ISSN 2158-5296
AAWM JOURNAL VOL. 3 NO. 1 (2013)
Fractal Harmonies of Southern Africa

Martin Scherzinger

At stake in this article is a demonstration of the fractal-like logic undergirding harmonic processes found in the archaic lamellaphone music in the region of Zimbabwe, Zambia, and Mozambique. Fractal geometric shapes are generally attributed to objects found in opthalmic nature (clouds, snow flakes, frost crystals, etc.) and the visual arts (Giacometti's landscapes, Tuareg leatherwork, etc.). In most accounts, therefore, recurrence relations between geometric shapes (on reduced-size, or magnified, scales) are described in relation to points in space; less often do fractal relations pertain to aspects of time. This presentation reflects upon fractal relations in time, as shaped in specific musical traditions of southern Africa. By way of two detailed harmonic analyses, depicted on geometric graphs, the presentation will reveal the music's fractal-like temporal qualities.

In lamellaphone music of southern Africa, the time-transcending symmetric and near-symmetric harmonic shapes that ground the music's rhythmic-melodic flow are perhaps the most striking mathematical aspect of the music. In mbira, kalimba, njari and matepe music we find harmonic shapes – or, more precisely, subsets within their characteristic harmonic progressions – that constitute and resemble shapes found elsewhere in the progression. The resemblance frequently involves identity across an imaginary mirror axis, projected either horizontally or vertically. In other words, harmonic shapes recur in uncanny inversion or retrograde forms at various points in their respective cycles. Furthermore, harmonic shapes also recur in original (non-mirrored) form at various pitch-transpositions within the progression, which facilitates hearing near-identical harmonic trajectories at different points within the cycle. In other words, these harmonic structures facilitate a kind of phase-shifted experience of similitude in the context of transformation (no less than transformation in the context of similitude). The music's unexpected mimesis can thus be heard in various ambiguous "contrapuntal" combinations.

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