#1 - Meter and Time Signatures
The purpose of this episode is to introduce the fundamental concepts required for further study. These concepts will be used for all subsequent episodes. They are:
Notation as representation of the beat
The anatomy and function of the time signature
Binary and Ternary meter
This episode (and those that follow) broadly differentiate meter from time signature. Here, time signature will refer
specifically to the two numbers that appear at the beginning of a section of music and denote the notational value of each measure, while meter refers to the more general concept of time signature, beat, rhythmic structure, and the rest. Essentially, meter is the general topic, while time signature refers to the specific item itself.
I. Representation of the Beat
This section outlines the concept of notation as representation of the beat. Because notation (and rhythm itself) is built on a system of division, specifically halving and doubling of the beat, we must begin by establishing a certain note type as the representative of the beat. Though this is an arbitrary choice, and can, in theory, by done by any note value, there are pragmatic reasons as to why certain note types will be favoured.
Once the beat is represented by a certain note type, any given rhythms can be plotted against that by using the structure of notes. A quarter note can halve to form two 8th notes, or two of them can combine into a half note. This structure allows for all rhythms to be plotted against the original quarter note, which itself represents the beat.
This concept is crucial in understanding the concept of the time signature.
II. Time Signature
A time signature is a functional device that fulfils many roles. It:
Denotes the total value of each bar
Determines how many of a certain note type are present
Denotes whether the meter is binary, ternary, or compound
Gives implications as to the beat or rhythmic groupings
Anatomically, a time signature is comprised of two numbers, an upper and a lower. The upper number is purely quantitative; it denotes how many of a certain note type are present in each bar. In theory, this number can be anything, though there are practical reasons why this would not commonly be the case.
The lower number corresponds to one of the note types: 2 for half notes, 4 for quarter notes, 8 for 8th notes, and so on. Combined with the upper number, the time signature therefore tells us how many of a certain note type are in each bar. This simultaneously provides a total value for the bar, and various implications as to the meter, beat, and fundamental rhythmic groupings.
A time signature can easily be understood with the following sentence: there are top bottoms per bar, such that 4/4 can be read as follows: there are four quarter notes per bar. Note that this does not fundamentally determine anything else about the bar, save for the total value.
III. Binary and Ternary Meter
We have already established that certain note types are used to represent the beat itself. We can now divide time signatures into three fundamental types to see how the further implications of time signatures.
Binary time signatures are any time signatures with a 4 on the bottom. In binary time signatures, the beat is always represented by quarter notes, such that the time signature not only determines how many quarter notes are in each bar, but also how many beats are in each bar. This is because, in this case, the quarter note represents the beat. A measure of 3/4 contains three beats; 5/4 contains five beats, and so on: the quarter notes correspond to the beat.
The rhythms in binary time signatures are commonly referred to as straight rhythms. These binary rhythms are so called because they are based on the fundamental grouping of 2, and this is due to the quarter note which represents the beat. A quarter note contains two 8th notes, and two quarter notes combine to create a half note. Because of this fundamental two-part grouping, all binary rhythms are based on this fundamental principle, and this is represented by the binary time signature itself.
Ternary time signatures are differentiated by the simple fact that the beat is represented by dotted quarter notes rather than standard quarter notes. Dotted quarter notes contain three 8th notes instead of two, which fundamentally changes the rhythmic framework. In binary, a quarter note beat contains two 8th notes, four 16th notes, and eight 32nd notes, all stemming from the quarter note itself. Here, in a ternary meter, a beat contains three 8th notes, six 16th notes, and twelve 32nd notes. This is a fundamental shift in meter.
Ternary time signatures are recognised by having an 8 on the bottom, and a non-prime number on top. Taking 6/8 as an example, we begin with the sentence which tells us there are six 8th notes per bar. However, this time the time signature does not explicitly state the number of beats; there are not six beats per bar, simply six 8th notes. We have already stated that ternary time signatures use dotted quarter notes to represent the beat, so to arrive at six 8th notes, we need two dotted quarter notes. 6/8 therefore contains two beats to the bar, each of which comprised a group of 3.
Because of this, we can differentiate 2/4 from 6/8 very simply; both contain two beats to the bar, but the binary 2/4 contains two groups of two, while the ternary 6/8 contains two groups of three. Likewise, we can differentiate 3/4 from 6/8 in a similar way. Both contain six 8th notes in total, making them mathematically equivalent, but 3/4 comprises three groups of two (two quarter notes), while 6/8 comprises two groups of three (dotted quarter notes).
We have stated that ternary time signatures can be recognised by having an 8 on the bottom and a non-prime number on the top. When time signatures with an 8 on the bottom have a prime number on the top, these can be considered odd. This should not be confused with time signature with an odd number on top, but specifically a prime number (which itself will always be odd).
Odd time signatures have irregular beat groupings represented by both quarter notes and dotted quarter notes, and are thus neither straight nor swung. A simple example of an odd time signature is 5/8, which is composed of a quarter note beat and a dotted quarter note beat. The is a group of 2 8th notes followed by a group of three 8th notes, equating five in total. In this instance, rather than the meter being composed of a regular pulse, it is composed of an irregular groupings or 2 and 3. Note that the order can be reversed, such that it can be composed as a 3 followed by a 2.
This brings us to the final topic of this episode. In speaking of odd time signature like 5/8, we encounter the concept of functionality. I have stated that 5/8 features an irregular beat comprising a quarter note and a dotted quarter note. We could alternatively say that it features a regular beat of the 8th notes themselves; in this instance, the beat is represented by the 8th notes. The way in which we choose to discuss 5/8 really comes down to how it functions in the piece.
In other words, for what reason did the composer choose to write in 5/8? Were they expressing a phrase comprising a two- and three-note grouping, or were they expressing a phrase that was simply five beats long?
Ultimately, there is no correct or incorrect when it comes to time signatures. Within the rules of rhythmic theory and the notational tools as we currently have them, any rhythm can feasibly be written in any time signature. However, by shoehorning a rhythm into a different time signature simply raises the question of why? We could write a rhythm in any time signature, but this is ultimately a practical decision; which time signature makes the most sense or most suitably conveys the information required to accurately interpret the piece?
By way of example, we would close by considering my snare drum piece entitled Numinous Measure. This piece was conceived on an underlying rhythmic pulse of three groups of five, and the thematic phrase was based on these groupings. This musical idea came before the act of deciding on a time signature, and so I had to decide how best to transfer this musical idea into score.
Three groups of five could be expressed in 3/4, comprising three quarter note beats per bar, with the five-note groupings coming from 16th note quintuplets. This format accurately expresses the three five-note groupings, and maintains a common time signature. However, due to the relative complexity of the rhythmic figures that occur within the piece, the presence of ubiquitous quintuplets would be problematic. Every beat would need to be a quintuplet just to establish the desired meter, which means that every rhythmic figure would need to be written (and subsequently read and interpreted) within a quintuplet.
Instead, I opted for an uncommon time signature: 15/16. This states that there are fifteen 16th notes per bar, and allowed me to group them into three groups of five without the need for quintuplets. Admittedly, a cursory glance of 15/16 does not necessarily suggest this particular grouping, but it was considered a worthwhile trade off the getting rid of the quintuplets.
Ultimately, this was a pragmatic decision in which I chose the time signature that was, quite simply, the most practical and suitable.