The General Direction of Melodic Movement

Abstract

n a previous article (Kolinski 1957:3-4) I challenged Hornbostel's contention that there is a basic opposition between Western and non-Western music with regard to the general direction of melodic movement. In order to test this thesis I devised a method which may be summarized as follows: The general direction of melodic movement of a body of music can be determined by means of level formulae which include the average values of the initial and final melody level. For example, the level formula for Polish folksongs, 350:22?, shows that in the average the initial tone lies 35 hundredths of the range above the lowest tone and, consequently, 65 hundredths of the range below the highest one; so we can say that the initial descent maximum equals 35? and the initial ascent maximum equals 65?. On the other hand, the final tone lies 22 hundredths of the range above the lowest tone and, consequently, 78 hundredths of the range below the highest one; so we can say that the final ascent maximum equals 22? and the final descent maximum equals 78?. Moreover, we see that the final tone lies 13 hundredths of the range below the initial tone so that the level shift equals -13?. This method seems adequate for objectives of a wide scope such as the aforementioned one. A more detailed approach is, however, advisable when dealing with the description and comparison of specific musical cultures and styles. In these cases it is important to break down the values comprised in a level formula (initial level, final level, and level shift) into a series of relevant components and then to determine their frequency distribution. With regard to initial and final level it seems appropriate to distinguish twelve components: the two border levels of 0? and 100? and ten intermediate level