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7 April 2020

Insight: Bach Inverted

Edward Primrose Image: Edward Primrose  

Edward Primrose explains his long-term fascination with Bach's work, particularly The Well-Tempered Clavier, and how this led to a re-imagination of all its preludes and fugues, Bach Inverted. This article is the latest instalment in our 'Insight' series, in which the AMC's represented artists take a close look at some aspect of their own work.

Do we remember the first time we hear a sound? It's an important moment for associations. As a new-born, we are surrounded by a cacophony of vocal sounds that eventually are construed to be a language which we can decipher and speak. What, then, do we make of hearing a piece of music with virgin ears? And what exactly do we remember?

The first time I became impassioned by a composer with the name 'Bach' was on hearing the 'Dorian' Fugue on vinyl, played by Heathcote Statham on the glorious Norwich Cathedral organ. I lived in awe of that recording for many years, though remaining ignorant of its compositional construction. Patently, its effect was profound.

It wasn't until I was studying at the Canberra School of Music that there emerged some understanding of J.S. Bach through the guidance of the inspiring composer, pianist and teacher (and one of the dedicatees in this project), Dr Donald Hollier.

From that time, the gradual discovery of diatonic processes, of the intricacies of counterpoint and functional harmony, and of what preceded and proceeded them, has spurred on a lifelong journey.

During the many dark periods as a composer, it is of some solace to be able to return to the source from time to time. And so, to grapple with Bach's (among others') compositional technology can lead to a better understanding of music composition as a general concept, not to mention producing a general sense of wellbeing.

Analysis is one thing, however, to tamper with musical master works from the past might present some with issues of authenticity, of respect, or perhaps even of religious fervour. The fact that our notions of harmony have advanced under the influence of the last three hundred years leaves us with a much richer auditory palette. And yet, Bach's extraordinary feats as an aural architect on the vertical and horizontal planes make The Well-Tempered Clavier one of the great musical landmarks.

So, then the question arises: why tamper with it? A noble defence might be that of the perpetual student who believes in engaging in the past as a pathway towards a deeper understanding of current musical processes. Or is it a classical conservative's delayed reaction to that postmodern practice in which anything can be considered to be music? In reality, it is simply a way of allowing a composer to muck around in Bach's workshop for a while, listening to him hum and tap his feet - something usually only reserved for performers and musicologists.

The process of re-imagining of course, is also a lot of fun. Cheekily I would like to think that Bach himself might have enjoyed such an exploration of these epic works. A suggestion of this perhaps can be gleaned from his original preface (see below).

The Well-Tempered Clavier

Part 1 of Johann Sebastian Bach's Well Tempered Clavier (hereinafter the WTC) is prefaced with a long title:

"The Well-Tempered Clavier, or Preludes and Fugues through all the tones and semitones, both as regards the tertiam majorem or Ut Re Mi [i.e., major] and tertiam minorem or Re Mi Fa [i.e., minor]. For the profit and use of the studious musical young, and also for the special diversion of those who are already skilful in this study, composed and made by Johann Sebastian Bach, for the time being Kapellmeister and Director of the Chamber-music of the Prince of Anhalt-Cothen. In the year 1722."1

Part 2 was completed 20 years later in Leipzig. Together, the two parts not only provide a dictionary of harmonic functions for every diatonic key, but also a magnificent compendium of contrapuntal devices. It's a rich vein of musical wonderment and yet one that went by virtually unnoticed in Bach's lifetime.

The current Bach Inverted project sprang originally from a desire to discern more clearly the independence of voices within complex counterpoint, hence leading to some form of instrumentation. The Dorian Fugue as played on a grand 20th century organ seems perfectly clear. Its subject and countersubject are distinct, the pace is slow and long notes sustain. However, the WTC, be it played on a piano or other type of keyboard, seem to present far more intricacy in the part-writing to the extent that voices could potentially disappear, in particular the fugues with over three voices. Vertical sonorities would maintain their harmonic clarity but horizontal lines seem to be easily submerged. Many of them appeared to beg for an orchestration that would expose the voices more clearly and hence the form, both musically and dramatically. Perhaps it was these thoughts that brought composers as far afield as Mozart, Beethoven, Webern, Elgar, Stravinsky and Peter Maxwell Davies, among others, to orchestrate some of these works for very different ensembles.

Glenn Gould was one exceptional pianist who, more than most, was able to retain a better independence of parts, an ability that I would account to Gould's refined ear and a wonderful technical artistry.

