On the Well-Tempered Clavier's title page, J.S. Bach wrote that these works were "…for the profit and use of the musical youth eager to learn as well as for the pastime of those already skilled in this study." How we interpret the meaning of "learning" and "pastime" is up to each of us. For me, the most striking characteristic of this work is its perfect relationship between counterpoint and harmony. I have always desired to understand the mechanisms behind this relationship, to find the source of Bach's harmonic awareness, and to then play these compositions with this understanding.
The current prevailing paradigm is that the scores of the WTC are essentially composed of pitches and intervals directly projected from Bach's mind into different voices. Under this paradigm, the harmony is widely considered, at least in many of Bach's fugues, to be the inexplicable result of the constant encounters between the different voices, thus disregarding any possibility to find structured harmonic progressions in the preludes and fugues. Therefore, any harmonic study is reduced to a theoretical exercise, with no link to the mental process of the composition's creation or performance.
Despite the alleged insignificance, the urge to understand Bach's harmonic thinking is hardly a new one. In 1773, a student of Kirnberger's, J.A.P. Schulz wrote a treatise at his teacher's request. This treatise, "Die wahren Grundsätze zum Gebrauch der Harmony", (The true principles for the practice of harmony) includes harmonic interpretations of Bach's Fugues in B Minor, bk. I, and in A Minor, bk. II. As part of this harmonic study, the treatise adds a realized thorough bass and two figured fundamental basses on independent staffs to each fugue.
By the time I read this treatise, I had already begun to discover that logical progressions of implied fundamental basses—which I believed were representations of a mental process—lay at the core of many of Bach's compositions. Schulz's work was an important step, as his thorough bass showed that these fugues could be understood beyond the given contrapuntal lines, but he did not describe the progressional logic to be found across entire compositions. I accomplished the next step by completely dissociating the bass from a staff, since writing these basses on a staff contradicts their abstract nature. This also avoids any confusion with the natural resonance's bass.
By seeking to break away from conventional understandings of Bach's compositional process, I was able to come at the problem from a new direction. Through my search for how Bach's melodic lines may have resulted from a far deeper mental process, I was led toward the mental-bass concept, and these mental basses allowed me to formulate harmonic solutions for all 96 pieces of the WTC.
This edition of the Prelude and Fugue in E-flat Major from the Well-Tempered Clavier, bk. II, presents a full score harmonic interpretation illustrated by a new graphical concept (explained with a quick reference card) within the score itself, permitting study and understanding of the harmony's logic through the music itself, and without "blather".

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