The pleasure of a cumulative note, of a satisfying finisher, the note that takes you out of the chasm and into the light — such a note has power. Harmony, the multiplying, hardy relation of one thing to the other, is implicit in every system. Implicit models build up nature, and we in turn base our conclusions and motivate conclusive actions towards preconceived implicit models, in search of that satisfying end; a constructed architecture of narrative we lean on.
Structures are how we see and aspire to see the world. We scrawl along the ridges of universe to outline physical models. Constantly, we procure psychological models. By the structure of mathematics, we set loose deep learning algorithms, multi-use by the rhyme of transient predictive models. Even our entire conception of understanding seems to be based on the belief that there is a model to explain what we don't yet know (Weinberger 2). This is induction, motivated by manipulable precepts.
Sir William Rowes Hamilton indirectly influenced an epiphany of new reach in physics by his seeing of a constant analogy between mind and nature. This idea of analogy and symmetry is seen to be true everywhere from the artisan's aesthetic to fundamental physical laws, motivating physicists' method of hypothesis. The legacy of physical understanding can be seen as built on what looks to be a serendipitous assumption: "More and more, as our understanding of fundamental physics has progressed, we have come to ascribe the rich texture of reality to ideally simple laws acting in a complex environment."
The bases of music are rhythm and harmony. Rhythm is ordered recurrence in time. Pure tones are those whose vibrations are particularly simple and periodically orderly. Tones harmonize if their intervals of tonal vibration are in rhythm — that is, when their periods are proportional. Einstein compared the pursuit of music and scientific research as seeming to offer "a point of union between the lonely world of subjectivity and the shared universe of external reality."
If our interpretation of what's going on in the world is "a comparison of our raw perception with our preconceptions" and if the fabric of reality is composed of harmonious structures, then analogy may have some discrete basis, and the pursuit of understanding across disciplines may lend insight to one's hypothetical intuition.
The composition of music presents the most abstracted example of methodized harmonic form. In Fundamentals of Music Composition, Arnold Schoenberg takes the concept of form to mean that "[a piece] consists of elements functioning like those of a living organism." The presentation, development, and interconnection of ideas is based on relationship, differentiated according to importance and function. Motive can be perceived as the germ of the idea: "the features of a motive are intervals and rhythms, combined to produce a memorable shape or contour — which usually implies an inherent harmony." The narrative of the composition is then controlled by the treatment and development of this initially defined motive. Flow is the establishment of a continuous flux, in perfect proportions. Through this, music produces a "stream of intention."
A story, to our tastes, requires a bit of impedance of flow to make the "good stuff" have relative flavor. Story is from what we ascribedly center life. It has such pull. There is a certain narrative structure by how we live our life, base our life off of, and make sense of it all. In 1995, Kurt Vonnegut theorized the existence of a few common functional story arcs from which literature is pieced. Twenty years later, Vonnegut's theory was validated. By determining the emotional valence of a segment of story text, then analyzing how this sentiment changes from moment to moment, a piece of literature may be plotted as a function of sentiment vs. time. The result is the mapping of a story arc. Andrew Reagan, with the University of Vermont's Computational Story Lab, comprehensively used this method of sentimental analysis for over 1,700 stories with data mining techniques. The study's result is remarkable: "we find a set of six core trajectories which form the building blocks of complex narratives."
Contour is hard-wired into our brains. It's our means of creating and comparing narrative — the basis for our agentive self-awareness. Similarly, Gestalt psychologists formulated two rules inherent in our perception of melody: With the Law of Completeness, our minds prefer complete patterns, with few melodic skips. With the Law of Good Continuation, our minds are observed to unite two melodic lines lying along the same trajectory. Profoundly, "melodic forms that consistently contradict these laws do not exist."
We search for what is architecturally sound. It is in this search that logic and spirit coincide. Logic and the idealization of value alone is benign, a construct without a soul. There's an inherent futility to it, a lack of life to all of our personal ideals when they aren't connected to a larger construct. If there is life then, there is a bright shining point to all our efforts. It is spirit that gets us there, that possesses us to an aim.
If a feeling of what is satisfying is inherently harmonic, then different relations between notes must express different feelings — the spectra of which being connected by a spirit of value and desire. Without truly sound structure, there is no balance, no storehouse, no perception of beauty, and no sustained or honest pleasure.
Works Cited
- Alexander, Stephon. Jazz of Physics. Basic Books, 2016.
- Jourdain, Robert. Music, the Brain, and Ecstasy. Harper Perennial, 2002.
- Moore, Carol-Lynne. The Harmonic Structure of Movement, Music, and Dance According to Rudolf Laban. Mellen, 2009.
- Reagan, Andrew J, et al. "The Emotional Arcs of Stories Are Dominated by Six Basic Shapes." EPJ Data Science, 2016.
- Schoenberg, Arnold. Fundamentals of Music Composition. Faber and Faber, 1967.
- Weinberger, David. "Our Machines Now Have Knowledge We'll Never Understand." Backchannel, 2017.
- Wilczek, Frank. Longing for the Harmonies. W.W. Norton, 1989.