Meters and Beat Hierarchy

Meter determines the number of beats per measure and the type of beat subdivision.  There are two types of beat hierarchy: simple and compound.

Simple meters have a binary hierarchy, that is, the unit of time is sub-divided in multiples of two -subdivision of the beat in two equal parts.  

Compound meters follow a termany subdivision -subdivision of the beat in three equal parts.

Any time signature whose numerator is a multiple of three (i.e., 6, 9, 12, etc.) symbolizes a compound meter, otherwise, it represents a simple meter. In simple time, a binary is represented with time signatures whose numerator is 2, the ternary with 3 and the quaternary with 4.
The process to find the corresponding compound version of a simple meter is done by multiplying the numerator of the given time signature times three (the number of beat subdivisions) and the denominator times two. The compound meter that corresponds to, for example, a 2/4 meter is found by:
multiplying the given numerator by three, that is, 2 * 3 = 6
multiplying the denominator by two, that is, 4 * 2 = 8 .
The simple meter that corresponds to a 6/8 is found by the inverse operation in which the numerator is divided by three and the denominator is divided by 2. Figures 5a, 5b, and 5c illustrate the correspondence between, respectively, binary, ternary and quaternary meters, presented side by side in their simple and compound beat subdivisions.
Figure 5a, for example, shows, on the left side, a binary simple meter identified by a 2/4 time signature and, on the right side, a 6/8 time signature corresponding to the respective compound version. The bottom staff in figure 5a illustrates how the beat unit is subdivided differently in two or three parts for, respectively, simple and compound meters.