Bach’s Incredible ‘Google Doodle’

Elias Gottlob Haussmann portrait of J.S. Bach holding his puzzle canon for 6 voices

No question, the guy loved codes. The famous Haussmann portrait shows him holding one of his puzzle canons. The letters of his last name add to 14 and scholars and music lovers with a lot of time on their hands discover this number (and 41, its reverse, that happens to encode his last name plus the initials of his first and middle name) embedded and structuring much of his music. In his magnum opus, The Art of the Fugue, he weaves his name with musical tones into the fabric of the final fugue using a four note subject , notes B-A-C-H (In German, B is B flat and H is B natural). Bach clearly loved codes.

The problem with codes is how far they are meant to unravel. Do they add another layer of meaning to a piece, or do they literally explain and justify every note of the music? If some Bach pieces, like The Art of the Fugue, clearly use the number 14 (as in 14 contrapuncti), then should we be assuming hidden “14s” structure all Bach’s music? That can be a dangerous rabbit hole to go down.

This is all a preamble to the most mind-blowing Bach code discovery of all made just in 2005 by Bradley Lehman (“Bach’s extraordinary temperament: our Rosetta Stone,”  Early Music, Vol. xxxiii, No. 1, © Oxford University Press, 2005).  On the title page of Bach’s famous Well Tempered Clavier is a decorative doodle right above the words of the title Das Wohltemperierte Clavier.

No one thought anything of it. But Lehman believes that this doodle is not a decoration, but actually a cleverly disguised set of instructions embedded to show the method Bach used to tune his own harpsichord. Talk about codes! This one survived almost 300 years without detection!

How does it work? Well, first notice that the top of Bach’s scripted ‘C’ in his title “Clavier” ends with a clear small circle attached to the ‘doodle.” Now turn the page and ‘doodle’ upside down.

Reading from far right to left, there are 12 circles (including the tiny circle from the handwritten C)—one for each of the 12 tones. The order goes up in 5ths (tones 5 notes apart). That’s how keyboards are tuned—first by tuning the 5ths. In fact, adjusting the 5ths in the Baroque era was called “tempering” (hence “well-tempered”). So with the title page turned upside down, from far right to left, are the notes F-C (C is the small circle attached to F)-G-D-A-E all with circles that have multiple knots inside of them, then B-F#-C# circles with no knots, and finally G#-D#-A# (circles with just one knot inside).

The decoding goes like this: Lehman believes the “knots” inside the circles indicate the amount of beating a tuner hears as he adjusts pitch. You can try this yourself with a guitar or violin. Tune one string very slightly lower. Now play two strings together and you can actually hear the beating. The farther apart the strings are tuned, the more beats you will hear.

So in Bach’s doodle, a clear circle might mean a purely tuned interval— no beating. A circle with one “knot” might mean tuning with 1 beat, or slightly lowered. A circle with multiple knots meant to tune the 5th much more down so that you would hear 2 or 3 beats. 

Have I lost you? It’s beyond me too! The point is this: Lehman claims that tuning with this method reveals precisely how Bach meant his preludes and fugues to be heard, a system different from the equal temperament we use in modern tuning. That means the harmony will sound quite different at times. Certain moments will be more dissonant than in our tuning system, and other moments will be more pure.

Incredible, yes? I just recently learned about this discovery, first from a wonderful Bach lecture given by conductor Andrew Manze, and then in far more depth from a phenomenal article on tuning titled “Tampering with Nature: Playing in Unequal Temperaments” by local LA guitarist, composer, tuning expert, KPFK Global Village host, and (as of last month) Grammy Award winner John Schneider. John’s article is from the book 1001 Microtones (ed. Sarvenaz, S. & Stahnke, M.). Neumünster: Bockel-Verlag, 2014).   You can buy it here.

John discusses the Lehmann code discovery, but he has his eye on a bigger issue than Bach’s codes. He challenges modern listeners to consider and explore the fluidity of tuning in the Baroque era. In his article, John explains that tuning in the Baroque era was a dynamic artform. The intervals so immutable to our modern ears accustomed to equal temperament essentially came in many different flavors during Bach’s time.

Without getting too technical, the problem with tuning stretches at least as far back as Pythagoras in Ancient Greece. Pythagoras demonstrated a “flaw” in nature that prevents a tuning system that has both pure 3rds and 5ths. This became even more problematic as Baroque music increasingly insisted on chords outside a single key, (enter stage right “Mr. Notorious,” J.S. Bach, composing the Well-Tempered Clavier explicitly in all the major and minor keys!). Our modern equal temperament tuning system essentially gave up preserving any pure intervals. They’re all false and beat to a greater or lesser degree. But in the Baroque era, musicians actively devised different tasteful compromises to control dissonance between 5ths and 3rds, choosing which ones were more or less pure.

John’s point is that an entirely new listening experience awaits us hearing familiar Baroque music in well-tempered tunings. He writes, “Forcing the expressively unequal scales and chords of yesteryear into the Procrustean Bed of Equal Temperament is more akin to viewing Wide-Screen Technicolor movies on an old Black& White television.”

Ok. We get that John is a partisan player. But he makes a fascinating case that different tuning systems were highly prized in their own right:

It could also be that there is a surprisingly simple reason why no single Baroque temperament has emerged victorious: like ornaments, dynamics, and the other myriad subtleties of interpretation, tuning is a personal, artistic decision. Surely the keyboard players relished the creative control over their intervals no less than the violinists or singers of the era. Perhaps one size does not fit all – otherwise the greatest tuning minds of the 18th century would have agreed with one another, suggesting that today’s performer should be equally free to choose a tuning that fits one’s own personal temperament.

All of this helps clarify that tuning was not a casual affair during the Baroque era. It makes sense then that composers and performers might have wanted to jealously guard their tuning systems from competitors just as they hid secrets of their unique musical effects and techniques. The notion of Bach embedding a hidden code for those in his “inner circle” might have something to it. Conspiracy theorists unite! Who doesn’t love codes?

No question this is fun, provocative, and well worth study. But it would be sad if this inquiry took precedence over the miracle of the music itself. That’s my primary concern with the investigation of numerology in music. When the search for these patterns become the explanation for a masterpiece like Bach’s Art of the Fugue, we have crossed into a fool’s errand. Make no mistake, the greater code is the unfolding of the musical ideas themselves. That is the true grand hunt!