Musical Meter 2

Summary of What is Known about Meter

• The input is segregated into streams.
• Elements are organized into rhythmic groups, usually of 2, 3, or 4.
• The grouping may be hierarchical.
• Grouping can be induced by many different variables: intensity, duration, pitch, timing, etc. These work together to favor particular groupings. They may reinforce or compete with each other.

A Theory of Musical Rhythm (Lerdahl and Jackendoff, Povel and Essens)

• Rhythmic organization consists of two separate hierarchies
  • Meter hierarchy: relative strengths of beats
  • Grouping hierarchy: organization of beats into phrases
• There are many possible ways to assign meter and grouping to a pattern. A theory should constrain the set to those which people pick.
• Two kinds of rules to constrain the choices
  • Well-formedness rules: specify legitimate shape for hierarchies
  • Preference rules: specify tendencies of the listener
• Well-formedness rules
  • Meter
    • At each level of the hierarchy, beats are equally spaced
    • Beats at each level are synchronized with beats at lower levels
    • Beats at each level are equally strong
    • Relative strength of an event is derived from the number of levels at which beats appear for that event
  • Grouping
    • Only adjacent elements may form groups
    • An element may be in only one group on a given level
    • Group boundaries do not cross the boundaries of groups at lower levels
• Preference rules
  • Meter
    • A strong beat should not occur on a rest
    • Within each run of adjacent elements, a strong beat occurs on the first or last element
    • Strong beats occur in the same places in repeating phrases
    • Strong beats occur every two or three beats
    • Strong beats occur on more intense or longer elements
    • Strong beats occur at the beginning of changes of various kinds
  • Grouping
    • Place elements in equal-sized groups
    • Avoid groups of one or two elements
    • Elements close to each other tend to be grouped together
    • More intense or longer elements partition elements into groups
    • Elements are partitioned by changes of various kinds
    • Elements within groups are similar to one another
    • Relations between successive elements in groups are similar to one another
    • Corresponding elements in successive groups are similar to one another
    • Corresponding inter-element relations in successive groups are similar to one another
• Interaction of meter and grouping hierarchies
  • Meter and grouping hierarchies may reinforce each other (tend to place boundaries in the same places) or conflict with each other (tend to place boundaries in different places)
  • Rhythm (in this theory) results from the complex interaction of meter and grouping constraints

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Last updated: 12 October 1995
URL: http://www.indiana.edu/~gasser/meter4.html
Comments: gasser@salsa.indiana.edu
Copyright 1995, The Trustees of Indiana University