In Zulu, harmony is called Isigubudu, which means “a beast with converging horns so that the horns touch the skin of the animal”.
It is said that harmony in music is of particularly emotional characteristic, it evokes pain or sorrow; it invokes the heart of performer and listener alike.
Melody in Zulu is called Indlela, which means a path. This is something more linear or directional, or even solitary, small modifications to add colour to a journey. When a second or third voice is added, these small modifications may add tension exponentially.
See: A study in Nguni and Western Musical Syncretism by Bongani Mthethwa, for more
In my opinion, it is particularly the harmony of the 5th harmonic, the major and minor 3rds and 6th, that add this emotive character to harmonious music. I believe the higher harmonics, when used functionally and contextually suited for their roles, evoke another state of interaction with consciousness. While it may still be emotive, the 7th harmonic does not pull the heart-strings in the same way at the 5th, is seems to me more of the realm of acceptance, of chaos passing through, similar to meditations on non-thinking, or non-interaction with thoughts as they pass through.
Of course, if the 5th and 7th harmonics are used together, this synthesis takes the relation to an even greater level.
And the 11th harmonic seems to transcend, and the 13th to hold a great mystery, the 17th and 19th to be like cogs or elementary particles holding the low structures intact.
“That one has no name, it has no use” – referring to a plant