Our World Is Made More Beautiful By Harmonics (and Python)

Our World Is Made More Beautiful By Harmonics (and Python)

What makes a guitar sound nice? Is it the chords, the key or the notes that are played? Not quite, as an A note on its own is rather boring. If you have ever heard an A note on an audio generator it sounds rather dull and plain. In fact, it is just a 440 Hz sine wave [here], with a single frequency in the frequency domain:

So why does a guitar sound so interesting? Well, it produces harmonics of the fundamental frequency, such as at three times the fundamental frequency, and five times the fundamental frequency. Our ear generally likes these odd harmonics, and a well-designed guitar will make sure that these are well supported. In the following we have a wave that has a 3rd harmonic with 40% of the amplitude of the fundamental and a 5th harmonic with 20% of the amplitude of the fundamental [here]. We see a more characteristic waveform for sound, and also see three spikes for the frequencies in the frequency domain:

In Python, we can easily convert from the time domain into the frequency domain using an FFT (Fast Fourier Transform) and using mighty Numpy (np) library:

Y = np.fft.fft(y)/n # fft computing and normalization

In Python, we can also use the matplotlib library, too, in order to illustrate the time and the frequency domain plots. And, so, here is the full code. I have used a 5 Hz fundamental wave, and which gives a period of 0.2 seconds:

If you are interested, here is a demo of analysing signals in Python [tutorial]:

and with some theory:

Conclusions

Go do some Python. It is a great tool kit for learning. If your kids are learning maths, it is a great playground for coding and learning. For you, just go learn Python!