We will be assuming that you are already familiar with the basics of rhythmic notation, so we will be skipping most of the basic rhythmic terminology. If you would like to review, I have included some materials from Open Music Theory in the Further Reading.
Instead, we will be skipping ahead into classifications for meters. For today’s topic, we will be focusing exclusively on simple meters, one of the two classifications for regular meters.
First, a few basic terms: Meter is the manner in which we organize strong and weak pulses in music over time, and it is from this grouping that we determine the length of each measure. At its most basic, meter tells us two things:
If we imagine meter as a hierarchy, beats are the highest level. Beats are then divided into divisions, and divisions can be further divided into subdivisions. A regular meter is one in which every beat is the same length.
Finally, remember that meter is somewhat subjective and can be greatly altered by many factors, especially tempo. Where one listener might listen to a piece with four quarter-notes per measure and feel that the quarter notes are the beat, another listener may listen to the same piece and hear the beat in a slow two with the half-note as the beat.
Using the following examples, determine:
This is always an interesting class discussion, because creating objective definitions depends on the students differentiating their opinions from the underlying principles of the concept.
While most students intuitively understand what a simple meter, it is often difficult to agree on the common characteristic of all simple meters. When asked to identify what all simple meters had in common, they landed on, they often focus on the visual or mathematical representation of the time signature–for example, “The top number of the time signature is divisible by two.” Not only is this not true for all simple meters (e.g. 3/4) as shown in Examples 4a, it still would not differentiate this class of meters from compound meters. 6/8 and 12/8 are both compound time signatures that have a top number that is divisible by two.
The common characteristic of simple meters is how the individual beats are divided. Simple meters are any regular meters in which the beat is divided into exactly two equal parts.
When looking at the above examples, simple meters can be divided into collections of duple, triple, and quadruple meters:
While this is correct for the meters above, it does not provide a definition of what these numbers mean. These words–simple, triple, quadruple, and so on–are used to signify how many beats are in a measure.
Most students correctly identify the function of the top and bottom numbers of the simple time signatures (but struggle with the same concept for compound meters.)
For simple meter time signatures:
To easily figure out the bottom number’s rhythmic value, I tell students to imagine that the bottom note becomes the denominator (lower number) of a fraction under a numerator of 1. A bottom number of 4 becomes 1/4 – a quarter. A bottom number of 2 becomes 1/2 – a half.
It seems that for every unique syllable, there is a beat-counting system for affixing syllables to beats, divisions, and subdivisions. Each of these have their strengths and weaknesses, but for this theory course, we will be using the following for simple meters:
beat numbers for each beat (e.g. 1, 2, 3, etc.)& for the division (e.g. 1-& 2-& etc.)e (pronounced ‘ee’) and a (pronounced ‘ah’) for the first level subdivisions (e.g. 1-e-&-a 2-e-&-a)While this system can blend together aurally if said quickly, its primary benefit is that it has a unique syllable for each level through the first subdivision, and this makes communicating easier with higher specificity. For example, it is easy to ask, “Is the G4 on the ‘e’ of beat four a non-chord tone?”, and this does not require further information.
The two examples of Examples 4a demonstrate something I term “theoretically ideal” beaming versus two counterparts of the same rhythm beamed in a more commonly used manner. For these:
This is very much inline with my general intention. Well-engraved music is meant to look pleasing and be easy for a performer to read. This often leads to grouping rhythmic patterns according to non-rhythmic ideas: lyrics, spacing measures across the page, phrasing, a limited number of systems, etc. Theoretically ideal beaming would never obscure a beat in order to provide the easiest reading of harmony within a score. Of course, no musician will ever use this in its strictest form because it would become difficult to read in many situations; imagine not using a whole note in 4/4 time and instead using four tied quarter notes.
That being said, it is important for students of music to begin trying to understand how grouping and beaming decisions are made, because in harmonic analysis, it is easy to sometimes miss voices because of obscured beats. It is also an excellent thought exercise to help students to begin demonstrating mastery of meters and rhythmic values.