Review | How Equal Temperament Ruined Harmony (and Why You Should Care), by Ross W. Duffin

How Equal Temperament Ruined Harmony (and Why You Should Care), by Ross W. Duffin. New York: W. W. Norton, 2007. [208 pp. ISBN-13: 9780393062274, $25.95 (hardcover); ISBN-13: 9780393334203, $14.95 (paperback).]

Historical temperaments — that is, the way instruments were tuned and the way musicians realized intonation in performance — may be the most critically understudied sub-discipline of historical performance practices. Scholar-performers have transformed our understanding of the instruments for which historical repertories were composed, of the techniques with which they were played, of historical understandings of rhythm, sound, tempo, character… virtually everything about the music-making process, in fact, except temperament. Especially with keyboard instruments, where tuning and intonation lie entirely outside the player’s control, there has been a strange reticence to address a completely obvious and troubling point. That point is, simply, that equal temperament — the division of the octave into twelve equal semitones — is historically anachronistic for most of the performed repertoire. Perhaps the most obvious indication that this is the case is the instructions to be found in the vast majority of tuning treatises and instruction books up to the beginning of the twentieth century, which achieve their results by tuning the fifths differently, some slightly wider and some a bit more narrow. It follows that the succession of whole and half steps in each of the major and minor keys would be somewhat different, as would the major and minor thirds in each triad — thus, a unique quality for major and minor key, and the availability of a kaleidoscopically changing array of harmonic colors on, for example, the pianos on which Schubert, Chopin, and Liszt composed and performed. Many of these temperaments have been painstakingly collected and summarized by Owen Jorgensen (his most exhaustive work being the 1991 compendium Tuning1); the one thing that they will not produce is anything like the uninflected, electronically assisted temperaments with which we are familiar today. It should be acknowledged that because of a maddening terminological inexactitude (particular fifths might be tuned “rather wide” or “slightly narrow,” leaving the precise amount to the individual tuner), we cannot be sure that attempts to follow such instructions achieve the precise results intended, and so we cannot establish “right” and “wrong” with any certitude; all that we can establish for sure is that they were not equal.

Another, perhaps more alluring proof of unequal temperaments is that written descriptions of various tonalities in terms of their different characters extend throughout the nineteenth century and even into the twentieth. These descriptions, which continue the tradition of ascribing a unique character to each major and minor key established in the seventeenth and eighteenth centuries, occur primarily (though not exclusively) in discussions of piano music, and they make no sense in the context of true Equal Temperament. Clearly there is, so to speak, an elephant in the room.

The acoustic effects of historical temperaments can be revelatory. Required listening on this subject are two recordings by the pianist Enid Katahn, made in collaboration with the piano technician Edward Foote: Beethoven in the Temperaments and Six Degrees of Tonality.2 On these recordings the listener encounters both the myriad different qualities of major and minor harmonies, the palpably different characteristics of the different keys (as collected and discussed in Rita Steblin’s admirable study3, 2nd ed. (Rochester, NY:  University of Rochester Press, 2002).]), the progression of the crunching dissonance of a diminished triad resolving to the reposeful consonance of major, and (yes) the timbral differences an unequally tuned piano can produce. At one magical place (the middle section of Chopin’s Fantaisie-Impromptu on the Six Degrees CD), there is even a wholly vocalistic vibrato on a significant melody note. The advantages to investigating historical temperaments are, therefore, available to be heard. Still, resistance is tenacious; temperament scholar Reinhart Frosch, in a book titled Meantone is Beautiful! (no less), suggests that

For live performances of piano music by Haydn, Mozart, Beethoven, Chopin, and by later composers, equal temperament is preferable… because that music often deviates strongly from the diatonic scales, for example by making use of chromatic scales or of diminished seventh chords.4 (Bern: Peter Lang, 2002), 19.]

