Temperamental Differences

By: Blake Howe (Louisiana State University) //

In their lessons, violinists must train very hard to play “in tune.” Singers face the same challenge; some, fearful of sounding “pitchy,” might even use Auto-Tune to prevent mistakes in live performance. The slightest change in temperature and humidity can knock a piano “out of tune,” so concert halls usually hire a professional tuner to “retune” the instrument before each concert—a grueling process that can take hours.

To play or sing in tune is to match the pitch frequencies prescribed by a tuning system. Despite an infinite number of possible systems, for the past 200 years most Western musicians have used just one, called “equal temperament.” Listeners have become so accustomed to the sound of equal temperament that its organization of pitch frequencies sounds normal, and a performer’s failure to match those frequencies produces music that sounds wrong. But equal temperament, much like the very concept of normality, is a product of its time and place. It reflects the politics of a culture that values consistency over variety, uniformity over difference—and, as we will learn, a prototypical nondisabled body over the extraordinary diversity of human morphology.

Carl Radford plays Frédéric Chopin’s Funeral March in two tuning systems: well temperament and equal temperament. Since the 1800s, most performers have only played in equal temperament, but early generations of musicians had many more options and could choose a tuning system that suited their preferences.

According to legend, the mathematician Pythagoras (ca. 500 BCE) discovered the ratios underpinning musical intervals: the ratio of 2:1 governed the interval of an octave (e.g., low do to high do), while the ratio of 3:2 produced the interval of a perfect fifth (e.g., do to sol). Underpinning music, so followers of Pythagoras argued, were the simplest numbers (1, 2, 3) of rudimentary arithmetic. Early tuning systems were modeled upon Pythagoras’s ratios: there seemed to be something ideal and divine in the simplicity of his numbers. But this simplicity concealed a problem—a big one. Beginning from do, a rising sequence of perfect fifths will eventually work its way back to a much higher do (3:2 of 3:2 of 3:2, for twelve times). However, attempting to cover that distance by octaves (2:1 of 2:1 of 2:1, for seven times) will result in a slightly different pitch. Or, to put things mathematically: (3/2)12 ≠ (2/1)7. In practice, this means that a perfectly tuned fifth (do to sol) will result in an out-of-tune octave (do to do). Likewise, a perfectly tuned octave will result in an out-of-tune fifth.


In this fifteenth-century illustration, Pythagoras hears the sound of banging hammers (upper left) and then experiments with the pitch relationships of other proportionally shaped objects: bells, cups of water, pipes, and weighted strings (clockwise from upper right).

To resolve this conundrum, some musicians invented temperaments—that is, tuning systems that produce perfectly tuned octaves but temper (adjust) other intervals. In the 1700s (the century of J. S. Bach, Joseph Haydn, and W. A. Mozart), a type of temperament called “well temperament” was popular. In a well-tempered tuning system, frequently used intervals (e.g., the fifth from do to sol) are tuned as closely as possible to their Pythagorean ratios. Other intervals, used less frequently (e.g., the fifth from mi to ti), would then be tempered. Music performed in a well-tempered system can sound really great (some intervals are perfectly in tune) and also really wonky (other intervals are purposefully out of tune). Listeners likewise developed a kind of sonic tolerance: an out-of-tune interval wasn’t wrong—just different and uniquely expressive.

Performers in the 1700s and early 1800s could choose from dozens of well-temperament systems, usually named after their inventor’s last name: WerckmeisterKellnerVallotti (my favorite), among many others. Different performers in different regions had different preferences. A piece of music that sounded out of tune in one system might sound amazing in another system. The key feature of well temperament is variety—a variety of tunings within a single well-temperament system (some intervals in tune, some out of tune), plus a variety of well-temperament systems to choose from.

By contrast, the key feature in equal temperament is uniformity. Promoted throughout the 1800s and in near-exclusive use by Western musicians today, equal temperament tempered all intervals except the octave by the same amount. In equal temperament, every fifth—from do to sol, from re to la, from mi to ti—is imperfectly tuned in exactly the same manner. Because all intervals are tempered, the adjustments are quite small, almost imperceptible. The result? A piece of music performed in equal temperament will sound pretty good—not really great, but also not really wonky. Listeners to music played in equal temperament have developed a kind of sonic intolerance: if all fifths are supposed to sound the same, then an out-of-tune fifth will sound like a mistake.

