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According to Bach’s first biographer, when the great composer was asked to explain the secret of his success he replied “I was obliged to be industrious. Whoever is equally industrious will succeed equally well”. I respectfully disagree.

First, Bach didn’t have to drive the twenty kids he fathered over his lifetime to soccer practices, arrange their playdates, prepare and cook dinners, and do the laundry. To his credit he did teach his sons composition (though notably only his sons). But even that act was time for composition, an activity which he was seemingly able to devote himself to completely. For example, the fifteen two part inventions were composed in Köthen between 1720 and 1723 as exercises for his 9 year old son Wilhelm Friedemann, at the same time he was composing the first volume of the Well Tempered Clavier. In other words Bach had the freedom and time to pursue a task which was valued (certainly after Mendelssohn’s revival) by others. That is not the case for many, whose hard work, even when important, is trivialized and diminished when they are alive and forgotten when they are dead.

The second reason I disagree with Bach’s suggestion that those who work as hard as he did will succeed equally well is that his talent transcended that which is achievable by hard work alone. Although there is some debate as to whether Bach’s genius was in his revealing of beauty or his discovery of truth (I tend to agree with Richard Taruskin, whose view is discussed eloquently by Bernard Chazelle in an interview from 2014), regardless of how one thinks of Bach genius, his music was extraordinary. Much was made recently of the fact that Chuck Berry’s Johnny B. Goode was included the Voyager spacecraft record, but, as Lewis Thomas said,  if we really wanted to boast we would have sent the complete works of Bach. As it is, three Bach pieces were recorded, the most of any composer or musician. The mortal Chuck Berry and Wolfgang Amadeus Mozart appear just once. In other words, even the aliens won’t believe Bach’s claim that ” whoever is equally industrious will succeed equally well”.

Perhaps nitpicking Bach’s words is unfair, because he was a musician and not an orator or writer. But what about his music? Others have blogged him, but inevitably an analysis of his music reveals that even though he may have occasionally broken his “rules”, the fact that he did so, and how he did so, was the very genius he is celebrated for. Still, it’s fun to probe the greatest composer of all time, and I recently found myself doing just that, with none other than one of his “simplest” works, one of the inventions written as an exercise for his 9 year old child. The way this happened is that after a 30 year hiatus, I recently found myself revisiting some of the two part inventions. My nostalgia started during a power outage a few weeks ago, when I realized the piano was the only interesting non-electronic instrument that was working in the house, and I therefore decided to use the opportunity to learn a fugue that I hadn’t tackled before. A quick attempt revealed that I would be wise to brush up on the inventions first. My favorite invention is BWV 784 in A minor, and after some practice it slowly returned to my fingers, albeit in a cacophony of uneven, rheumatic dissonance. But I persevered, and not without reward. Not a musical reward- my practice hardly improved the sound- but a music theory reward. I realized, after playing some of the passages dozens of times, that I was playing a certain measure differently because it sounded better to me the “wrong” way. How could that be?

The specific measure was number 16:bach1bach2This measure is the third in a four measure section that starts in measure 14, in which a sequence of broken chords (specifically diminished seventh chords) connect a section ending in E minor with one beginning in A minor. It’s an interesting mathomusical problem to consider the ways in which those keys can be bridged in a four measure sequence (according to the “rules of Bach”), and in listening to the section while playing it I had noticed that the E♮notes at the end of measure 15 and in measure 16 were ok… but somehow a bit strange to my ear. To understand what was going on I had to dust off my First Year Harmony book by William Lovelock for some review (Lovelock’s text is an introduction to harmony and counterpoint and is a favorite of mine, perhaps because it is written in an axiomatic style). The opening broken diminished seventh chord in measure 14 is really the first inversion of the leading note (C♯) for D minor. It is followed by a dominant seventh (A) leading into the key of C major. We see the same pattern repeated there (leading diminished seventh in first inversion followed by the dominant seventh) and two more times until measure 18. In other words, Bach’s solution to the problem of arriving at A minor from E minor was to descend via D -> C -> B♭ -> A with alternating diminished sevenths with dominant sevenths to facilitate the modulations.

Except that is not what Bach did! Measure 16 is an outlier in the key of E minor instead of the expected B♭. What I was hearing while playing was that it was more natural for me to play the E ♭notes (marked in red in the manuscript above) than the annotated E♮notes. My 9 year old daughter recorded my (sloppy, but please ignore that!) version below:

Was Bach wrong? I tried to figure it out but I couldn’t think of a good reason why he would diverge from the natural harmonic sequence for the section. I found the answer in a booklet formally analyzing the two part inventions. In An Analytical Survey of the Fifteen Two-Part Inventions by J.S. Bach by Theodore O. Johnson the author explains that the use of E♮instead of E ♭at the end of measure 15 and in the beginning of measure 16 preserves the sequence of thirds each three semitones apart. My preference for E♭breaks the sequence- I chose musical harmony of mathematical harmony. Bach obviously faced the dilemma but refused to compromise. The composed sequence, even though not strictly the expected harmonic one, sounds better the more one listens to it. Upon understanding the explanation, I’ve grown to like it just as much and I’m fine with acknowledging that E minor works perfectly well in measure 16. It’s amazing to think how deeply Bach thought through every note in every composition. The attention to detail, even in a two part invention intended as an exercise for a 9 year old kid, is incredible.

The way Bach wrote the piece, with the E♮can be heard in Glenn Gould‘s classical recording:

Gould performs the invention in 45 seconds, an astonishing technical feat that has been panned by some but that I will admit I am quite fond of listening to. The particular passage in question is harmonically complex- Johnson notes that the three diminished seventh chords account for all twelve tones- and I find that Gould’s rendition highlights the complexity rather than diminishing it. In any case, what’s remarkable about Gould’s performance is that he too deviates from Bach’s score! Gould plays measure 18 the same way as the first measure instead of with the inversion which Bach annotated. I marked the difference in the score (see oval in battleship gray, which was Gould’s favorite color).

Life is short, break the rules.

This post is dedicated to the  National Endowment for the Arts and
the National Endowment for the Humanities who enrich our lives by supporting the arts and the humanities.

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