A computational comparison of theory and practice of scale intonation in Byzantine chant

Byzantine Chant performance practice is quantitatively compared to the Chrysanthine theory. The intonation of scale degrees is quantified, based on pitch class profiles. An analysis procedure is introduced that consists of the following steps: 1) Pitch class histograms are calculated via non-parametric kernel smoothing. 2) Histogram peaks are detected. 3) Phrase ending analysis aids the finding of the tonic to align histogram peaks. 4) The theoretical scale degrees are mapped to the practical ones. 5) A schema of statistical tests detects significant deviations of theoretical scale tuning from the estimated ones in performance practice. The analysis of 94 echoi shows a tendency of the singer to level theoretic particularities of the echos that stand out of the general norm in the octoechos: theoretically extremely large scale steps are diminished in performance.