Chaos Hides in Recorded Monodic Music: What is the Role of Timbre?
P. Di Lorenzo · PsycEXTRA Dataset · 2003
At first sight, music shows a complex behaviour: at every instant components (in micro and macro scale: pitch, timbre, accent, duration, phrase, melody, harmony, etc.) are closely linked to each other. These relationships typically play the role of back-forward channel of information and they are similar to feedback rules. All these properties (above stated in an heuristic characterization) are peculiar of systems with chaotic, self-organized, and, generally, nonlinear behaviour. Therefore, the analysis of music using linear and deterministic frameworks seems to be not useful. On the contrary, non-linear time series analysis also allows to investigate order and chaos structures hidden into a signal recorded as numerical array. I select a melodic fragment from historical vocal Neapolitan barocco repertoire (aria “A Serpina penserete” from “Serva Padrona” by G.B.Pergolesi). In the original version of the score, the melody is played by a soprano accompanied by a strings orchestra and a basso continuo. I record several audio fragments of the same original soprano melody with different instruments: guitar, flote, soprano voice (with the linked words, without words but with one single vowel phonema for all notes; with the identical vowels of the original text without consonants), violin, cello, oboe, harpsicord etc. Each record (in mono wave format) is sampled in a numerical array of amplitude points. Then I investigate it to recognize and analyze orbits, attractor, power spectrum, Poincare sections, correlation functions, etc. Finally, for each record I compute, compare and classify some of significant analytic chaotic parameters (fractal dimension via correlation and capacity dimension, Lyapunov exponents etc.). The results can be used to characterize music and timbre into different intervals belonging to chaotic parameter space.