Happy Birthday, Well-Tempered Clavier

Not about books, but certainly about creative genius. Plus, an incalculable number of books have been written and read with Bach playing quietly in the background.


This year marks the 300th anniversary of J. S. Bach’s The Well-Tempered Clavier, the most audacious and influential volume of music ever written for keyboard. Even if you’re not a diehard baroque fan, you’ve no doubt heard selections from The Well-Tempered Clavier in the background of your life—in movies scores, at Starbucks, and choppy iterations through the wall as the neighbor kid practices her piano lesson. You’ve also heard it remixed by other composers. The famous “Ave Maria,” a meditation on The Well-Tempered Clavier’s opening piece, the Prelude in C Major, was penned by French composer Charles Gounod a hundred years after Bach’s death. The theme was repurposed yet again by Yo-Yo Ma and Bobby McFerrin in the 1992 album Hush. Or maybe­­ you’ve heard the opening of Lady Gaga’s 2009 hit “Bad Romance,” which quotes the final piece in the book, the Fugue in B minor.

The Well-Tempered Clavier is a set of preludes and fugues, that is, forty-eight short pieces in all twenty-four keys, major and minor. Although these pieces are regularly performed in professional settings, Bach originally presented his collection as a pedagogical work for advanced students, “for the profit and use of musical youth desirous of learning, and especially for the pastime of those already skilled in this study,” as he wrote on the title page for Book One, which he completed in 1722. Twenty years later, he wrote a second complete set of preludes and fugues in all keys, Book Two. Both volumes were hand-written, hand-copied, and widely circulated during Bach’s lifetime, but they weren’t published in printed form until fifty years after his death.

What’s so “well-tempered” about this clavier? And, what’s a “clavier,” in the first place? Is it a sort of old-fashioned piano on Prozac? If you’ve been wondering, you’re in good company. For more than a century, early music specialists have been sparring over these very questions. The second is easier to answer than the first: Over the years, partisans for various ancient keyboard instruments have tried to claim The Well-Tempered Clavier for themselves, including the Italian composer Ferruccio Busoni, who misnamed the collection “’Das Wohltemperierte Clavichord,” and the famous twentieth-century Polish harpsichordist Wanda Landowska, who insisted the pieces were meant for her instrument, only. There’s now consensus that when Bach wrote “Das Wohltemperirte Clavier,” he meant “clavier” to signify any musical keyboard—harpsichord, clavichord, organ. He did not mean the modern piano as we know it, the very instrument upon which The Well-Tempered Clavier is played most often now, because modern pianos had yet to evolve. (More on that later.)

As for what Bach meant by “well-tempered”— a clue is in the structure of the volume. To modern sensibilities, a systematic book for aspiring keyboard students seems like a sensible pedagogical project sprung from an orderly mind: start in C major with prelude and fugue. Next, a prelude and fugue in the parallel key, C minor. Then C# major and minor, then D and so forth, all the way through B minor. As they work their way through the book, students practice all the key signatures sequentially. Indeed, that’s how the book functions today for contemporary concert pianists and students of piano. But the simplicity of the concept belies the audacity of its origin. While completely playable on modern pianos, The Well-Tempered Clavier would have been impossible to perform on keyboards of Bach’s time—not without a radical new approach to tuning the very instruments it was written for.

To understand why the manuscript was so revolutionary back in 1722, and why 300 years later it continues to foment controversy among baroque music aficionados, we need to keep in mind that the baroque keyboards were tuned differently than today’s pianos. If you fancy a deep dive into the physics of music, check out the links below; you will not be disappointed. For the rest of us, in simple terms, the drama comes down to an unsolvable problem of math. Imagine the twelve tones of a true chromatic scale as clock, or maybe an oozy pizza, in which twelve slices almost, but don’t quite fit.

Link to the rest at JSTOR

2 thoughts on “Happy Birthday, Well-Tempered Clavier”

  1. Artifacts from the un-tempered world still survive.

    For example… Wind instruments, both woodwind and brass, are constructed in particular keys (e.g., B-flat clarinet). They have a fundamental physical resonance that is modified by keys. Such resonance will always be un-tempered, though it can be refined by performance practice.

