How Equal Temperament Ruined Harmony

[mjzee]

The Sound of Unheard Melodies

By PETER PESIC

December 29, 2006; Page W6

Do you ever worry about your piano? Not how to pay for it or whether the kids are practicing or why it may sometimes sound out of tune -- but what it means for your piano to be "tuned" at all?

You may consider this on a par with worrying about the shape of the Big Dipper -- the notes on a piano seem inevitable, as if determined by nature itself -- but the keyboard is a deeply human device. In "How Equal Temperament Ruined Harmony," Ross Duffin, a musicologist and performer of early music at Case Western Reserve University in Cleveland, presents a delightfully informative and provocative argument that we should rethink our common musical habits at the most basic level: the way we tune musical instruments. He is not happy with the current way we divide up the musical scale -- what we call "temperament."

It all began when Pythagoras discovered that the most pleasing musical intervals -- that is, the sonic distance between two pitches -- correspond to simple whole-number ratios. Thus two taut strings whose lengths match a 2-to-1 ratio (one string twice as long as the other) when struck will sound an octave, the interval between middle C and the next C above it. A 3-to-2 ratio of string lengths will sound a perfect fifth -- what we imagine to be, say, C to G on a piano. A 4-to-3 ratio sounds a perfect fourth (C to F). A whole step -- the interval between a fourth and a fifth (F to G) -- requires a 9-to-8 ratio. For Pythagoras, these primal intervals were the cosmic harmonies or ratios regulating the planets' relative motions, the mysterious "music of the spheres," as it came to be called.

Missing the Octave

But an odd thing happens when you stack up perfect intervals -- a kind of imperfection shows up. If you begin with a low C and go up by perfect fifths -- C-G-D-A-E-B-F#-C#-G#-D#-A#-F-C -- you will miss returning to an exact octave of C by a tiny but definite interval, called the "Pythagorean comma." (Expressed as a ratio, it comes to exactly 531441:524288, if you are curious.) In short, the first C and the last one will sound slightly, but painfully, "out of tune."

This minute but audible discrepancy threatens to wreck music: If you begin on one pitch and keep singing perfect intervals, you might never be able to find that starting pitch again. The comma inevitably sneaks in. Theoretically, God himself should have to confront this problem, which imperils celestial harmony.

HOW EQUAL TEMPERAMENT RUINED HARMONY (AND WHY YOU SHOULD CARE)

By Ross W. Duffin

(Norton, 196 pages, $25.95)

What to do? "Temperament" is a (human) solution. It means redefining musical intervals so as to avoid the comma problem, smoothing its harshness by distributing that unruly remainder somehow throughout the scale. Pythagorean temperament does so by dividing the whole step into two unequal "semitones," one having an extra comma in it. This works if you are singing while strumming your lyre but becomes increasingly problematic when several melodic lines intertwine.

A different kind of temperament was eventually developed in the 16th century, offering a draconian, ruthlessly egalitarian solution: Divide the octave into 12 mathematically equal semitones. Such a division requires that the semitone "ratio" be a highly irrational quantity, the 12th root of 2. So much for the Pythagorean dream of simple, whole-number ratios.

Distributing 'Impurities'

Equally tempered instruments are equally out of tune throughout. In contrast, other Renaissance temperaments (such as "just" or "meantone") kept some intervals pure and concentrated the comma "impurities" in others.

By the time of J.S. Bach -- who flourished in the first half of the 18th century -- ingeniously constructed unequal temperaments were common. Bach's "Well-Tempered Clavier," a tour de force of preludes and fugues in all 24 major and minor keys, was written for such an unequal temperament, not the equal one of modern pianos. Most of us have never heard Bach's music as he himself heard it.

Mr. Duffin is bothered by this -- by what he sees as a wrong turn in the history of music, leaving us today stranded in the arid precincts of equal temperament. He makes his argument forcefully and tells his story well. He has an eye for the whimsical and includes thumbnail biographies of some interesting characters, such as the 18th-century composer Johann Joachim Quantz, who added a key to the bottom of the flute so that players could make a distinction, on the instrument's lowest note, between D-sharp and E-flat. To us, these are the same note; to Quantz, E-flat was an important comma higher.

Pitch Changes, Please

Naturally, Mr. Duffin emphasizes that medieval and Renaissance music ought to be heard in the unequal temperaments appropriate to their times, just as we now try to use authentic instruments and performance practices for that repertoire. When it comes to Bach, he believes that we should insist on the genuine, well-tempered article. (He mentions in passing the scholar Bradley Lehman's recent discovery that Bach encoded his own favored temperament in the apparently ornamental doodles and knotted squiggles he put on the title page of his "Well-Tempered Clavier." I would have liked to hear more about this remarkable claim.)