Frosch’s justification makes no sense. The slight inequalities in the chromatic scale are part of what the composers were composing for, after all, and there is no explanation given for the supposed preferability of hearing the works of (for example) these four composers in a tuning from the distant future. Odder yet is Stuart Isacoff’s paean to the status quo titled Equal Temperament: The Idea that Solved Music’s Greatest Riddle.5 So desperate is the author to “prove” that J. S. Bach’s “Well-Tempered Clavier” really was equally tempered that he uses his author’s page at the Knopf website to play the C Major Prelude from Book One in unequal temperament… in C-Sharp. Of course, it sounds awful. The point of course is that Bach composed a C Major piece for C Major and it would not work in a different key, precisely because that key was different. Isacoff proved Bach right, but not in the way he thought.

Enter Ross Duffin, lifelong scholar of historical performance and professor at Case Western Reserve University. The intent of this wonderfully concise book, as Prof. Duffin explains, is not the delectation of specialists; it is to clarify an abstruse subject for a more general audience — in fact, as he points out in the “Prelude,” it is for readers like his son, who is a physicist and amateur musician. For this reason, Duffin takes pains to make the book clear and economical in its use of math (which is particularly helpful for readers such as this one, though comments like “note to mathophobes: this is not math, it’s arithmetic”6 sting a bit even as they reassure), and thorough in its explanations of jargon bandied about by the temperament and early music fraternities but somehow rarely explained to the rest of us. He starts at the very beginning: the harmonic series, the circle of fifths, and the Pythagorean comma (the “discrepancy between twelve pure fifths and seven pure octaves”7). From that discrepancy comes the art of temperament itself, which consists of delicate adjustments to the pure intervals (except, in almost all cases, unisons and octaves) to enable more than a very few chords and scales to be usable at any given time. 

The temperament narrative that most of us learned — that as more and more keys and complex intervals became musically desirable, temperaments got more and more “equal” to the point that atonal music is completely free of the tonal idiosyncrasies of the unequal temperaments — is basically true. What is left out of that narrative is what has been lost as the historical temperaments disappeared, and a window into this issue is the main goal of Duffin’s book. At the core of the issue are two largely contradictory approaches: melodic intonation and harmonic intonation. Consider: piano majors are usually astounded to learn, from their string-playing friends, that in violin, viola, and cello sections, F-Sharp is by no means the same thing as G-Flat. What is usually explained to them is melodic intonation, usually associated with the cellist Pablo Casals, which holds that “leading notes should lead,” or in other words that (for example) a melodic F-Sharp in the key of G Major should be raised — played slightly high—so as to pull even more toward the G resolution. Similarly, a melodic G-Flat in the key of B-Flat Minor would be played low so as to pull down to the F resolution. It would follow that F-Sharp would be higher than G-Flat, since the former pulls up and the latter down.

Harmonic intonation, in direct contrast to melodic, is primarily interested in the integrity of chords and tonalities, and thus it seeks to distort the pure intervals and their resultant harmonies as little as possible. To raise the F-Sharp even further in order to “lead” to G, for example, would distort the D-to-F-Sharp major third — the prevailing harmony of the dominant triad, after all — past desirability. Paradoxically, then, harmonic intonation results in an F-Sharp that is lower than G-Flat, the opposite of melodic intonation. It is no surprise that discussions of pre-equal temperaments soon become murky, and the convenient default of Equal Temperament gained such ascendancy.

Fortunately, Duffin is no strident polemicist; he simply opens the door wide and invites the reader through. His case for the hegemony of unequal temperaments well into the nineteenth century is airtight (I myself think the practice survived well into the twentieth), his explanation of the different principles and different kinds of unequal temperament clear, and his proposals moderate. (“Do not be afraid to be out of tune with the piano” is the one point upon which he and Casals are in perfect — ah — harmony.) I wish that somehow there would have been a way to demonstrate, via perhaps an included CD or a weblink, the way Equal Temperament has blanched and homogenized some of the most interesting and piquant aspects of much of the historical art music we cherish and continue to perform, such as the coloristic changes caused by progressing from chord to chord in a subtly unequal tuning system. That, however, would have been a different book, a different project, and (probably) a different market. Besides, the discoveries are far more effective in person than on recordings, and so the rediscovery of forgotten possibilities will have to be a gradual one, musician by musician and listener by listener.

