Time signatures.
Hi everyone, and welcome to this theory lesson on time signatures. By the end of this one you will have a clear definition of time signatures, what they are and how to classify each different time signature.
But first, few words on the history of time signatures and barlines...
We can start saying that the main purpose of time signatures is to set an exact and constant duration of musical phrases through the use of barlines, and this mainly for two purposes: allow an easier sight read for the musician, and a more organized notation for the composer.
In other words, a time signature quantizes the musical piece into small, invariable increments, and its history and evolution is necessarily related to that of the barlines.
With regard to these last ones, we must say that the need to organize the notation with a consistent note duration didn’t start until the XVI Century. In the keyboard notation of the early polyphonic music (900 to 1600 D.C.), barlines were used inconsistently, so that each bar was considered more of a musical phrase of any length, rather than of a set duration.
The first known case of keyboard notation with a consistent and exact use of barlines is found in an Italian keyboard score of 1523 (Marcantonio da Bologna, Recerchari, Mottetti, Canzoni). More in general, in the organ works of the Italian and French Schools of that time we can see a consistent use of barlines, while it took few more decades for the English keyboard composers to implement this innovation in their writing.
Coming back to our days, we will start from the definition: time signatures or metre (they refer to the same concept) are expressed by a numeric symbol, representing the number of beats contained in every bar (the upper number), and the duration of each beat (the lower number). They’re found at the beginning of a music chart, after the clef symbol and before the key signature. Let's explore this concept further with two examples.
Remember, the lower number indicates the note value for every beat, and the upper one how many beats for each bar. This means that on a 2/4 time signature, the lower 4 indicates the value of every beat, which is quarter notes, while the upper 2 indicates how many quarter notes per bar.
On a 3/8 time signature, the bottom number indicates eighth notes, while the top one refers to 3 beats per bar.
Now that we know what the two numbers represent, we can study more closely how the time signatures have been theorized.
Regarding the lower number, time signatures can be simple or compound. In the first case, each beat is divisible by a value of two, while in the second one by three. In musical terms, in simple time signatures the basic beat is expressed with a half note or one of its corresponding lower values (quarter, eighth, and so on), while in compound the basic beat is represented by a dotted half note, quarter, eighth and so on.
As for the upper number value, time signatures can be duple when there are 2 or multiples beats per bar, triple with 3 or multiples beats per bar. Keep in mind that time signatures in 6, like 6/4 or 6/8, are considered duple when the basic beat is counted as a quarter note, triple when the beat is a quarter dotted note.
Duple 6/4: the time signature is counted as 6 quarter notes.
Triple 6/4: the time signature is counted as 4 dotted quarter notes.
Other multiples of 3 commonly used, like 9 and 12, are considered always triple.
From a more practical point of view, when analyzing a time signature, always ask yourself these two questions:

how many beats per measure? Answer this question with DUPLE or TRIPLE;

what is the value of each beat? Answer this question with SIMPLE or COMPOUND.
Let’s see few practical examples to understand this better.
How many beats per measure?
4, multiple of 2. Therefore duple meter.
What is the value of each beat?
Quarter note, therefore simple.
ANSWER: duple simple.
How many beats per measure?
3, therefore triple meter.
What is the value of each beat?
Quarter note, therefore simple
ANSWER: triple simple.
How many beats per measure?
6, multiple of 3. Therefore triple meter.
What is the value of each beat?
Dotted quarter note. Therefore compound.
ANSWER: triple compound.
How many beats per measure?
12, multiple of 3. Therefore triple meter.
What is the value of each beat?
Dotted quarter note. Therefore compound.
ANSWER: triple compound.
Another question arises at this point. What about all those time signatures that don’t belong to any of the category above descripted, like for example 5/4, 7/4 or 11/8? In music theory they’re known as mixed meters, being a mix of duple and triple, simple and compound meters.
In 5/4 time signature, the quarter notes indicate a simple meter. Being divided alternatively in 2+3 or 3+2, it incorporates a duple and triple meter.
DUPLE SIMPLE + TRIPLE SIMPLE.
Like in the previous example, in 7/4 too the quarter notes indicate a simple meter. Being divided alternatively in 4+3 or 3+4, it incorporates a duple and a triple meter.
DUPLE SIMPLE + TRIPLE SIMPLE
In 11/8 time signature, the compound is expressed by the three dotted quarter notes, the simple by the only quarter note. Each dotted quarter note represents a 3/8, therefore a triple meter, while the last quarter note is a 2/8, or duple.
TRIPLE COMPOUND + DUPLE SIMPLE.
In 15/16, we have 5 dotted eight notes, therefore compound meter. Since every note can be considered in 3/8, we have a triple meter. TRIPLE COMPOUND.
For you convenience, following here a short recap.
Thank you for reading and see you in the next lesson!