After a quick review of our general definitions from Overview, the class quickly worked through compound meters. Compound meter is a regular meter in which the beat is divided into three equal parts. This definition took a few tries to find its simplest form, because the students struggled to differentiate regular versus irregular meters. We will not be covering irregular meters until later in the course, so I asked them to consider the subjective nature of meters that will be discussed in the next topic, 4c - Metric Perception. After that discussion, we will see if this concept makes more sense.
For a compound time signature, the class suggested that:
These definitions actually took quite a few tries to reach. The students were somewhat careless with their use of the terms beat, division, and subdivision, but these three terms are the keys to separating compound from simple meters and their time signatures. In a simple meter, the top number is the number of beats in the measure, and the bottom number is the note value of the beat. Contrast that with compound meter time signatures. The top and bottom numbers represent entirely different concepts, and for compound meters, this requires a slight bit of math to find the actual number of beats. One student simplifed it to:
Of course, this highlights the primary problem with our time signature system. It requires the user to already understand the system by being able to differentiate between simple and compound meters, because the system is not uniform across all meters. This is why the pedagogical method of grouping meters by simple vs compound and then attaching a word to denote the number of beats (i.e. single, duple, triple, quadruple, etc.) is useful.
The terms duple, triple, and quadruple refer to the number of beats in the measure. In compound time:
Within a given meter classification, there are many different time signatures. For example, in compound duple, there is 6/8, 6/16, 6/4, and many others.
## Differentiating between compound and simple meters
The simplest method to differentiating is to memorize the standard groupings of all meters. That being said it is fairly easy to remember that if the top number of the time signature is a multiple of three, then that is a compound meter, assuming that the tempo does not become too slow or too fast.
Like simple time, theoretically ideal beaming in compound time does not obscure beats. Unlike simple time, compound time is written this way in common practice with few exceptions and only one that is notable. Occasionally a compound meter will create hemiola – a feel of two against three – by having three consecutive groups of two divisions over two compound beats. The most common notation of this occurs in 6/8 when three quarter notes are placed in a row. If written using quarter notes rather than tying two eighth notes together, this will obscure the second beat. The tune “America” from West Side Story highlights this rhythm as its primary melodic motif.
As with simple meters, there are various systems for counting beats and their divisions. One of the most common systems condenses the method for counting beats in simple time to 1-&-a. The other most common counting method uses 1-la-li. For this course, we will use the -la-li method to help differentiate the counting from a simple meter.
The problem with both of these systems is that there is not a unique syllable for each subdivsion. Generally speaking, students are asked to insert “ta” between each of the division syllables creating 1-ta-la-ta-li-ta. This is adequate for practice aloud, but it is poor for specificity because there are three ‘ta’ syllables in each beat. For our class, we are going to try using: 1-to-la-ta-li-ti
After listening to the two examples in 3/4, the class easily identified that the two examples were identical except for the tempo. In the slower example, every person in the class heard it in a simple triple meter with the quarter note as the beat. For the faster example, all but one student changed to hear it as a fast compound single meter with the dotted half note as the beat. Meters such as 3/8, 3/4, and 3/2 are all dependent on tempo as to whether they are a compound or simple meter. While a good rule of thumb is to consider these meters as simple until you have listened to the piece at tempo, 3/8 meters are commonly fast and conducted in one. Make sure to look at the tempo if determining a meter’s classification when only looking at the score.
Meters that divide the beat into three equal parts are compound meters.
When combined with simple meters, there are six types of standard meter in Western music:
In a time signature, the top number (and the top number only!) describes the type of meter. Following are the top numbers that always correspond to each type of meter:
In compound meters, the bottom number of the time signature corresponds to the type of note corresponding to a single division of the beat. If a compound meter is notated such that each dotted-quarter note corresponds to a beat, the eighth note is the division of the beat, and thus the bottom number of the time signature is 8. If a compound meter is notated such that each dotted-half note corresponds to a beat, the quarter note is the division of the beat, and thus the bottom number of the time signature is 4. Note that because the beat is divided into three in a compound meter, the beat is always three times as long as the division note, and the beat is always dotted.
"Shiver," Radiohead
Strong Quartet No. 17 in B-flat Major, K. 458, "The Hunt," Movement I., Wolfgang A. Mozart
"The Tourist," Radiohead
Sonata No. 42 in G Major, Hob. XVI:27, Movement II., Joseph Haydn
"Exogenesis: Symphony Part 3," Muse
Sonata No. 14 in C-sharp Minor, Op. 27, No. 2, "Moonlight," Movement I., Ludwig van Beethoven
St. Matthew Passion, No. 1, Chorus, "Kommt, ihr Töchter, helft mir klagen," J.S. Bach