One-hundred years after Kepler, J.S. Bach creates a revolution in the language of harmonics by subjugating the sounds of the harmonic system to the higher harmony of the mind.
Having gotten at least a preliminary sense of the musical context from which Kepler was working, look ahead a century, to what Kepler had unleashed—where his life's works, and what he had demonstrated about the method by which the human mind can to discover a new principle, had revolutionized the very foundation of scientific thought and culture.
As told by his first biographer, Nikolaus Forkel, J.S. Bach at an early age abandoned the idea that musical composition should be dictated by sound, what he termed “finger composing”—where the "fingers" pick out the notes at the keyboard, the composer having to hear them before judging the tones to be right or wrong. Instead, Bach developed the conviction that composition is a mode of thought and expression, and therefore the harmonies ought to be dictated by the mind, by what one intended to say, not the other way around. It was this shift in Bach's thinking, of the dominance of mind over material, which was to transform the language of music forever. Forkel describes the revolution that Bach brought to musical expression in this way:
“So long as the language of music has only melodious expressions, or only successive connection of musical tones, it is still to be called poor. By the adding of bass notes, by which its relation to the modes and the chords in them becomes rather less obscure, it gains not so much in richness as in precision. A melody accompanied in such a manner, even if not merely bass notes were struck, but, by means of middle parts, even the full chords, was still called by our forefathers, and with justice, homophony. Very different is the case when two melodies are so interwoven with each other that they, as it were, converse together, like two persons of the same rank and equally well informed. There the accompaniment was subordinate, and had only to serve the first or principal part. Here there is no such difference; and this kind of union of two melodies gives occasion to new combinations of tones and consequently to an increase of the store of musical expression. In proportion as more parts are added and interwoven with each other in the same free and independent manner, the store of musical expressions increases, and finally becomes inexhaustible when different time and the endless variety of rhythms are added. Harmony, therefore, is not to be considered as a mere accompaniment of a simple melody, but a real means of increasing the stock of the expressions of the art, or the riches of musical language. But to be this, it must consist not in mere accompaniment, but in the interweaving of several real melodies, each of which may be, and is, heard sometimes in the upper part, sometimes in the middle, and sometimes below.”
Bach's chorales are a simple, yet profound embodiment of this discovery.
Compare what you just heard to another, four-part setting of the same melody.
The difference of the two can be felt by all quite clearly, though it's very difficult to describe to someone who hasn't heard it themselves. Tempting as may be, dissecting the two versions, looking to ascribe that difference to any particular part (one of the vocal lines, or a particular note or series of intervals) is impossible. You can't find the difference in the parts, because it's not contained in the parts. By searching among the parts, you remove from your purview the exact thing which provoked the search in the first place. Bach, as Forkel makes clear, was not looking to harmonize a melody with pleasant sounds. He was stretching the boundaries of the musical language in order to express the richness of his thoughts.
Though it's but a shadow, examining two of the vocal lines should help to clarify that point, and nicely illustrates what Forkel described as “two melodies [which] are so interwoven with each other that they converse together, like two persons of the same rank and equally well informed...”
Compare the alto lines of the two settings.
Bach's is a melody in its own right, with its own, sovereign personality; the other is a mere accompaniment of the soprano's melody. When we pair Bach's alto line with the soprano line, we have two independent thinkers, in discussion over the same topic.
Adding the tenor and bass lines gives a complete whole: four voices, conversing, and saying all that could be said on the topic at the time; adding a fifth voice does not say anything new.
It is this weaving together of such diversity into a unity which generates Bach's harmonies. The sequence of consonances and dissonances are not generated as a sequence of sounds; they are the artifacts of a developed form of polyphony, a higher form of harmony.
Before, we identified harmony as the ear perceiving two or more tones, and the mind constructing within itself the harmonic interval, their unifying relationship. Here, the mind constructs the unifying relationship between two or more independent statements of an idea. (It is this, as we'll see, which is more closely related to Kepler's discovery of gravitation.)
Now return to the musical modes. If, with the achievements of Bach, music, and thus the harmonic system, has fully broken from restriction by the laws of mere non-living sounds as such, we can more clearly define what is meant by the mode in which a composition is written. No longer are we discussing a sequence of intervals, even if that's the form in which we first experienced it. Instead, where we've now arrived, is a greatly broadened concept: a specificity of characteristic of the space itself, which is molded by the musical idea, and contains the diverse colors and qualities of the voices and instruments used, and is present in all of the tones and melodic movements within it. In this way, we get behind the sounds, to their real source: rigorous creative thought.