    Stringed instruments can be either true-tempered (violin) or even-tempered (viol, more or less) in their tuning, but (if unfretted) the finger on the string can adjust as needed for all but the open strings.

    Voice on the other hand… I sing tenor (as a female, since puberty), so I am rather, um, attuned to the arbitrary character of defined ranges for voices. There is nothing so arbitrary as claiming that there is a natural range of voices, such that saying “Ab is a better key for X vocal range” is supposed to be defensible. Individual voices (of course) cover a continuous range, each with a lowest and highest note, and are grouped together as “baritone” or “alto” based on arbitrary fit. Nonetheless, I have encountered any number of professional musicians who think that there’s nothing wrong with scoring an a capella (unaccompanied) choral work in, say, Ab instead of G, despite the increased difficulty of reading that from the score (3 flats vs 1 sharp, for two keys that are only half a step apart) — as if the voices were so many clarinets, in an un-tempered world, and had to be so-accommodated in the score.

  2. Further to the article linked:

    As said there, you can use equal temperament (which all modern keyboard instruments use) or any of several unequal temperaments. With the simplest, or Pythagorean temperament, a ‘perfect fifth’ represents a frequency ratio of 3:2, which is extremely harmonious and pleasing to the ear. But to tune the 12 semitones of a full octave, you go through the ‘circle of fifths’. You can produce this circle by going up a fifth for each successive note (and dropping an octave when necessary, to stay in your instrument’s range). Twelve perfect fifths add up to a ratio of 531,441:4,096, or about 129.75:1. But each octave is a ratio of 2:1, and seven octaves are 128:1. So some of your semitone intervals, if played in the same octave, will sound sharper and some flatter. This makes for some awful discords. A ratio of 129.75:128 is big enough that even untrained ears can hear it. It doesn’t sound like two different notes, but two instruments playing the same note, and one of them is badly out of tune. The sounds ‘beat’ together in a weirdly unpleasant way. The game was to smooth out that ratio, or ‘comma’, by hiding bits of it at various points in the scale where they would be less noticeable. Thus some of the intervals would not be quite perfect, but none of them would be totally unusable.

    Several systems were developed to do this. In Bach’s time, organ makers liked to use ‘just temperament’, which fudged the perfect fifths by making them slightly smaller. There are 12 possible fifths: C to G, D flat to A flat, D to A, etc. In just temperament, eleven of those fifths sound very sweet, but the twelfth one is so off-key that it sounds like a howling wolf – it was actually called the ‘wolf chord’. So organ makers would cheat and actually add an extra black key to each octave. Typically, I believe, the tuning put the ‘wolf chord’ at D flat (= C sharp) to A flat. So they two black keys in between G and A – one to make a nice-sounding fifth with C sharp below it, the other to make a nice fifth with E flat above it. These keys were mashed right up together, and naturally, if you pressed them both at once you got an awful noise.

    Bach favoured ‘well temperament’, invented (so far as we know) by Andreas Werckmeister. This carefully distributed the discordant ‘comma’, not exactly evenly, but closely enough that the ‘wolf chord’ disappeared. It thereby got rid of the extra key between G and A, and made it possible to transpose keyboard music from any key to any other. Each key had its own characteristic sound, based on which intervals were slightly sharp or slightly flat. Bach wrote his Well-Tempered Clavier for this type of keyboard, and almost immediately performers began to insist on having instruments tuned in this fashion.

    Nowadays, keyboards all use equal temperament, in which every semitone interval is the same, with a ratio of (12√2):1. (The ‘12’ should be superscripted, but the comment box won’t let me use the HTML tag for that.) Twelve semitones thus add up to exactly an octave (2:1), but no other interval is quite accurate. However, they are quite close, and the discords and ‘beating’ are so mild that most people, even trained musicians, just don’t notice. Bach’s pieces don’t sound quite as interestingly mellow on a modern keyboard, but they still work. They wouldn’t have worked at all on the old-fashioned keyboards with their wolf tones.

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