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Drummers & The Geometric Sequence

This sounds scary, right? Drummers inadvertently use the Geometric sequence to play the infamous 4/4 drum groove.

I am sure you heard this groove in many songs.





Geometric Sequences are sequences of number where each number after the 1st term is multiplied or divided by a constant term called the common ratio. For example, if we have the following set of numbers 1, 3, 9, 27, etc., we notice that each term is multiplied by 3 (the common ratio). The image displays the sequence.



It is evident that a music aficionado would be interested in the musical notes. To validate the relationship between geometric sequences and rhythmic notes, I will use the American equivalent names of the notes. The notes are shown below:



Do you notice a pattern in these words: Whole, Half, Quarter, Eighth, Sixteenth, Thirty-second note?
Can you determine the pattern? Hint: The name of the notes may help.

Presenting the Geometric Sequence of Drumming using the notes mentioned above:




The geometric sequence of drumming is demonstrated in the following link. This recording has a metronome to demonstrate the sub-divisions of the beat.  
Geometric Sequence & Drumming.


We can use a website like Desmos to enter these values and plot a graph for the various Sections and Number of Beats used in each section. For example, Section 1 uses a Whole Note (4 beats), Section 2 uses a Half Note (2 beats), and so on.


Use the values from the graph to find the exponential function that represents this pattern.

The image below shows a sample answer that you may obtain.
 




  
We can see many mathematical concepts that are applicable to music. The applications may not be limited to geometric sequences, but many mathematical concepts like symmetry, combinatorics, permutations, etc. can be integrated to music. I will post more blogs about that in the future. This is just a snippet to get you started.

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