Numbers: Their Tales, Types, and Treasures.
Chapter 5: Counting for Poets
5.3.THE PROBLEM OF COUNTING METRIC PATTERNS
When we start counting verse meters, it is tempting to start analyzing poems, where each line contains a certain number of syllables. You could then ask how many different verse patterns with a certain number of syllables can be identified. However, for a quantifying language, like Sanskrit, we could also think of another approach, which emphasizes the time needed to recite a line of the poem. The linguistic unit for measuring the time is called mora. A mora is the time needed to pronounce a short, unstressed syllable. A long syllable is then said to have two moras (or morae) because it takes about twice as long to pronounce than a short syllable. Of course, a mora is not a physical time unit that can be measured in seconds, because verses can be pronounced with different speeds, depending on the individual interpretation. So instead of attempting to give a more precise definition of a mora, we stick with the sloppy definition of linguist James D. McCawley (1938–1999), who stated that a “mora is something of which a long syllable consists of two and a short syllable consists of one.”1
· The duration of a short syllable is one mora.
· The duration of a long syllable is twice as long (two moras).
We will use the following definition of a verse meter:
· A meter is defined by a succession of short and long syllables.
We can represent meters in a graphical form, using the symbol ¯ (called a macron) to denote a long syllable, and the symbol ˘ (breve) to denote a short syllable. For example,
˘ ¯ ˘ ¯ ˘ ¯ ˘ ¯ ˘ ¯
is a meter that consists of ten syllables (and has a duration of fifteen moras). It is called iambic pentameter. Another example from old India is a meter called varatanu, which means “woman with a beautiful body”:
˘ ˘ ˘ ˘ ¯ ˘ ˘ ¯ ˘ ¯ ˘ ¯
Varatanu is a meter with a duration of sixteen moras. It takes its name from a poem written in this meter, in which a young man greets his lover after a long night spent together.
When analyzing the possible number of different meters, we start by considering only verses where each line takes the same time to recite. Verse lines with the same total duration consists of a given number of, say, n, moras.
The following problem can, with some justification, be traced back to Pingala. We now state Pingala's problem in full generality. Remember that here we do not attempt to classify meters with a given number of syllables; instead, we are going to count the number of different meters with a given duration measured in moras.
Pingala's first problem:
How many different verse meters exist that have a total duration of n moras?
This problem is about counting the members of a particular set of objects—namely the set of all possible meters (arrangements of long and short syllables) with a fixed total duration. But it is of a different quality than the problem of counting the pebbles in figure 1.2 of chapter 1. Therefore, the usual counting method cannot be applied in a straightforward way. How do we put a finger on the “first” meter, and then on the second meter, and so on?