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Exploring Pythagoras Music Theory using Python

Writer's picture: Annauen RavacioAnnauen Ravacio

Concept of Octave Higher

First Harmonic and Second Harmonic Frequencies


Do you wonder how to generate a code that can simulate the Open D string, its first harmonic, and second harmonic?


Here is the ChatGPT-generated Python script. Please feel free to run the script in your myenv environment. Please do not forget to install the numpy and sounddevice libraries.


pip install numpy sounddevice


Tech-awesome: The output of the Python script is the sound of each frequency. We would be able to hear how the Open D string, First Harmonic, and Second Harmonic sound like on the guitar.


Music Theory of Pythagoras:

Distances between notes in a piece of music that sounds good should always be whole numbers. Example:

  • First Harmonic: Half the length of the open D string shall produce double (2x) the frequency of the open D string.

  • Second Harmonic: One-third the length of the open D string shall produce triple (3x) the frequency of the open D string.


Observe: Please look at the snippet and divide the first harmonic Hz by the open D string Hz. What is the quotient? Is it a whole number? Do the same for the Second Harmonic.

Divide the second harmonic Hz by the open D string Hz. What is the quotient? Is it also a whole number?


What are your findings and conclusion?



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