However, I'm of the opinion that many of the works from the WTC were not necessarily designed uniquely for a keyboard at all but, rather, to satisfy more general urges: to prove the possibilities of well-tempered tuning across all major and minor keys, certainly, but also to explore systematically the possibilities of counterpoint along with a consolidation and appraisal of diatonicism in its horizontal and vertical aspects. This advanced contrapuntal research continued with Bach's later Musical Offering and The Art of Fugue.

A hint lies in the use of pedal points. A clavichord or harpsichord cannot sustain. Even a modern piano can only sustain certain bass registers and so, unless played on an organ, the many works that contain pedal points with a duration longer than a bar lose some of their tension and complexity.2

The Bach Inverted project

Edward Primrose: Bach Inverted, Fugue 15, p. 1 - larger view.

Not being satisfied with a mere adaptation to another sound source, the challenge went begging to firstly adapt a work to its opposite mode. If nothing else, it was just to see whether it was possible and what would be the effect. The exercise began with the Eb major Prelude in Book I. Arranging this in Eb minor was such an interesting exercise and ultimately fulfilling. The thought then occurred: why not the Fugue as well … why not the entire volume … then, why not both volumes?

Thus, Bach Inverted was initiated - to arrange all preludes and fugues of The Well-Tempered Clavier into their opposite mode - major to minor, and minor to major. Initially the process was thought to be straightforward and simply another way of further uncovering the magic of diatonic composition. But a more complex challenge lay in the interpretation of contrapuntal lines in the forging of modulations within each work.

After attempting a few, it was necessary for rules to be established so that the results would still resemble Bach's style and in order to have some consistency. And so the following strictures were adhered to:


1. The tonic key of each of the 96 works is converted to its opposite mode (E.g. Part 1, number I is now in C minor);
2. Every note has to be accounted for, and no notes are added3;
3. Every note is to maintain its alphabetic identity hence its scale degree within each key. e.g. 'G' can become Gb, G# or G## but never F## or Abb)
4. Aside from the tonic key, during each work where possible, reverse the original mode (major to minor, minor to major);
5. The subject and counter subject in each fugue are to be treated consistently in parallel with the original;
6. Those works in the extreme key signatures were moved to their enharmonic equivalents (e.g. C# major to Db major);
7. Each work is to be reassembled in its original keyboard format thus assuring playability and providing means for comparison; The Urtext - G. Henle Verlag edition was a guide;
8. Nomenclature - Each of the works is given a unique ID e.g. BI-WTC-2 10B. This represents 'Bach Inverted - Well Tempered Clavier, part or volume 2, number 10, Fugue'. (A = Prelude, B = Fugue). The titles also reference the original BWV numbering.


The current revision necessitated a re-think in approach to some of the works, while others have passed through with only minor adjustments. It was important to discover how many mistakes I had made initially, even in misreading the original manuscript, while some errors keep reappearing due to an issue with the process in which notation software sometimes misinterprets an enharmonic spelling.

It's clear that there is no 'one way' of undertaking this task. There still remain questions of style and diatonic coherence. Others may find superior solutions, and it was interesting to learn how many possibilities exist.

Bach's compositional evolution is apparent in the two parts of WTC and this is displayed by his increasing harmonic dexterity and extended diatonicism. This, incidentally, had a noticeable impact on the facility with which the works could be transformed. Part 2 is a lot more exploratory of chromaticism, sometimes leading to passages where major and minor modes are less distinguishable. This is typically the case when thematic ideas utilise chromatic movement as in WTC 2 Fugue XIII in F# major (now BI-WTC-2-13B in F# minor).

Further in Part 2, the A minor Prelude XX, and the fugues in G# minor XVIII, and Bb Minor XXII, both offer passages in which chromaticism pushes towards the notion of a type of hybrid major/minor mode.

Modulations and transitions are often the lifeblood of variation in particular within the fugues. They are also the major hurdle in a mode-reversal exercise like this one. An example occurs with one of the more challenging fugues - Part II, Nº9 in E major (BI-WTC-2 09B, now in E minor). This is so perfectly formed in its original key structure that it is difficult to imagine a more refined musical utterance. At bar 16 there is a cadence into the sub-mediant minor region (C# minor). In its reworking into E minor, one choice could be to replace the sub-mediant minor with the sub-mediant major region (C# major). However, this is a very long way from the new tonic and so the flattened sub-mediant major (C major) was chosen. This is the sort of choice that one is obliged to make, with differing results depending on each piece. In this case, getting to and from C major while following the rules is relatively easy and made permissible within a minor tonic. An even more abrupt solution can be found in Part 1 Fugue X for two voices (BI-WTC-1 10B) now in E major. For some, its resultant key scheme might venture a little too far from Baroque sensibilities.

