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Rhythm Trees Structure

Traditionally, rhythm is broken up into several data : meter, measure(s) and duration(s). Rhythm trees must enclose these information in lists and sub list.

This elementary rhythm :

can be expressed as follows :

• ( ? ( (4//4 (1 1 1 1) ) ) )
• ( ? ( ( (4 4) (1 1 1 1) ) ) )

A tree structure can be reduced to a list : (D (S)).

Main Components : Duration and Subdivisions

• D = a duration , or number of measures : ( ? ) or a number ( n ).

When D = ?, OM calculates the duration.

By default, this duration is equal to 1.

• S = subdivisions (S) of this duration, that is a time signature and rhythmic proportions.

  1. Time signature = n // n or ( n n ).

It must be specified at each new measure, even if it remains unchanged.

2. Rhythm =  proportions : ( n n n n )

Here, the (1 1 1 1) sub list represents four equal subdivisions of a 4/4 measure. OM calculated that the tree has two measures.

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Parenthesis Levels

A rhythm tree has at least three levels of parenthesis :

1. number of measures

2. list of measures

3. time signature and proportions.

Note that different rhythm trees with equal proportional structures produce the same rhythmic result :

( 1 1 1 1) = (2 2 2 2) = (124 124 124 124)

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Durations

Manipulating Durations

By default, the duration of a measure is equal to 1. 1 represents the global measurement unit traditionally expressed by the time signature, such as : 4/4, 2/2 = , 3/8 = etc.

Changing this value multiplies or divides all the durations by a given coefficient.

Subdivisions : Measures and Groups

Measures

Trees define the way ** measures ** are split into proportional durations.

The following rhythm :

is written : ( ? ( (4//4 (1 2 1) ) ) **)** .

Groups

Trees also define internal subdivisions, or ** groups[1] ** , within a measure .

The following rhythm :

is written : ( ? ( (4//4 (1 ( 2 (1 1 1) ) 1) ) ) **** )** .

Writing Groups

Note that groups must be written with a new subordinate level of parenthesis.

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References :

1. Group

An internal subdivision, that is, a list of proportions within a measure. A group can enclose a sub group. Basic examples are tuplets, groups of eighth, sixteenth notes. Groups of quarter, semibreves, whole notes or any other values are also admitted in rhythm trees.

For instance :

(? ((4//4 ( (2 ( 1 1)) (1 ( 1 (1 (1 1 1)))) (1 (1 1 1 1 1)) )))).

This one measure tree has one group - two quarter notes - , one group with a sub group - one eighth note and a sixteenth notes triplet, and a last group - a quintuplet.

Contents :

• OpenMusic Documentation
• OM User Manual
  • Introduction
  • System Configuration and Installation
  • Going Through an OM Session
  • The OM Environment
  • Visual Programming I
  • Visual Programming II
  • Basic Tools
  • Score Objects
    • Presentation
    • Rhythm Trees
      • Rhythm Trees Structure
      • Notation : in Practice
    • Score Players
    • Score Editors
    • Quantification
    • Export / Import
  • Maquettes
  • Sheet
  • MIDI
  • Audio
  • SDIF
  • Lisp Programming
  • Errors and Problems
• OpenMusic QuickStart

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