Music is not sound. Though it appears to us dressed in the attire of audible tones, music as such is not a consequence of those tones. In fact, many a tone has been sounded under the banner of “music” or “art” which in fact has nothing to do with it! Music which is rightly called such, as in the Classical tradition of Bach through Brahms, has characteristics drawn not from sound, but from the creative function belonging to the human mind, and stands above any particular sense domain.

While music per se is not dictated by the laws of sound, the lawfulness of Classical musical composition does have a relationship, as does a substance to its shadow, to the shape and ordered structure of the medium of musical composition, the interconnected system of major and minor keys. The discovery and development of the structure of the musical language has always originated from the insight of composers and performers into the creative mind of man. This insight drove breakthroughs in the use of the musical language, rather than any derivation from the “mathematics” of combining notes and intervals. The notes on the page, and the sounds that they correspond to, are merely stand-ins which demand the presence of a living idea on the stage of the imagination.

Here we will explore, in an introductory way, the relationship between the structure of the musical system and the soundless realm of ideas underlying it.

Harmonic Structure

The structure of the harmonic system, the medium of music, is inherently a paradoxical one. Though the system of major and minor keys is physically (and not arbitrarily) derived by lawful methods of construction, within it are discrepancies in tuning and ambiguities about exact note values which cannot be resolved except from the higher domain of musical composition and performance—the soundless domain of the creative action of the mind, rather than in anything derivable from sound and harmonics. The fact that there are hundreds of “answers” to the tempering problem is an indication of this.

Here we will focus on one of the ironical features of the musical system, its inherent dissymmetry, and related to that, the principle of inversion, to see how a physical system such as musical harmonics looks to a higher, noetic cause for its meaning; a cause to which it makes itself susceptible as a medium of expression.

In order for the dissymmetry of the musical system to become apparent, first look at its symmetry. Take, for starters, the harmonic (or consonant) intervals which come from the division of the string.