, at other times brightly boisterous, often haunting and otherworldly.

A flourishing circle of just-intonation advocates with ties to Eastern mysticism includes clusters of adherents in New York and California. One is W. A. Mathieu, whose mammoth book Harmonic Experience explores music’s inner workings and its resonance with human experience. Mathieu, who first became known as a jazz musician, studied with Blackwood, whom he credits with imparting important mathematical insights into the nature of temperament. “Then I heard Northern Indian music,” he relates, “and found in it a kind of purity that I longed for but couldn’t achieve or understand.” He studied under Indian master musician Pandit Pran Nath, became friends with innovative composer Terry Riley, and developed his own approach to the similarities and differences between pure and equal-tempered tunings.

“Each one is a complete universe unto itself,” he explains, “but they own mutual territory. Equal temperament is not a substitute for just intonation, just as adulthood is not a substitute for childhood. You could say that just intonation is like the pure child that lives inside every equal-tempered adult.” In his view (and it comes close to Rameau’s), the tonal world of equal temperament brings with it the kind of ambiguity that manages to fool the ears into thinking they are hearing pure ratios. But, says Mathieu, we are actually built to resonate with the pure musical proportions. “Human beings don’t have to know about just intonation to understand it,” he says. “We already are it.”

New York pianist and composer Michael Harrison also studied with Pandit Pran Nath, and worked extensively with composer La Monte Young, becoming the first person besides Young to perform that composer’s six-hour just-intonation work, The Well-Tuned Piano. Harrison converted a seven-foot grand piano into an instrument he calls the “harmonic piano,” which affords him, with the shift of a pedal, the ability to play up to twenty-four different notes per octave. There are also devices for controlling which strings are free to vibrate sympathetically. In 1991 he used this instrument to record an album, From Ancient Worlds.

One cold evening at the end of November 1999, I was invited to Harrison’s brownstone for a private recital. Earlier in the month, he had participated in a festival in Rome as one of four composer/pianists in the minimalist mode—a style of writing in which brief, repeating melodic fragments undergo a process of change over time, like precious stones turned slowly under a light. The other pianists on the program were Philip Glass, Terry Riley, and Charlemagne Palestine. The morning after his recital, Harrison awoke with a new tuning in mind—he calls it his “revelation tuning.” It had come to him clearly, like a revelation, he reported. When he returned home and tried it on his harmonic piano, he found the results extraordinary: “It creates undulating waves of pulsating sonic energy,” he later related. “It is a tuning of so many beautiful sounds that every time I play it I discover new harmonic regions and feel like an explorer.” The secret, he revealed, was the inclusion in the tuning of three commas—those tiny “wolf” intervals that are usually avoided as too sour. He had found a way to weave them into a unique tapestry of sound.

The private recital at his home was an opportunity for Harrison to play his new tuning for a few friends and musicians, including composer Philip Glass. Glass, an icon of contemporary music whose credits include several operas, such as Einstein on the Beach and Satyagraha, and collaborations with poet Allen Ginsberg and pop artists Paul Simon, David Byrne, and Laurie Anderson, arrived with a retinue. We all shared some wine and small talk before descending to a basement room, the locus of which was a glistening, ebony harmonic piano. The floor was strewn with cushions, and we each quickly settled onto one. Glass found a couch at the far end of the room and assumed a cross-legged position. And then, in the dim light, the music began.

It sounded like a jumble at first—a drone, or a room full of drones. Then, from within the din, high-pitched sounds seemed to rise and float toward the ceiling. The deeper Harrison played into the bass end of the instrument, the more he seemed to free an angelic choir above. Were these sympathetic vibrations? I wondered. Overtones? The clashing of strings just slightly out of tune? I couldn’t tell.

Now the texture changed. The pianist’s fingers engaged in a furious rhythmic interplay, and a groaning mass of sound in the low end of the piano gave birth to more phantoms above. Musical concords seemed to emerge and shake hands above the fray.

After a considerable amount of time, the music stopped. No one moved. Someone on the floor said, “My whole body is resonating.” The piano was silent, but we were all still spinning in a musical vortex. I looked at Glass on the couch; his eyes were closed. My mind wandered to the lamps in the room, the decorations on the walls. . . .

And then I thought fleetingly of Renaissance seekers like Bartolomeo Ramos and Marsilio Ficino and Pico della Mirandola. I remembered the kabbalistic masters who described the sympathetic resonance between what is above and what is below. I contemplated the curious story of Huai Nan Tzu, his temperament theories and his ascent to heaven.

And I once again recalled the latest trend in modern physics, known as string theory, which holds that everything in the universe is composed not of atoms, but of infinitely thin vibrating strings—filaments that wriggle and oscillate incessantly in a great cosmic dance. What were once described as different elementary particles are, say physicists, really just different notes in an enormous celestial symphony.

And I thought: Perhaps Pythagoras was right after all.

Stuart M. Isacoff, a recipient of the ASCAP Deems Taylor Award for excellence in writing about music, is a pianist, a composer, and the editor in chief of Piano Today magazine. He has contributed to The New Grove Dictionary of American Music and has written for The New York Times. He lives in Bergen County, New Jersey.