These so-called overtones creates the timbre of the piano and because of these overtones, the piano sounds like a piano. Every instrument has a different timbre, that is created by the ratio (loudness) of individual overtones in the overtone series. So when pressing down a C1, you are actually hearing all the notes shown above + infinity. Generally, the higher the partial (number) of the overtone is, the quieter it gets. So you must be thinking: “What does any of this have to do with thirds?”.

Look at which notes are repeating itself the most in the overtone series. The bass note (in our example C) repeats itself 5 times in 5 octaves, The fifth (G in our example) repeats itself 3 times in 5 octaves. And the major third (E in our example) occurs only 2 times in 5 octaves. So bassically you are hearing a C major chord every time you hit a C on the piano. Training yourself to hear harmonics is very useful, but let’s leave this subject for another day. So what did we learn now? The fundamental tone (bass note) is repeated naturally the most, the second most is the fifth and the least is the third. This is the natural harmony between the notes in the overtone series, something you should keep in mind when orchestrating a well-balanced chord.