A comparison between these two temperaments reveals their ideological bases. In well temperament, perfectly in-tune intervals complement significantly out-of-tune intervals. In equal temperament, all intervals (save the octave) are slightly out of tune. The former system fosters variety and difference, while the latter preserves consistency and uniformity. In How Equal Temperament Ruined Harmony (And Why You Should Care), Ross Duffin argues that these two systems also reflect tension between two branches in the philosophy of science: vitalism (popular before the 1800s) and mechanism (popular since the 1800s). He writes, “The vitalists saw life in the irregularities, the elusive, indefinable aspects of things, while the mechanists saw strength and ‘progress’ in the regularization of things. … It is certainly easy to see unequal [well] temperaments as vitalist and equal temperament as fitting a rationalistic ideal.”

These oppositional qualities—variety versus consistency, difference versus uniformity, vitalism versus mechanism—map onto contemporaneous sociological concerns, particularly regarding the relationship between disabled and nondisabled bodies. Before the 1800s, bodily perfection was an elusive ideal, only manifested by the body of God or the King. In their infinite variation, all other bodies were considered imperfect. Perfection was rare, while imperfection flourished; there was, to return to Duffin’s description of vitalism, “life in the irregularities.” This is not so dissimilar from well temperament, in which a few choice intervals are “perfect” (they align with those divinely inspired Pythagorean ratios), while others are “imperfect” (they are tempered by man, and thus out-of-tune). This imperfection was an asset, not a defect: as music theorist Johann Georg Neidhardt argued, variety in the tunings of intervals produced a “heightening of emotion” in the listener.

In the 1800s, which saw the rise of statistics (in tandem with eugenics), psychiatry (in tandem with the psychiatric ward), and industrialization (in tandem with mass production), a concept of normality and abnormality replaced that earlier model of perfection and imperfection. Human variation was placed on a bell-shaped curve, which identified most bodies as normal and other bodies as above or below that norm. For example, the bell curve presumes that most people have a typical height, while some are too tall and others are too short. Rather than accommodating the infinite variety of human morphology, followers of the bell curve privileged a constructed (and wholly imaginary) normal body, one to which most bodies could conform or aspire. To borrow from Duffin’s description of mechanism, the promotion of normality allowed for the “regularization of things,” improving the life of “normal” people, but leaving bodies deemed abnormal excluded and stigmatized.  

As disability scholars Jan Branson and Don Miller write, “A view of a diverse humanity that was imbued with almost infinite difference [i.e., pre-1800] gave way to a view of an essentially uniform humanity that was surrounded on its edges, on its margins, by the pathological foils to that uniformity or ‘normality’.” This conception of humanity emerged at the same time as equal temperament, and the similarities are striking. Nothing should lie in the out-of-tune fringes of the bell curve. Nothing should vary from the prototypical norm. Everything should sound the same. Everything should be, well, average.


Emerging in the 1800s with the rise of statistics, the concept of normality placed human variation on a bell-shaped curve. (Image by Mwtoews [CC BY 2.5 (http://creativecommons.org/licenses/by/2.5)%5D, via Wikimedia Commons)

A number of modernist composers (Harry PartchTerry RileyLa Monte Young, and Georg Friedrich Haas) have sought to undo the supremacy of equal temperament by developing new tuning systems or reverting to earlier ones. But equal temperament’s main advantage, the reason for its astonishing staying power, is its efficiency: like the machines of mass-production, equal temperament produces a product that works for most music, most of the time, for most listeners. We listen within a bell curve. But by suppressing the delightful twangs of an out-of-tune chord, perhaps we’ve lost something in the process—the beauty of difference.

For Discussion

  1. Is it always desirable to play music in tune? Why might a composer or performer want to make music on an out-of-tune instrument?
  2. Should music of earlier centuries be performed in a historic or modern tuning? Why or why not?
  3. The pianist Frederic Chiu has recently recorded music of George Gurdjieff and Thomas de Hartmann, with tracks alternating between equal temperament and a Middle Eastern tuning system. Can you identify the tuning system for each piece? Which system do you prefer for this repertoire? Why?

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