I am often asked how music and physics overlap, due to my background in both areas. Typical answers include acoustics, instrument design, tuning systems, etc. However, the general consensus is that science and art are two discreet phenonena and that neither of which can be understood in terms of the other. Having deeply invested myself in both disciplines for a substantial period of time, I believe that the two are intimately intertwined.
For much of the twentieth century many theorists and historians assumed that the terms “consonance” and “dissonance” were based primarily in human experience and prejudice.
To quote Arnold Schoenberg from Composition with Twelve Tones (1941), “What distinguishes dissonances from consonances is not a greater or lesser degree of beauty, but a greater or lesser degree of comprehensibility. In my Harmonielehre I presented the theory that dissonant tones appear later among the overtones, for which reason the ear is less intimately acquainted with them. This phenomenon does not justify such sharply contradictory terms as concord and discord. Closer acquaintance with the more remote consonances—the dissonances, that is—gradually eliminated the difficulty of comprehension.”
However, as Pythagoras and Helmholtz believed, our perception of consonance and dissonance are very well grounded in science. A scientific study on this subject was conducted in 2010 by McDermott, Lehr, and Oxenham and published in Vol 20 No 11 of Current Biology. The study found both that “consonance preference did widely exist,” and that it depended mainly on how close a given harmony resembled a portion of the harmonic series.
My own research into the area of harmonic entropy, following some of the work of Paul Erlich, has convinced me of this as well. The more I have looked into information theory as a possible explanation for psychoacoustic structure in music, the more I am convinced (as were the ancient Greeks) that our aesthetic preferences correlate very well to mathematical relationships, geometries, and structures.
Am I saying that we can reduce music to mere math equations? To an extent, yes I am. However, that is not to demean it in anyway. What is says is that human beings, our artistic and aesthetic values, and our capacity to appreciate and enjoy those values are all contained within the laws of the universe in which we live. The ancient Greeks believed that the same laws which governed the heavens must also govern the Earth and human beings.
For instance, many attempts have been made to program computers to perform and compose music. While many are quick to point out the shortcomings of this, seeing it as a threat to the financial health of composers and performers, what is often missed is how much we learn about ourselves through the process of attempting to do this.
How might one program a computer to compose a classical sonata? Let’s sample a whole range of data about classical sonatas which currently exist. A probability distribution exists which describes all the many options a composer might have for a given cadence, melodic note, accompaniment, etc. at a given point in the piece. In theory, if we could sample enough of this type data we could create a perfect artificial replica of Mozart or Bach. In practice we are mainly limited by memory and computing speeds.
Again, this isn’t meant to demean Mozart just because we can represent his compositional abilities with a very complex probability distribution. In fact, this probability distribution would still be innately human because we still needed Mozart’s output from which to sample the data in the first place. What it gives us, instead, is the ability to comprehend a composer not in some sort of abstract way but instead as a mathematical creature which can be quantified and measured.
In the end, I think we will learn that music, mathematics, and physics are in fact deeply intertwined and completely inseperable. They don’t fall neatly into three separate disciplines, majors, and departments as we are led to believe by the structure of academia. The implications of this are rather profound.