From my perspective, Duffin’s book ought to be read not only by the curious general reader but also by all music students. The slow passage of time and gradual evolution of tuning practice has meant that the sound-worlds of the music we study have receded into the mists without our taking much note, with the ultimate result that we study and advocate for what are notably incomplete musical traditions. It is all too easy to dismiss the historical discussions of key characteristics in Steblin’s book, for example, as the quaint preoccupations of a bygone time, and the effusive descriptions of the shimmering harmonic effects in a Chopin improvisation as nineteenth-century purple prose. Yet in-person exposure to an effectively realized unequal temperament clarifies, immediately, that the harmonic effects so often described by listeners were quite real, and — with but a little practice in learning to hear them — they are capable of permanently altering one’s musical worldview. How Equal Temperament Ruined Harmony clearly and patiently explains the process by which so much was lost (and, indeed, something else was gained, though that is not Duffin’s focus), and makes an irresistible case for further research and experimentation in this area, particularly by performers. In sum, for anyone interested in understanding historical music on anything more than the most superficial level, Duffin’s book is not simply recommended; it is required reading.


Jonathan Bellman is the Area Head of Academic Studies in Music, and Professor of Music History and Literature at the University of Northern Colorado. He earned piano performance degrees from the University of California, Santa Barbara and the University of Illinois, and a Doctor of Musical Arts in Piano Performance Practices at Stanford University in 1990. His latest book, Chopin’s Polish Ballade: Op. 38 as Narrative of National Martyrdom, was just published by Oxford University Press; he has also published books with Northeastern University Press (The Style Hongrois in the Music of Western Europe, 1993, and The Exotic in Western Music, 1998), and one with Longman, A Short Guide to Writing about Music (2000; 2nd ed. 2007). He is one of the writers for the musicology weblog Dial M for Musicology; his research interests include musical exoticism and the music and performance practices of Frédéric Chopin.


Works Cited

Frosch, Reinhart. Meantone is Beautiful! [1993]. Bern: Peter Lang, 2002.

Isacoff, Stuart. Temperament: The Idea that Solved Music’s Greatest Riddle. New York: Alfred A. Knopf, 2002.

Jorgensen, Owen. Tuning: Containing the Perfection of Eighteenth-Century Temperament, the Lost Art of Nineteenth-Century Temperament, and the Science of Equal Temperament, Complete with Instructions for Aural and Electronic Tuning. East Lansing, MI: Michigan State University Press, 1991.

Katahn, Enid. Beethoven in the Temperaments: Historical Tunings on the Modern Concert Grand. Gasparo CD GSCD-332, 1997.

_____. Six Degrees of Tonality: A Well Tempered Piano, Gasparo CD GSCD-344, 2001.

Steblin, Rita. A History of Key Characteristics in the Eighteenth and Early Nineteenth Centuries [1983], 2nd ed. Rochester, NY: University of Rochester Press, 2002.

  1. Owen Jorgensen, Tuning: Containing the Perfection of Eighteenth-Century Temperament, the Lost Art of Nineteenth-Century Temperament, and the Science of Equal Temperament, Complete with Instructions for Aural and Electronic Tuning (East Lansing, MI: Michigan State University Press, 1991).
  2. Enid Katahn, piano: Beethoven in the Temperaments: Historical Tunings on the Modern Concert Grand, Gasparo CD GSCD-332 (1997), and Six Degrees of Tonality: A Well Tempered Piano, Gasparo CD GSCD-344 (2001).
  3. Rita Steblin, A History of Key Characteristics in the Eighteenth and Early Nineteenth Centuries [1983
  4. Reinhart Frosch, Meantone is Beautiful! [1993
  5. Stuart Isacoff, Temperament: The Idea that Solved Music’s Greatest Riddle (New York: Alfred A. Knopf, 2002).
  6. Quoted in Duffin, 25.
  7. Quoted in Duffin, 54.