Counting rhythms
In a song, a short sound lasts 1 beat. A long sound lasts 2 beats. A rhythm is the order of short and long sounds. How many different rhythms fill 4 beats?
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Step 1 of 4
- All five rhythms of 4 beats.
- Three start with a short beat.
- Two start with a long beat.
- 3 + 2 = 5 rhythms.
The rule
There are 5 different rhythms of 4 beats. In the rule, n is any number of beats.
A rhythm of n beats starts with a 1 or a 2. After a 1, any rhythm of n − 1 beats can follow. After a 2, any rhythm of n − 2 beats can follow. Add the two counts.
| Beats | Rhythms | Add these two counts |
|---|---|---|
| 1 | 1 | Start here |
| 2 | 2 | Start here |
| 3 | 3 | 2 + 1 |
| 4 | 5 | 3 + 2 |
| 5 | 8 | 5 + 3 |
| 6 | 13 | 8 + 5 |
| 7 | 21 | 13 + 8 |
These counts are the Virahāṅka–Fibonacci numbers. The next counts are 34, 55 and 89. Scholars of poetry in India studied them long before Fibonacci. Virahāṅka wrote the rule over 1,200 years ago. Fibonacci wrote about them in 1202 CE.