The Fundamentals of Education

A Socratic Perspective on
the Cultivation of Humanity

by Max Maxwell and Melete

Page 35

Repetition, Variation, Complexity and Meaning

Repetition and variation, and their relationship to increasing complexity, are fundamental to the human quest for meaning in the arts and life. The foundation of the relationship of repetition and variation to complexity and meaning is always some context of association. As I mentioned at the begining of Part I, the existence of any human perception of meaning requires a context of association. Nothing means anything in pure isolation unto itself. The most persistent and immanent basis of all context is the existence of variation. Without variation (differences), the concept of context does not exist. Without variation, existence as we know it does not exist. Pure repetition is blind. It is only through the persistence of continuing variation that the eyes of the universe have opened up to look upon itself. Variation is the ground upon which meaning is able to walk.

The functioning of repetition and variation is at the heart of human expression in the arts. Our ability to "speak" in the languages of the arts, with any depth of virtuosity at all in regard to meaningful expression, demands repetition and variation. George Steiner wrote on the artist's ability to create intelligent and responsibly answerable commentary, locating it in the actions of repetition and variation. Of the artistic/musical type of commentary, where art speaks to art and artist to artist, such as Rachmaninoff's musical commentary on twentieth century music, which I focused on in Part I of this essay, Steiner says:

"In ways closely analogous to those we have cited in texts, paintings or sculptures, the criticism of music truly answerable to its object is to be found within music itself. The construct of theme and variation, of quotation and reprise, is organic to music, particularly in the west." (Steiner, P. 20 - bold emphasis mine)

Our capacities to create meaning, in both verbal and non-verbal forms, resolve their potentials for creation through the fertilities afforded us in the relationship between repetition and variation. Variation, who's journey into the future faces a vast ocean of possibilities, is only possible through structures of repetition.

Leonard Bernstein's Norton Lecture series, The Unanswered Question: Six Talks at Harvard,[22] is a meditation on the structure of music using linguistics as a framework of exploration. Bernstein spoke about the capacity of repetition and variation to create the meanings of music in the third lecture on the semantics of music. After demonstrating how antithesis provides structures of variation that contributes to meaning in both a psalm and a Mozart sonata, Bernstein said that "antithesis itself is founded on an even more basic structural principle─that of repetition...Indeed, all figures of speech, and all metaphors, in speech and in music alike, depend ultimately on repetition, which is then subjected to variation, or as the linguists say, transformation."

The "figures of speech" in music, to which Bernstein referred, are complexities of musical composition that have arisen beyond the days when we first learned we could create rhythms and vocalize different pitches . This increase of complexity in music is fundamentally mediated through structures of repetition and variation. Bernstein said that, "all musical transformations (variations) lead to metaphorical results..these are the meanings of music. And that is as close as I can come to a definition of musical semantics." (Bernstein p.153 - italics in parenthesis is mine)

Repetition, variation and the increasing complexity that lead us to meaning are tightly correlated as illustrated in Hofstadter's description of increasing complexities in the composition of canons[23] . A canon is constructed from a melody that copies of itself (repetition). The measure of the complexity of a canon is given by Hofstadter in terms of increasing variation. From the simple repetition of a row in different voices, to variations in pitch, to variations in the interval structure of the melody, increasing variation and rising complexity within a canon walk hand in hand, step by step. The generation of complexity through repetition and variation is a pattern that is not restricted to music or the arts. Although I am sure that Bernstein's 'definition' of musical semantics is not as complete or as usefully systematic as he would have liked, it does touch upon a fundamentally useful dynamic that must be faced by any definition of musical, or any other, semantics. Namely, that repetition and variation are a powerful and persistent basis for creating the complexity we associate with meaning.


[22]Leonard Bernstein, The Unanswered Question: Six Talks at Harvard, (Harvard University Press, 1976), p. 145-146

[23]Douglass Hofstadter, Gödel,Escher,Bach,(Basic Books, Inc., 1979), p. 8

SIDENOTE: Regarding the Bernstein Norton Lecture, I have found it very useful to use both the video and the book. The video is nice in order to hear Bernstein's tremendous heart for music. The book has all the sheet music of everything he plays on the video.