Original sentence: Harmony is the use and study of pitch simultaneity and chords, actual or implied, in music.Some traditions of music performance, composition, and theory have specific rules of harmony.These rules are often held to be based on a natural properties such as Pythagorean tuning's low whole number ratios ("harmoniousness" being inherent in the ratios either perceptually or in themselves) or harmonics and resonances ("harmoniousness" being inherent in the quality of sound), with the allowable pitches and harmonies gaining their beauty or simplicity from their closeness to those properties.Very often, harmony is a result of counterpoint or polyphony,  several melodic lines or motifs being played at once, though harmony may controll the counterpoint
Edited sentence: Harmony is based on harmonics and resonances.Harmony is the art of using pitch simultaneity (or chords, actual or implied) in music.Notes may be considered to be in harmony with each other when some of the harmonics of each note, especially the louder harmonics (which are often the lower ones), share the same frequency (with a small margin of error).Some traditions of music performance, composition, and theory have specific rules of harmony, typically amounting to a simplified description of harmonics and resonances, which will be more or less appropriate depending on the instrument(s) to which they are applied.Very often, harmony is a result of several melodic lines or motifs being played at once, creating counterpoint and called polyphony