Melody, Rhythm, Harmony?

In the introduction to Alice Parker’s groundbreaking “The Anatomy of Melody: Exploring the Single Line of Song, she writes,

Western music is the only society to list harmony right up there in the trinity of msical greats. But I don’t think it belongs there. If melody (tones) and rhythm (time) are intrinsic to human beings, then harmony is a subset of melody. It is no more on the same level as melody than vertical combinations of rhythmic figures would be equal to rhythm itself. Should we say melody, harmony, rhythm, and polyrhythms?

Take a moment to think about this.
Alice is saying that the ascendance of harmony to primary musical importance is a mistake four centuries in the making.
As someone who looks to the harmonically rich writing of Gene Puerling, Clare Fischer, and others as a prime influence, it makes me distinctly uncomfortable. However, I’m willing to follow this line of thinking.
I expect to spend the next three months articulating the questions this raises for my writing, so I’m ready to properly ask Alice. Then I fully expect to spend a lifetime studying the answers.

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