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Who wrote this ignorant post? (sorry to be blunt)
“The most important functions to understand are those of scale degree 1 (tonic), scale degree 5 (dominant) and scale degree 7”
What about the third? Isn’t it important?

The harmonic series suggests consonance and strength, and in further depth, it hints at the gravity between different functions as mentioned.

Consider the order and ratios(strength) of the first six intervals of the harmonic series:
1:1 fundamental/unison, 2:1 octave, 3:2 perfect 5th, 4:3 perfect 4th, 5:4 major 3rd, & 6:5 minor third.

Then consider the pitch-class repetition in the first 16 harmonics:
root 5x, perfect fifth 3x, major third 2x, minor seventh 2x.

Some instruments favor either even or odd harmonics – strings favor even, so, of this set:
root is even 4x, fifth is even 2x, the rest are even once.

But of course, your third is going to define the color, even if it’s substituted(/sus’d) with a second or fourth.
Still, there’s nothing incorrect with the information provided.

src: sengpielaudio(dot)com(slash)calculator(dash)harmonics(dot)htm

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