TIPPING THE SCALES: A NEW PERSPECTIVE ON

BACH'S WELL-TEMPERED CLAVIER

BACH'S WELL-TEMPERED CLAVIER

*'We must not be misled by the fact that we possess hardly any sketches or drafts of his...Bach worked like the mathematician, who sees the whole of a problem at once, and has only to realize it in definite values.'*

- Albert Schweitzer

*What follows is an evaluation, or argument, in abridged form on Bach's Well-Tempered Clavier. It demonstrates a high degree of interconnectedness in that the likelihood of a single statement invariably increases the likelihood of another. Like the example above, for instance. It seems fairly self-evident that Bach intended to account for all twelve-tones within the subject of this fugue, and in this sense it may be regarded as twelve-tone. However, we generally regard a twelve-tone sequence as one without pitch-repetition. Consequently the parameters of our judgement are presumably different to those of Bach, therefore we ought not rule out what Bach most likely had in mind by imposing parameters which for him did not*

*exist.*

*If Bach conceived of this subject as twelve-tone entailing pitch-repetition, which seems very likely, it follows that in a hypothetical, twelve-tone non-chromatic symmetrical scale - which given the b minor fugue subject and the chromatic scale was a familiar concept to him - a repeated pitch will simply retain its original numeric value. Therefore, acknowledging Bach's fondness for gematria (the substituting of numbers for letters), a twelve-tone scale producing B (Bb) = 2, A = 1, C = 3 and H (B-natural) = 8 seems a justifiable assumption. (As demonstrated in the evaluation, the version of the B-A-C-H scale shown above is the most economical variant of this scale. The lettering is not affected by the C#.) The example illustrates a correspondence suggesting that the fugue subject might have been based upon this scale. If so, it may be said that the scale is quite literally 'tempered' through a tonal realization, and 'well-tempered' given that the subject is musical poetry transcending scale-theory. Hence 'Well-Tempered' - considered in this context - may refer to the translation of atonal symmetry into tonal poetry as conveyed through the instrument, 'Clavier', of Bach's imagination.*

PREFACE TO THE EVALUATION

I wish to lend some historic perspective to provide a brief context for the WTC argument. Gottfried Leibniz - the German philosopher/mathematician to whom the invention of modern calculus is attributed - was a contemporary of Bach, and in fact lived much of his life in relative proximity to him. He believed in a

So for example, if 'animal' and 'rational' equal the numbers 2 and 3 three respectively, then 'man' - a rational animal - equals 6 (i.e. 2 x 3 = 6); hence, man is a

And…

With regard to the above, the following argument clarifies almost conclusively in my view that Bach created something strikingly similar to what Leibniz recalls. It may be worth noting that Bach found himself incarcerated in November 1717, exactly one year after Leibniz's death which, despite his earlier fame, passed virtually unnoticed. Given that the earliest surviving autographed manuscript of the WTC dates from 1722 it would appear naive to ignore the distinct possibility that these coinciding events may have directly influenced the creation of the WTC.

I wish to lend some historic perspective to provide a brief context for the WTC argument. Gottfried Leibniz - the German philosopher/mathematician to whom the invention of modern calculus is attributed - was a contemporary of Bach, and in fact lived much of his life in relative proximity to him. He believed in a

*deterministic*universe, one of*'pre-established harmony'.*Leibniz was a figure of profound influence in the sciences (a fact that would hardly have been lost on Bach), and among his many investigations, devised ontological arguments (i.e. pertaining to the existence of God, something else of which Bach would have been profoundly aware), as well as attempted to develop a theory pertaining to the unassailability of prime numbers, which were taken to represent simple concepts and consist of logically deducible properties. He writes:*All concepts are combinations of simple ideas, and the composition of concepts analogous to the composition of numbers from prime factors.*So for example, if 'animal' and 'rational' equal the numbers 2 and 3 three respectively, then 'man' - a rational animal - equals 6 (i.e. 2 x 3 = 6); hence, man is a

*product -*in mathematically derived language - of the two primes in combination. Leibniz's methods of observation also incorporated music (to a much greater degree than Schopenhauer, for instance). For example, Leibniz writes:*Music is a secret arithmetical exercise, and the person who indulges in it does not realize that he is manipulating numbers.*And…

*I recall once drawing a harmonic line divided in such a fashion that one could determine with the compass the different compositions and properties of all musical intervals.*With regard to the above, the following argument clarifies almost conclusively in my view that Bach created something strikingly similar to what Leibniz recalls. It may be worth noting that Bach found himself incarcerated in November 1717, exactly one year after Leibniz's death which, despite his earlier fame, passed virtually unnoticed. Given that the earliest surviving autographed manuscript of the WTC dates from 1722 it would appear naive to ignore the distinct possibility that these coinciding events may have directly influenced the creation of the WTC.

*A diagram taken from*

*the evaluation of*

*Bach's*

*Well-Tempered Clavier.*

*It charts*

*each division*

*of*

*the symmetrical scales*

*with*

*the relevant pitches*

*derived*

*from*

*the corresponding*

*fugue subjects.*

EVALUATION OF BACH'S WELL-TEMPERED CLAVIER

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