It became quickly apparent that moving from major to minor was potentially much easier than minor to major, simply due to an important aspect of diatonic harmony: minor keys have the use of two extra notes on the 6th and 7th degrees. Naturally, then, the reverse is made more difficult due to the loss of those two notes in the major mode, although this limitation seems to have less importance in volume 2 in which there is a great deal more chromaticism.

The ingenious B minor fugue in Part 1 has a 'dodecaphonic' subject employing all 12 chromatic notes, possibly the earliest work to do so. Its re-imagined major version (BI-WTC 1-24B) loses two of those notes (following Bach's own example from within the Fugue - bars 44-46, beginning D major). Fortunately, the full 12-note version can be employed when it replaces that very instance (now beginning in D# minor).

On the project's negative side, the gorgeous Part 1 Eb minor and Bb minor Preludes lose all their delicious piquancy when translated into major. On the positive, some interesting new works are revealed, particularly when translated from major to minor. The Part 1 number 15 Fugue (BI-WTC-1 15B) actually feels more satisfying with its subject seeming more at home in the minor mode.

The process has revealed a little about the nature of fugue. When we talk of remembering a sound, it is the fugue's subject that is heard at the start and which continually beckons the ear as it is 'subjected' to continuous transformation. In Bach's hands, the fugue becomes a condensation of elaborate composition tropes that reference, among other things, rondo form, variation technique, thematic development and diatonic structures that pre-figure sonata form. Due to the size of the WTC, it offers a wealth of examples of contrapuntal ingenuity that, although stylistically rooted in the security of late Baroque diatonicism, offers vast amounts of research data for any contemporary composer or songwriter.

I would encourage others to try out the exercise, or use it as a teaching tool. It may throw up questions of style but it will certainly lead to a fuller understanding of harmony, fugue and Bach's genius. And naturally it could go further with transformations into other scale forms - modes, whole tone and octatonic scales, dodecaphonic forms, Indian ragas, microtonal intervals and so on.


After spending some time tinkering, another thought occurred - that a new work could spring from this. Nothing much can be said while it is still in development but it will involve live players and electronics in performance (assuming there is life after Covid-19). It won't be Bach but it will involve Bach as its skeleton.


1. "Das Wohltemperirte Clavier, oder Praeludio, und Fugen durch alle Tone und Semitonia, So wohl tertiam majorem oder Ut Re Mi anlangend, als auch tertiam minorem oder Re Mi Fa betreffend. Zum Nutzen und Gebrauch der Lehrbegierigen Musicalischen Jugend, als auch derer in diesem studio schon habil seyenden besonderem Zeit Vertreib auffgesetzet und verfertiget von Johann Sebastian Bach. p.t: HochFürstlich AnhaltCöthenischen CapelMeistern und Directore derer Cammer Musiquen, Anno 1722" (p.iv-v, Das Wohltemperierte Klavier, Teil 1, G. Henle Verlag)

2. Works with extensive pedal points: WTC Part 1 - Preludes V, VII, X, & XII; Fugues I, II, IV, XI, XIV & XV. WTC Part 2 - Prelude I; Fugue III.

3. NB: No attempt was made to interpret ornamentation which has been copied from the original.

> Edward Primrose - AMC profile

> A new release of Edward Primrose's work, 'The Art of lies and obfuscation : cine-music-theatre' is available from.... See album details & audio sample (AMC Online).

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What about Bach backwards?

Congrats on the article and constructive approach, but it is really just the beginning. Bach played backwards sounds great - I had one of his solo violin sonatas  played backwards on the Inventionen Festival, Berlin in 1989. (Bach's own crab canons should give a hint). Then there is the tuning. Well Tempered does not mean equal tempered! In the time of Bach there were over a 100 different non-equal tuning systems including Bach's own - look it up. What would be the point of exploring different keys, if all the intervals sounded identical in each key (as they do in equal temperament)?

Re: What about Bach backwards?

Thanks for your comments Jon. Of course there is fun to be had with all the contrapuntal devices that Bach explored including palindromic devices. I guess I could have been clearer on the concerns of this exercise and article and these are the interplay of the melodic/contrapuntal (horizontal plane) with the harmonic (vertical plane) as well as the 'freeing' limits imposed by diatonicism. The point of the well-tempered system was that it now allowed modulation theoretically into any key within the same work - something without which would have made the later works of, for example, Beethoven or Schubert unimaginable.