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. 1. THE OCTOECHOS AND THE CHRYSANTHINE THEORY Byzantine Chant is the Christian liturgical song of the Eastern Roman Empire (Byzantium) that gradually emerged from the Roman Empire from the 4th century on. Byzantine Chant has been the dominant liturgy of the Eastern orthodox Christianity. Referring to various theoretic accounts on Byzantine Chant, Zannos in [18] argues that ‘none of them can be said to correspond with contemporary empirical study’. The main analysis tool used was a pitch class profile [17] with high bin resolution, extracted from audio recordings with the aid of specifically designed algorithms. These were applied on a music collection of 94 Byzantine Chants labeled after the scale they are performed in. The overall behavior and consistency of empirical scale degree tuning was computed and contrasted to theory through a series of tests and experiments. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. c � 2013 International Society for Music Information Retrieval. According to Mavroeidis [12] and Thoukididi [16], a mode (singular: echos, plural: echoi) in Byzantine Chant is defined by the following five characteristics: 1) the scale degree steps (SD) between consecutive scale degrees, 2) the most prominent scale degrees (two or three scale degrees out of which I III and I IV scale degrees are the most reoccurring pairs), 3) a short introductory phrase that marks the reference tone, 4) the cadences in the middle and the end of a phrase, and 5) the modulations (alterations) applied to particular scale notes depending on whether they are reached by an ascending or a descending melody. Subject to a reform in the 1880s in particular concerning the sizes of the intervals, the Chrysanthine notation method (from the 1820s) is used in the official chant books of the Greek Orthodox Church up to now [11]. In Chrysanthine theory, the octave is divided into 72 equal partitions, each of 16.67 cents (singular: morio, plural: moria). The scale degree steps are measured in multiples of a morio (cf. Table 1). According to this theory there are in total eight basic echoi, a system also referred to as octoechos (‘eight’ + ‘mode’). These eight modes occur in pairs of authentic and corresponding plagal modes: First Authentic, Second Authentic, Third Authentic, Fourth Authentic, First Plagal, Second Plagal, Grave, Fourth Plagal. The plagal mode has a different reference tone (tonic) than its authentic counterpart, usually a perfect fifth lower than the one of the authentic mode 1 but it may share the same scale step sequence. Furthermore, both differ in melodic characteristics. The scale degree steps may vary according to the chant genre (Heirmoi, Stichera, Papadika) [12, 16]. Our study is limited to the basic and simplest echos scales 2 . We will not consider the fact that scale degree steps of an echos can be modulated (altered) based on the melodic characteristics of a chant or other criteria [12,16] (cf. Section 4).