A statistic model of the distribution of rhythmic segments in the Tofalar traditional songs

Natalia Skvortsova

M.I.Glinka Novosibirsk State Conservatoire, Russia

On the basis of computer measurements of durations of different-level rhythmic units in traditional lyric songs of the Tofalars (Turkic Siberian people inhabiting the middle part of the East Sayan mountains) the certain microrhythmic regularities in the level of syllabic segments were found. These regularities observed as some sequences of musical two-syllabic feet which are the iambes (where the first syllabic segment is longer than the second one) and the chorees (with the reverse disposition of syllables) have a statistic nature. For the most of feet the ratio of the first syllable duration to the second one lies between 0.5 and 1 but with statistic attraction to 1, i.e. the inequality of the syllable durations cannot usually be audible. However, the observed picture with alternation of feet is secondary because the deep-level statistic mechanism manages the appearance of the feet. The regularities follow from the traditionally established distribution of inequality coefficients of the feet. The inequality coefficient is defined as the ratio of the difference between durations of syllabic segments of a foot to the sum of them. There are three statistic factors in the songs which cause observed iambes / chorees distribution: the mean inequality coefficient of a given singer, the mean-square deviation of this coefficient and the correlation between coefficients of two adjacent feet forming the song half-line. From this point of view two types of half-lines exist in the Tofalar songs. For the first type the inequality in the first foot is more than the inequality in the second one. The second type of half-lines is characterized by the reverse order of foot inequalities. Into the Tofalar song tradition the first type half-lines spreads more widely and is dominating in the songs of the singers from all the Tofalar kins and villages. Its prevailing is connected probably with influence of the Tofalar accent, the structural rests into songs, some common processes in development of musical rhythm of indigenous Siberian song traditions and the Samoyedic substratum.