Prelude 13 in F-sharp (The Well-Tempered Clavier, Book I)

Last updated February 16th, 2021


Aside from painstakingly/painfully rebuilding my technique with Hanon exercises and Czerny studies, I am slowly playing through the less technically-demanding Preludes from WTC I for a touch of much-appreciated musicality in my routine. My current work-in-progress is Prelude 13 in F-sharp, it is light and mellow. I am also experimenting with different settings on my instrument; to be “historically informed”, I used the Werckmeister temperament with Baroque tuning (A4 = 415 Hz) and a harpsichord sound for the below video.

How does Bach’s music really sound in the tuning of his time?

Last updated February 6th, 2021


I do not know whether I learned this as a music student in my youth or simply assumed (wrongly) from the name “well-tempered”, but I was previously under the impression that Bach used equal temperament. Apparently this is not the case, although it seems to be a common misconception. As noted in the preface to the Bärenreiter Urtext score for the Well-Tempered Clavier (WTC), based on (among other evidence) the systematic increased complexity of fugue motifs in “uncommon” keys (i.e., keys with a large number of sharps or flats), Bach’s well-tempered tuning likely differentiated keys beyond absolute frequency.

I have absolute pitch, thus different keys already sound different to my ears, and I have always been interested in the “emotional colouring” of different keys that would arise from an unequal tuning. In order to test this, I compare different temperaments (equal, just, Werckmeister, and Kirnberger) with Bach’s Prelude 2 in c (WTC I) in the video below, which is probably the first proper introduction to the WTC for many pianists—moody, dramatic, and relentless. The piano recording at the beginning is a “modern” benchmark, where the A is tuned to 440 Hz. All other recordings use a harpsichord voice and have the A tuned to 415 Hz.
Even though the just temperament showcased in the video is tuned on a minor triad with a base of C, it likely is a natural minor and not harmonic minor tuning. Clearly, E♮, A♮, and B♮ are all quite dissonant, and F♯ and C♯ even more so. Normally just intonation is more harmonically pure and thus pleasing compared to equal temperament, but the amount of modulation in this piece makes this tuning a bad choice. Werckmeister also seems more pleasing compared to Kirnberger, again evident in the accidentals.
Compare this with the exuberant Prelude 3 in C♯, we avoid the problem with accidentals in the harmonic minor scale. Here just intonation works better, although still not perfectly due to modulation to different keys. It is worth noting that like equal temperament, Werckmeister and Kirnberger are universal tunings designed to be feasible for all keys, whereas just intonation works best for the tonic key, but its quality deteriorates the farther (in fifths) we are from the fundamental. The bonus clip (7:00) in the above video demonstrates this, where a tonic of C is used to play the piece with rather disastrous (and amusing) results.
Here is my human rendition without any exotic tuning. It is not perfect, but has a little more musicality than the MIDIs I generated and also my playing in the past, which is certainly reassuring. I am working on my technique again after a 15-year hiatus from practicing regularly. (Conveniently, this will also help with my profession as a computational chemist by allowing faster and more precise typing!)

As an aside, I remember reading somewhere that this piece was originally written in C instead of C♯, and that Bach later changed the key signature to make it fit within the theme of the WTC. This hypothesis seems consistent with how the piece plays out, as the development section contains modulations to several keys with 1–4 double-sharps which is quite unintuitive to play (and write, I imagine), but would be much more reasonable if these were simply (single-)sharps instead in the case of C.
For a rather different flavour, give the contemplative and anguished Prelude 22 in b♭ a listen. I have changed up the ordering of the temperaments slightly, they are now in order of most to least “equal”, and this also makes for an easier comparison between the modern equal temperament and Baroque Werckmeister, allegedly very close to Bach’s well-tempered tuning. Interestingly, although the dissonance in just intonation is clearly audible, it almost isn’t as irksome as it has been in the previous two examples. I also do not hear as much of a difference between Werckmeister and Kirnberger for this particular piece, although they are different from the recording with equal temperament.

To conclude this mini-analysis, I would like to present a more well-known piece and one of my favourites: Prelude 10 in e. In fact, there are a number of similarities between this one and Prelude 2—for example, both are driven by a steady stream of sixteenth notes, and both contain a marked tempo change. However, whereas Prelude 2 expresses its storminess outright, the emotion in Prelude 10 is more subdued, leading to a tense build-up that culminates with a diminished chord just before the tempestuous stretto. The pure tuning in e has noticeable dissonant notes as usual (in particular the F♮ which appears several times), and Werckmeister has a flatter tonic triad compared to equal temperament.

“Picture in Picture”

Last updated February 2nd, 2021


Here is my transcription of the music from an old Bell Canada commercial.