Jennifer Shafer

Unveiling the Invisible: An Examination of Structure through Wavelet Analysis

Wavelet analysis is a digital signal processing technique that is related to Fourier analysis but provides better time localization and the ability to analyze simultaneously at multiple scales.  This paper proposes an application of the Haar wavelet to pattern recognition in music by first providing examples of applications to music with recognizable motivic patterns and then summarizing the results of an application to a more complex piece of music.
Iannis Xenakis’ Evryali (1973) defies traditional consideration of motives and structural patterns.  Large-scale structures can be seen in the various sound configurations used to construct the work, but relationships between these structures cannot be easily identified beyond the type of sound configuration.  This paper proposes an analysis of macroscopic and microscopic relationships in Evryali by use of wavelets.

Examples with pre-determined patterns, intended to test the effectiveness of wavelet analysis for pattern recognition in music, are first presented.  The wavelet analysis technique is applied to a sequence of ascending thirds, a two-voice example demonstrating rhythmic augmentation, and an excerpt of a two-part invention by Bach; each example presents satisfactory results.
After tracing out predominant lines in each of the sound configurations of Evryali, wavelets are used to analyze the pitch content of select lines.  The wavelet analysis reveals ‘motivic’ relationships between different configurations and also recurring ‘motives’ within single configurations, suggesting a sense of motivic parallelism within the work.  Furthermore, wavelet analysis also leads to the discovery of Ur-shapes which recur in each configuration over different periods of time, demonstrating a close internal cohesion that varies from the micro level to the macro level within this piece.  These relationships lead to an analysis of the large-scale form of Evryali based on the recurrence of certain patterns and Ur-shapes.