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Number Play n = 5 1 + 1 + 1 + 1 + 1 2 + 1 + 1 + 1 1 + 1 + 1 + 2 2 + 1 + 2 1 + 1 + 2 + 1 2 + 2 + 1 1 + 2 + 1 + 1 1 + 2 + 2 Thus, there are 8 rhythms having 5 beats! Thereasonthismethodworksisthatevery5-beatrhythmmustbegin with either a ‘1+’ or a ‘2+’. If it begins with a ‘1+’, then the remaining numbers must give a 4-beat rhythm, and we can write all those down. If it begins with a 2+, then the remaining number must give a 3-beat rhythm, and we can write all those down. Therefore, the number of 5-beat rhythms is the number of 4-beat rhythms, plus the number of 3-beat rhythms. How many 6-beat rhythms are there? By the same reasoning, it will be the number of 5-beat rhythms plus the number of 4-beat rhythms, i.e., 8 + 5 = 13. Thus, there are 13 rhythms having 6 beats. Use the systematic method to write down all 6-beat rhythms, i.e., write 6 as the sum of 1’s and 2’s in all possible ways. Did you get 13 ways? This beautiful method for counting all the rhythms of short syllables and long syllables having any given number of beats was first given by the great Prakrit scholar Virahāṅka around the year 700 CE. He gave his method in the form of a Prakrit poem! For this reason, the sequence 1, 2, 3, 5, 8, 13, 21, 34, . . . is known as the Virahāṅka sequence, and the numbers in the sequence are known as the Virahāṅka numbers. Virahāṅka was the first known person in history to explicitly consider these important numbers and write down the rule for their formation. Other scholars in India also considered these numbers in the same poetic context. Virahāṅka was inspired by earlier work of the legendary Sanskrit scholar Piṅgala, who lived around 300 BCE. After Virahāṅka, these numbers were also written about by Gopala (c. 1135 CE) and then by Hemachandra (c. 1150 CE). In the West, these numbers have been known as the Fibonacci numbers, after the Italian mathematician who wrote about them in the year 1202 CE — about 500 years after Virahāṅka. As we can see, Fibonacci was not first, nor the second, not even the third person to writeaboutthesenumbers!Sometimestheterm“Virahāṅka–Fibonacci numbers” is used so that everyone understands what is being referred to. So, how many rhythms of short and long syllables are there having 8 beats? We simply take the 8th element of the Virahāṅka sequence: 1, 2, 3, 5, 8, 13, 34, 55, ... Thus, there are 34 rhythms having 8 beats. 141 Reprint 2026-27