The Hierarchical Structure of Time and Meter
Masato Yako · Computer Music Journal · 1997
This article considers interrelationships of hierarchy, time, and meter in music. Music is an art form that organizes time and reflects different attributes of time. A unique point in flow of time is the In physical terms, present is a point in time; in practical terms, however, present is understood to have a certain span, extent of which varies depending on context in which present is placed (Mach 1906; Husserl 1928; Fraisse 1963, 1982). Similarly, in music, present has a time-span. For example, present could mean note A, first subject, or development, etc., depending on context in which music belongs. If a random point in time happens to be in development section, section began before that point and is likely to continue after it. Basically, selection of a musical present is also attributable to character of a piece of music (a musical style). However, selection is not sole choice for a piece. The interpretation of a piece of music varies, depending on time-span that is adopted as present. There are a number of possible time-spans for a musical present. This fact is inseparable from hierarchy that is latent as a structural element in music. Specifically, that different time-spans can be adopted as present indicates existence of hierarchical levels in music, from higher strata (longer units) to lower strata (shorter units). In other words, ability to select a musical present in a number of time-spans is a positive indication of hierarchical structure of music.