It is called the natural tone series because its tones, at least up to the 16th member, are formed “naturally” without further ado when a fundamental is made to sound on one side.
The name overtone series wants to suggest that the tones, which cause the interval sequence, ascend from the fundamental in a lawful way.
In this series, the vibrations of successive overtones always increase in the same way by the frequency of the fundamental, or in other words, the product of the number of overtone steps and the frequency of the fundamental gives the number of vibrations of the overtone in question……….
For example, the 3rd overtone forms with the second overtone the interval 3:2, that is, the pure fifth…..
The remaining intervals result in the same way, for example, 2:1 = octave, 3:2 = fifth, 4:3 = fourth, 5:4 = natural major, 6:5 = natural minor, 9:8 = major whole tone, 10:9 = minor natural whole tone, 16:15 = natural semitone, 4:1 or 8:2 = double octave, 45:32 = natural augmented fourth….., 64:45 = natural diminished fifth, and so on.
In other words: it is the scale of nature.
The harmonic series is the chord of partials that vibrate simultaneously when a natural tone is played.
The harmonic series is the foundation of all musical scales and tuning systems, because it is the only natural scale.
As soon as a tone sounds, overtones resonate.
This scale does not come from humans, but originates directly from the laws of vibration of nature. It follows a universal wave principle and we are able to hear and experience it.