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(3) “
Orgel-Büchlein
, in which a beginner at the organ is given instruction in developing a chorale in many divers ways, and at the same time in acquiring facility in the study of the pedal since in the chorales contained therein the pedal is treated as wholly obbligato.

In Praise of the Almighty's will

and for my neighbor's greater skill.”

[A volume of 182 pages (many unfilled) in quarto format; undated and primarily written in Weimar; the title page was added in Cöthen, ca. 1722–23.]

 

None of these collections was specifically composed for Leipzig, but the final preparation of the fair copies of
The Well-Tempered Clavier
and the
Aufrichtige Anleitung
and, in particular, the carefully coordinated phraseology of all three title pages would have gone a long way toward impressing the authorities in Leipzig, especially an experienced master teacher like rector Ernesti. Bach's organist, concertmaster, and capellmeister background would have sufficed to establish his credentials as music director and leader of vocal-instrumental ensembles, but private instrumental lessons and especially keyboard instruction was an integral part of the cantor's daily activity at St. Thomas's. (Indeed, most resident students of the school had a keyboard instrument in their study cubicles.)
103
Therefore, these keyboard volumes epitomizing a fundamentally pragmatic approach to musical science would not only demonstrate Bach's didactic experience but, more important, underscore his stature as musical scholar, deemed essential for a successor to the learned Johann Kuhnau and for as ambitious and demanding an academic environment as St. Thomas's.

Not without reason did Prince Leopold, in his wonderfully supportive letter of dismissal, characterize Bach as “well learned” in order to introduce him into his new Latin school ambience: the new cantor, ranking in the faculty hierarchy of the school immediately below the rector and conrector, deserved proper recognition as
musicus bene doctus
or
musicus pereruditus
. At the time, Leopold knew and understood his capellmeister better than most, and he could genuinely appreciate the kind of musical science represented in a work such as
The Well-Tempered Clavier
. The three collections offer a systematic exploration of clearly defined musical goals in the form of well-structured, sophisticated keyboard exercises and lessons addressing the various needs of “the musical youth,” the “beginner at the organ,” and generally “those desirous of learning.” And the
Orgel-Büchlein
's title page summarizes Bach's pedagogical credo in a homespun poetic two-liner: “in Praise of the Almighty's will / and for my neighbor's greater skill” (“Dem Höchsten Gott allein zu Ehren / dem Nechsten, draus sich zu belehren”).

In the
Aufrichtige Anleitung
, Bach demonstrates, in two sets of fifteen contrapuntal pieces, how a coherent musical setting can be developed out of a single short and clearly delineated yet freely conceived idea (
inventio
, or
invention
), first in the form of strict two-part compositions (one voice each for the right and left hands) with emphasis on voice leading; then in the form of strict three-part compositions, with emphasis on triadic harmonies, that is, on three voices “sounding together” (
sinfonia
, from the Greek
symphonia
). At the same time, the book teaches basic keyboard technique and fingering—in the first in vention, for example, the basic motive
demands through out the absolutely equal use of all five fingers of both hands—as well as a “singing style” of performance. Additionally, Bach explores the diatonic range of the tonal system without straying beyond the traditional framework of the fifteen keys (not exceeding four sharps or flats) that are playable in unequal temperament (a system of tuning in which the octave had not yet been divided into twelve equal semitones) and that endow each key with a distinct character. In the
Aufrichtige Anleitung
, Bach decided to organize the inventions and sinfonias systematically in an ascending key scheme; the earlier version of the collection presented the pieces in ascending and descending order, pursuing a different kind of structural logic—six ascending “white” keys, C to A, with their “natural” root triads (C major, D minor,…to A minor) followed by nine descending keys, B to C, with root triads requiring sharps and flats (B minor, B-flat major,…to C minor; see Table 7.6).

