A Quantitative Comparison of Chrysanthine Theory and Performance Practice of Scale Tuning, Steps, and Prominence of the Octoechos in Byzantine Chant

Byzantine Chant performance practice is computationally compared to the Chrysanthine theory of the eight Byzantine Tones (octoechos). Intonation, steps, and prominence of scale degrees are quantified, based on pitch class profiles. The novel procedure introduced here comprises the following analysis steps: 1) The pitch trajectory is extracted and post processed with music-specific filters. 2) Pitch class histograms are calculated by kernel smoothing. 3) Histogram peaks are detected. 4) Phrase ending analysis aids the finding of the tonic to align pitch histograms. 5) The theoretical scale degrees are mapped to the empirical ones. 6) A schema of statistical tests detects significant deviations of theoretical scale tuning and steps from the estimated ones in performance practice. 7) The ranked histogram peak amplitudes are compared to the theoretic prominence of particular scale degrees. The analysis of 94 Byzantine Chants performed by 4 singers shows a tendency of the singers to level theoretic particularities of the echos that stand out of the general norm in the octoechos: theoretically extremely large steps are diminished in performance. The empirical intonation of the IV. scale degree as the frame of the first tetrachord is more consistent with the theory than the VI. and the VII. scale degree. In practice, smaller scale degree steps (67-133 cents) appear to be increased and the highest scale step of 333 cents appears to be decreased compared to theory. In practice, the first four scale degrees in decreasing order of prominence I, III, II, IV are more prominent than the V., VI.,