Mr. Duffin's call for pitch changes, however, goes well beyond the 18th century. He argues that equal temperament only became prevalent after 1917, drawing evidence from texts and historical recordings by violinists like Joseph Joachim, Brahms's friend. Thus we really ought to be hearing the familiar 19th-century repertoire in the appropriate temperament, even though this would require an enormous "retooling" of the way that musicians are trained to play and sing, not just revamping our ill-tempered pianos.

As plausible as the argument sounds, the real test will be how the music sounds. I wish that somehow Mr. Duffin's book could have done more to help its readers hear what it describes. (This may be one case where an accompanying CD, folded into the book, would have been really essential.) Mr. Duffin's Web site, one discovers, gives Bach chorales and fugues electronically synthesized in different temperaments. The unlovely, though precise, pitches made me uncomfortably conscious of the artificiality of all such temperaments.

Indeed, I realized anew how human are the temperaments of our instruments, how varied the results of different piano tuners, how expressively cellists or singers can shade intervals. Mr. Duffin offers a striking critique of Pablo Casals's idea of "expressive intonation," in which string players are urged to raise certain pitches for additional expressive effect. He also cites Enid Katahn's interesting CD "Six Degrees of Temperament," which includes four different versions of Mozart's D minor Fantasy, each played on a Steinway grand in a different historical temperament.

How much difference will temperament make, next to all the other aspects of musical style and performance? We need to hear for ourselves. One aspect of Mr. Duffin's argument is especially intriguing: In nonequal temperaments, each musical key has a distinct, individual character because of its particular distribution of commas.

Many composers have alluded to such key differences over the centuries, though they make little sense to us today. For us, a C-major prelude transposed to C# sounds essentially the same, not fundamentally changed if played one semitone higher. But if pitch practice is allowed to follow Mr. Duffin's unequally tempered path, we may soon be able to hear for ourselves what Beethoven really meant when he called B minor "black."

[BruceH]

I read this in Friday's Journal. Interesting article.

[Joe G]

I think that "just intonation" should be much more widely taught and understood by musicians working in all styles. I'm always surprised by the many musicians I meet who have a music degree, yet know little or nothing about it.

Haven't read this book, but this guy sounds like a piano tuner's worst nightmare!

[Guest youmustbe]

Yes, interesting, but kinda late in the game!

[DukeCity]

Yeah, I think an excellent way to increase the audience for early music is to make the intonation sound "weird."

[DTMX]

I haven't tuned my piano in years. I tell people that it's tuned in "just" intonation because I "just" don't feel like getting it tuned!

Hello? Is this thing on?

[The Magnificent Goldberg]

I haven't tuned my piano in years. I tell people that it's tuned in "just" intonation because I "just" don't feel like getting it tuned!

Hello? Is this thing on?

MG

[mikeweil]

The Sound of Unheard Melodies

By PETER PESIC

December 29, 2006; Page W6

........ Most of us have never heard Bach's music as he himself heard it.

Listening to a good recording on period instruments can change that ....

I intend to get me Robert Levin's WTC on Hänssler Classics after reading an interview in Fono Forum.

[7/4]

http://www.artsjournal.com/postclassic/200...tide_turns.html

[Joe G]

Thanks, David. I wasn't aware of that website.

[rostasi]

Oh man - now I need to get that Levin/WTC out to listen again

...to the rodcast...

[7/4]

Thanks, David. I wasn't aware of that website.

Kyle Gann usually writes interesting articles.

[mikeweil]

Oh man - now I need to get that Levin/WTC out to listen again

Indeed! Found a used copy at a good price, got it today, and I like it a lot! Only complaint is that he plays the very first prelude too slow and not straight enough - the music shows the same time/tempo signature as the second prelude, which he plays considerably faster.

Nevertheless I strongly recommend this set.

[danasgoodstuff]

Basically this whole issue is keyboard-centric (dare I say 'pianist-centric'?) If you play a guitar, fiddle or any brass or woodwind, perfect fifths, thirds, whatever are available whenever you want them (provided your ear is good enuff). You can put the comas wherever you want, including right in the middle of a nicely bent note!

[Joe G]

comma yo mamma!

[GregN]

comma yo mamma!

commas you are

[Joe G]

comma yo mamma!

commas you are

Did you hear the one about the Hindu in Boston with bad comma?

[7/4]

comma yo mamma!

commas you are

Did you hear the one about the Hindu in Boston with bad comma?

His head exploded because he was out of tune.

[Guest youmustbe]

Check out Lou Harrison's Piano Concerto. perfromed by Keith Jarrett. Not only the piano but the orchestra is tuned to pre well tempered....

[GregN]

comma yo mamma!

commas you are

Did you hear the one about the Hindu in Boston with bad comma?

Was he a comma comma comma comma comma comma chameleon?!

Little Boy George for Jimmy