The revised key structure of the
Aufrichtige Anleitung
conforms to the uniformly ascending key scheme of
The Well-Tempered Clavier
, but illustrates how to differentiate between the conventional diatonic scheme, on the one hand, and the fully developed chromatic scheme of twenty-four keys based on the premise of equal temperament, on the other. Bach's use of Andreas Werckmeister's term “well-tempered”
(wohl temperirt)
indicates his preference for a slightly modified system of tuning with “all the thirds sharp,”
104
enabling him to play in all twenty-four keys without losing the characteristic features of individual keys—a loss that occurs if the octave is divided into absolutely equal semitones (what was to become a new standard would have been regarded then as a serious drawback). Bach's primary purpose in writing
The Well-Tempered Clavier
, then, was to demonstrate in practice the musical manageability of all twenty-four chromatic keys, a system that earlier had been considered only theoretically. Before and around 1700, the general spirit of discovery spurred by the Scientific Revolution had prompted a new spurt of mathematical and physical research, predominantly by German scholars like Werckmeister, to expand and systematize the conventional tonal system. Johann David Heinichen, a student of the Thomascantor Kuhnau, had by 1710 devised the circle of fifths, clarifying the harmonic interrelationships within a system of twenty-four modes or keys,
105
and several composers wrote small experimental pieces in remote keys. But as late as 1717, Johann Mattheson still deplored that “although all keys can now, per temperament [tuning], be arranged in such a way that they can be used very well, diatonically, chromatically, and enharmonically,” a true
demonstratio
was lacking.
106
It fell to Bach, who accepted this challenge, to demonstrate the compositional practicability of the new system of twenty-four keys, and he did so on an unparalleled level of compositional refinement and technical perfection.

The Well-Tempered Clavier
established the parameters of a twenty-four-key system, with twelve major and minor modes (since the terms “major” and “minor” were not yet in general use, Bach's title describes the modes in terms of the determining interval of a major or minor third). The “theme” of every Prelude and Fugue, therefore, is first and foremost its key, as shown in the most basic form at the beginning of the collection. The first Prelude introduces the C-major key in its most rudimentary form, the C-major triad, as a point of departure; the Fugue then completes the demonstration by introducing C major in terms of horizontal harmony, that is, by way of a linear subject that defines the key. This quasi-system of vertical and horizontal definition of the keys is pursued throughout the work. Bach also shows how to preserve the idiosyncrasies of the individual keys: in E minor, for example, he continues a tendency to stress the old Phrygian subsidiary “dominants” of the key—A minor and C major—that resulted from the need to avoid the B-major triad, which sounds extremely harsh in unequal temperament. The unique collection of twenty-four preludes and fugues also aspires to a second goal, the juxtaposition of two fundamentally different kinds of polyphonic musical settings: improvisatory and free-style scoring in the preludes versus thematically controlled and strict contrapuntal voice leading in the fugues. The preludes therefore present a wide variety of textural choices, from rudimentary chordal models (such as the
arpeggiando
and
perpetuum mobile
styles of the first two) to dance-type and imitative polyphonic settings. Fugal technique, on the other hand, is presented in various kinds of scoring, using two (1 fugue), three (11 fugues), four (10 fugues), and five voices (2 fugues). Additionally, the use of all metric categories (
,
, 3/4, 3/8, 6/4, 6/8, 9/8, 12/8, 12/16, 24/16), different stylistic models, and a multiplicity of special compositional features contributes to the overall kaleidoscopic spectrum of the collection.

More than any other of Bach's works composed before 1722, the preludes and fugues of
The Well-Tempered Clavier
manifest his resolve to leave nothing untried, even if it meant exploring avenues where no one had gone before. In demonstrating that the tonal system could be expanded to twenty-four keys not just theoretically but practically, Bach set a milestone in the history of music whose overall implications for chromatic harmony would take another century to be fully realized. He set the stage by exploiting fully the chromatic and enharmonic potential of the keys, especially in pieces such as the fugues in C-sharp minor (BWV 849/2), E Minor (BWV 855/2), F minor (BWV 857/2), F-sharp minor (BWV 859/2), and B minor (BWV 869/2). Each individual piece, whether prelude or fugue, helped push the limits of musical composition, resulting in twenty-four diverse yet internally unified structures of musical logic. Simultaneously, standards of musical performance were brought to a new high if only in the necessary and uncompromising application of all ten fingers of the keyboard player.

In establishing a multifaceted canon of technical standards and compositional and aesthetic principles,
The Well-Tempered Clavier
is complemented, and in part preceded, by works of similarly profound ambitions. Both the
Orgel-Büchlein
and the
Aufrichtige Anleitung
explore how to invent, develop, and elaborate on a precisely delineated musical idea, one that is either derived from given material (such as the melody and affect of a hymn) or freely conceived. In a similar systematic way, both also focus on the buildup of stylistically appropriate performing skills (c
antabile
, or “singing,” for example) for two hands managing a two-or three-part contrapuntal structure on the harpsichord, or for two hands and two feet negotiating the complex textures of an organ setting. But as we may ascertain by comparing the Weimar
Orgel-Büchlein
with the later collections, the refined and advanced compositional art that characterizes the Cöthen repertoire emerged gradually over the years. And although keyboard works play a decisive role in this respect—harpsichord and organ functioning as his experimental laboratory—Bach's musical efforts were from the outset much more encompassing and covered a broad range of instrumental and vocal compositions.

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