What does harmonic series mean? Are there any rules?

Harmony series is the relationship from one chord to the next, which belongs to the transverse series of chords in harmony acoustics theory. Therefore, when assigning chords to songs, we should not only consider the vertical relationship of chords, but also consider the horizontal relationship. There are many rules, such as traditional harmony, pop harmony, pentatonic harmony and so on. We should consider the relationship between mode, substitution chord, color chord, passing chord, tone modulation and out of tune, as well as the progress of harmony and voice.