Early in the last century, evolving musical developments burst the seams of the 300-year-old structures of Western composition. The old hierarchical tonal structures were not eliminated by the new ones, any more than Bach was eliminated by Schoenberg, or than Newton was eliminated by Einstein, but their roles were transformed. As new atonal horizons opened, all the notes, the black-and-white keys together, now held equal potential for compositional roles. This historical transformation in music is a paradigm for evolutionary change, and its theories and practices are models for navigation in a sea of change. Commingling of the old and new structures in motion are heard and seen in the music video:
Spring Sacrifice -Alexey Arkhipenko
In the second half of the 20th century, methods for analyzing and composing music continued to evolve, particularly in pitch-class set theory, which collapses the potentially infinite range of musical tones into a manageable space containing twelve members, who stand in for their comparable siblings in high and low places. Even this condensed space has possibilities that can extend infinitely, so navigational strategies had to evolve with the music. Generalized, these strategies for wayfinding and creative production can be applied in societal, organizational and other transformational contexts.
The pitch-class space makes crystal clear any of the relationships among the 4,096 possible groups and subgroups its twelve members can generate. In non-musical applications the members can stand for any objects or entities, such as persons, interest groups, institutions, nodes in a network, coordinates in a dimensional space, and others. Once the relationships are set in motion, their sequential operations raise the number of possibilities to 479,001,600. Thus one lesson offered by pitch-class space is that when time is frozen, relationships are clearly seen. Each group and subgroup is a scene that lends its character to anything that is enacted with, within, and from it. Once the music (or other process) starts, the tonal scene may persist for a while or may hand off some or all of the action to another scene/group. In the technical realm, digital pitch-class profiling is currently used in content-based audio retrieval algorithms that analyze audio for many purposes, including music genre browsing, musical structure analysis, composer identification, and rights protection.
In an everyday scenario, the people, animals, plants, objects and conditions of a household can be represented in a pitch-class space. Family members Alice, Fred, James, Wendy, Rohan the dog, and Alex the cat, the spider plant hanging in the front window, the vase on the table under the window, the board game in progress on the kitchen table, the view through the window of the house across the street, the smell of fresh-cut lemons for lemonade, and the indoor humidity can each be assigned a representative member or group in pitch-class space. Actual or fictional, any relationships among these entities can be selected and visualized at a glance, with potential for real-life analysis (James and Wendy may experience bonding when playing the board game), and for productive creation (what secret did Alice and Fred witness through “The Front Window”? — now playing at a theater near you).
By extrapolation, it is easy to imagine other scenarios, on the world stage, or in various organizations, institutions, movements, arts and sciences that can be analyzed or produced in pitch-class space. Other analytical and productive spaces are also possible, but the advantage of this one is that you can not only see and enumerate the features of relational structures, but once set in motion, you can also hear their music.
video and images source
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