Modelling of scales in traditional solo singing

Background in psychoacoustics. The scale in freely intoned music is characterised by pitch "zones" resulting from and reflecting categorical perception. Usage of the zones depends on aspects of performance as well as on melodic context. The central pitches and pitch zones corresponding to musical scale steps can be determined from frequency histograms. This approach, however, is generally not applicable in the case of floating tonality, i.e., if the pitch of the reference tone (e.g., pitch of the tonic) is slightly altered in the course of performance. Background in ethnomusicology. Archaic traditional solo singing features pre-diatonic scales which deviate from equal temperament. For instance, Alexeyev classifies embryonic scales of solo singing into three groups based on (a) contrast of voice registers and timbre (alpha-type), (b) gliding pitches (beta-type), and (c) made of approximately equidistant steps (gamma-type). Similar conceptions are also well known from early comparative musicology studies. There have been many acoustical investigations of musical scales; however, scales of archaic traditional solo singing, characterized by wide zones of intonation as well as somewhat floating tonality, have not yet been thoroughly studied. Aims. This paper aims (1) to develop mathematical-statistical models based on regularities of scale perception (categorical perception and neglect of floating tonality) to quantitatively describe of an insider's emic musical scale; and (2) to study, by means of the models, the regularities of musical scales in one idiolect. Method. Three mathematical-statistical models based on different assumptions of the nature of floating tonality were developed. Pitches of tones in songs belonging to one idiolect of Lithuanian traditional male solo singing were measured and reevaluated by means of the models. Results and conclusions. Approximately equidistant scales as well as modern diatonic scales are found in the samples under investigation. This suggests that there are different historical layers of musical thinking manifested in the idiolect.